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href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0_%D0%BF%D1%80%D0%B8%D1%98%D0%B0%D0%B2%D0%B0&returnto=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&returntoquery=variant%3Dsr-el" title="Iako nije obavezno, preporučujemo da se prijavite [o]" accesskey="o" class=""><span>Prijavi me</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out user-links-collapsible-item" title="Više opcija" lang="sr-Latn" dir="ltr"> <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Lične alatke" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button 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href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9E%D1%82%D0%B2%D0%BE%D1%80%D0%B8_%D0%BD%D0%B0%D0%BB%D0%BE%D0%B3&returnto=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&returntoquery=variant%3Dsr-el" title="Iako nije obavezno, preporučujemo da otvorite nalog i prijavite se"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Otvori nalog</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0_%D0%BF%D1%80%D0%B8%D1%98%D0%B0%D0%B2%D0%B0&returnto=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&returntoquery=variant%3Dsr-el" title="Iako nije obavezno, preporučujemo da se prijavite [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prijavi me</span></a></li> </ul> </div> </div> </div> </div> </nav> 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0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EУчествујте у \u003Cb\u003E\u003Ca href=\"https://sr.wikiquote.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D1%86%D0%B8%D1%82%D0%B0%D1%82:%D0%9A%D0%B0%D0%BC%D0%BF%D0%B0%D1%9A%D0%B0_SheSaid_2024\" class=\"extiw\" title=\"q:Викицитат:Кампања SheSaid 2024\"\u003Eкампањи писања цитата значајних жена\u003C/a\u003E\u003C/b\u003E на Викицитату.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EПридружите се \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%90%D0%BA%D1%86%D0%B8%D1%98%D0%B0_%D0%BF%D1%80%D0%BE%D1%88%D0%B8%D1%80%D0%B8%D0%B2%D0%B0%D1%9A%D0%B0_%D0%BA%D0%BB%D0%B8%D1%86%D0%B0\" title=\"Википедија:Акција проширивања клица\"\u003Eакцији проширивања клица\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sajt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Sadržaj" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">pomeri na stranu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Историја" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Историја"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Istorija</span> </div> </a> <ul id="toc-Историја-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Аритметичке_операције" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Аритметичке_операције"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Aritmetičke operacije</span> </div> </a> <button aria-controls="toc-Аритметичке_операције-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Aritmetičke operacije subsection</span> </button> <ul id="toc-Аритметичке_операције-sublist" class="vector-toc-list"> <li id="toc-Сабирање" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Сабирање"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Sabiranje</span> </div> </a> <ul id="toc-Сабирање-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Одузимање" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Одузимање"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Oduzimanje</span> </div> </a> <ul id="toc-Одузимање-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Множење" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Множење"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Množenje</span> </div> </a> <ul id="toc-Множење-sublist" class="vector-toc-list"> <li id="toc-Таблица_множења" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Таблица_множења"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Tablica množenja</span> </div> </a> <ul id="toc-Таблица_множења-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Дељење" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Дељење"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Deljenje</span> </div> </a> <ul id="toc-Дељење-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Децимална_аритметика" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Децимална_аритметика"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Decimalna aritmetika</span> </div> </a> <ul id="toc-Децимална_аритметика-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Референце" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Референце"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Reference</span> </div> </a> <ul id="toc-Референце-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Литература" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Литература"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Literatura</span> </div> </a> <ul id="toc-Литература-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Спољашње_везе" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Спољашње_везе"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Spoljašnje veze</span> </div> </a> <ul id="toc-Спољашње_везе-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="sr-Latn" dir="ltr"> <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaži/sakrij sadržaj" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prikaži/sakrij sadržaj</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading" lang="sr-Latn" dir="ltr"><span class="mw-page-title-main">Aritmetika</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sr-Latn" dir="ltr"> <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Članak na drugim jezicima. Dostupan na: 160" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-160" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">160 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Rekenkunde" title="Rekenkunde — Afrikaans" lang="af" hreflang="af" data-title="Rekenkunde" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Arithmetik" title="Arithmetik — Alemannic" lang="gsw" hreflang="gsw" data-title="Arithmetik" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%A5%E1%8A%90_%E1%89%81%E1%8C%A5%E1%88%AD" title="ሥነ ቁጥር — Amharic" lang="am" hreflang="am" data-title="ሥነ ቁጥር" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अंकगणित — Angika" lang="anp" hreflang="anp" data-title="अंकगणित" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ab mw-list-item"><a href="https://ab.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Abkhazian" lang="ab" hreflang="ab" data-title="Арифметика" data-language-autonym="Аԥсшәа" data-language-local-name="Abkhazian" class="interlanguage-link-target"><span>Аԥсшәа</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8%D9%8A%D8%A7%D8%AA" title="حسابيات — Arabic" lang="ar" hreflang="ar" data-title="حسابيات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Aragonese" lang="an" hreflang="an" data-title="Aritmetica" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%9F%E0%A7%80%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="পাটীগণিত — Assamese" lang="as" hreflang="as" data-title="পাটীগণিত" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Asturian" lang="ast" hreflang="ast" data-title="Aritmética" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Hesab" title="Hesab — Azerbaijani" lang="az" hreflang="az" data-title="Hesab" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8" title="حساب — South Azerbaijani" lang="azb" hreflang="azb" data-title="حساب" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Indonesian" lang="id" hreflang="id" data-title="Aritmetika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Malay" lang="ms" hreflang="ms" data-title="Aritmetik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Аритметика — Bulgarian" lang="bg" hreflang="bg" data-title="Аритметика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/So%C3%A0n-su%CC%8Dt" title="Soàn-su̍t — Minnan" lang="nan" hreflang="nan" data-title="Soàn-su̍t" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba badge-Q17437796 badge-featuredarticle mw-list-item" title="sjajan članak"><a href="https://ba.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Bashkir" lang="ba" hreflang="ba" data-title="Арифметика" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be badge-Q17437798 badge-goodarticle mw-list-item" title="dobar članak"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%80%D1%8B%D1%84%D0%BC%D0%B5%D1%82%D1%8B%D0%BA%D0%B0" title="Арыфметыка — Belarusian" lang="be" hreflang="be" data-title="Арыфметыка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D1%80%D1%8B%D1%82%D0%BC%D1%8D%D1%82%D1%8B%D0%BA%D0%B0" title="Арытмэтыка — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Арытмэтыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अंकगणित — Bhojpuri" lang="bh" hreflang="bh" data-title="अंकगणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Central Bikol" lang="bcl" hreflang="bcl" data-title="Aritmetika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Arithmetic" title="Arithmetic — Bislama" lang="bi" hreflang="bi" data-title="Arithmetic" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%9F%E0%A6%BF%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="পাটিগণিত — Bangla" lang="bn" hreflang="bn" data-title="পাটিগণিত" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Bosnian" lang="bs" hreflang="bs" data-title="Aritmetika" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Breton" lang="br" hreflang="br" data-title="Aritmetik" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D1%8D" title="Арифметикэ — Russia Buriat" lang="bxr" hreflang="bxr" data-title="Арифметикэ" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Aritm%C3%A8tica" title="Aritmètica — Catalan" lang="ca" hreflang="ca" data-title="Aritmètica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Cebuano" lang="ceb" hreflang="ceb" data-title="Aritmetik" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Chavacano" lang="cbk" hreflang="cbk" data-title="Aritmetica" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Huwandu" title="Huwandu — Shona" lang="sn" hreflang="sn" data-title="Huwandu" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Corsican" lang="co" hreflang="co" data-title="Aritmetica" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhifyddeg" title="Rhifyddeg — Welsh" lang="cy" hreflang="cy" data-title="Rhifyddeg" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Chuvash" lang="cv" hreflang="cv" data-title="Арифметика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Czech" lang="cs" hreflang="cs" data-title="Aritmetika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Danish" lang="da" hreflang="da" data-title="Aritmetik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Arithmetik" title="Arithmetik — German" lang="de" hreflang="de" data-title="Arithmetik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Aritmeetika" title="Aritmeetika — Estonian" lang="et" hreflang="et" data-title="Aritmeetika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B9%CE%B8%CE%BC%CE%B7%CF%84%CE%B9%CE%BA%CE%AE" title="Αριθμητική — Greek" lang="el" hreflang="el" data-title="Αριθμητική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="dobar članak"><a href="https://en.wikipedia.org/wiki/Arithmetic" title="Arithmetic — English" lang="en" hreflang="en" data-title="Arithmetic" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Spanish" lang="es" hreflang="es" data-title="Aritmética" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Aritmetiko" title="Aritmetiko — Esperanto" lang="eo" hreflang="eo" data-title="Aritmetiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Extremaduran" lang="ext" hreflang="ext" data-title="Aritmética" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Basque" lang="eu" hreflang="eu" data-title="Aritmetika" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8" title="حساب — Persian" lang="fa" hreflang="fa" data-title="حساب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Arithmetic" title="Arithmetic — Fiji Hindi" lang="hif" hreflang="hif" data-title="Arithmetic" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Arithm%C3%A9tique" title="Arithmétique — French" lang="fr" hreflang="fr" data-title="Arithmétique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhr%C3%ADocht" title="Uimhríocht — Irish" lang="ga" hreflang="ga" data-title="Uimhríocht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/%C3%80ireamhachd" title="Àireamhachd — Scottish Gaelic" lang="gd" hreflang="gd" data-title="Àireamhachd" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Galician" lang="gl" hreflang="gl" data-title="Aritmética" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%AE%97%E8%A1%93" title="算術 — Gan" lang="gan" hreflang="gan" data-title="算術" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gom mw-list-item"><a href="https://gom.wikipedia.org/wiki/Ank%E2%80%8Cgonnit" title="Ank‌gonnit — Goan Konkani" lang="gom" hreflang="gom" data-title="Ank‌gonnit" data-language-autonym="गोंयची कोंकणी / Gõychi Konknni" data-language-local-name="Goan Konkani" class="interlanguage-link-target"><span>गोंयची कोंकणी / Gõychi Konknni</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%85%E0%AA%82%E0%AA%95%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="અંકગણિત — Gujarati" lang="gu" hreflang="gu" data-title="અંકગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Kalmyk" lang="xal" hreflang="xal" data-title="Арифметика" data-language-autonym="Хальмг" data-language-local-name="Kalmyk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A8%D7%99%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="אריתמטיקה — Hebrew" lang="he" hreflang="he" data-title="אריתמטיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अंकगणित — Hindi" lang="hi" hreflang="hi" data-title="अंकगणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Croatian" lang="hr" hreflang="hr" data-title="Aritmetika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B9%D5%BE%D5%A1%D5%A2%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Թվաբանություն — Armenian" lang="hy" hreflang="hy" data-title="Թվաբանություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B9%D5%B8%D6%82%D5%A1%D5%A2%D5%A1%D5%B6%D5%B8%D6%82%D5%A9%D5%AB%D6%82%D5%B6" title="Թուաբանութիւն — Western Armenian" lang="hyw" hreflang="hyw" data-title="Թուաբանութիւն" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Aritmetiko" title="Aritmetiko — Ido" lang="io" hreflang="io" data-title="Aritmetiko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Iloko" lang="ilo" hreflang="ilo" data-title="Aritmetika" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Arithmetica" title="Arithmetica — Interlingua" lang="ia" hreflang="ia" data-title="Arithmetica" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%C3%A6" title="Арифметикæ — Ossetic" lang="os" hreflang="os" data-title="Арифметикæ" data-language-autonym="Ирон" data-language-local-name="Ossetic" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-arithmetic" title="I-arithmetic — Xhosa" lang="xh" hreflang="xh" data-title="I-arithmetic" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ubuphicinani" title="Ubuphicinani — Zulu" lang="zu" hreflang="zu" data-title="Ubuphicinani" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Talnareikningur" title="Talnareikningur — Icelandic" lang="is" hreflang="is" data-title="Talnareikningur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Italian" lang="it" hreflang="it" data-title="Aritmetica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%AE%97%E8%A1%93" title="算術 — Japanese" lang="ja" hreflang="ja" data-title="算術" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Ng%C3%A8lmu_%C3%A9tung" title="Ngèlmu étung — Javanese" lang="jv" hreflang="jv" data-title="Ngèlmu étung" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%98%E1%83%97%E1%83%9B%E1%83%94%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="არითმეტიკა — Georgian" lang="ka" hreflang="ka" data-title="არითმეტიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kl mw-list-item"><a href="https://kl.wikipedia.org/wiki/Aritmetikki" title="Aritmetikki — Kalaallisut" lang="kl" hreflang="kl" data-title="Aritmetikki" data-language-autonym="Kalaallisut" data-language-local-name="Kalaallisut" class="interlanguage-link-target"><span>Kalaallisut</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Kazakh" lang="kk" hreflang="kk" data-title="Арифметика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Niveronieth" title="Niveronieth — Cornish" lang="kw" hreflang="kw" data-title="Niveronieth" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Kyrgyz" lang="ky" hreflang="ky" data-title="Арифметика" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Hesabu" title="Hesabu — Swahili" lang="sw" hreflang="sw" data-title="Hesabu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%82%E0%B2%95%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಅಂಕಗಣಿತ — Kannada" lang="kn" hreflang="kn" data-title="ಅಂಕಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%B0%EC%88%A0" title="산술 — Korean" lang="ko" hreflang="ko" data-title="산술" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-kg mw-list-item"><a href="https://kg.wikipedia.org/wiki/Kutanga" title="Kutanga — Kongo" lang="kg" hreflang="kg" data-title="Kutanga" data-language-autonym="Kongo" data-language-local-name="Kongo" class="interlanguage-link-target"><span>Kongo</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Aritm%C3%A9tik" title="Aritmétik — Guianan Creole" lang="gcr" hreflang="gcr" data-title="Aritmétik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-lad mw-list-item"><a href="https://lad.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Ladino" lang="lad" hreflang="lad" data-title="Aritmetika" data-language-autonym="Ladino" data-language-local-name="Ladino" class="interlanguage-link-target"><span>Ladino</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="sjajan članak"><a href="https://la.wikipedia.org/wiki/Arithmetica" title="Arithmetica — Latin" lang="la" hreflang="la" data-title="Arithmetica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Aritm%C4%93tika" title="Aritmētika — Latvian" lang="lv" hreflang="lv" data-title="Aritmētika" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Nias" lang="nia" hreflang="nia" data-title="Aritmetika" data-language-autonym="Li Niha" data-language-local-name="Nias" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Lithuanian" lang="lt" hreflang="lt" data-title="Aritmetika" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Aritmetica" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/sapme%27ocmaci" title="sapme'ocmaci — Lojban" lang="jbo" hreflang="jbo" data-title="sapme'ocmaci" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Aritmetega" title="Aritmetega — Lombard" lang="lmo" hreflang="lmo" data-title="Aritmetega" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%A1mtan" title="Számtan — Hungarian" lang="hu" hreflang="hu" data-title="Számtan" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Аритметика — Macedonian" lang="mk" hreflang="mk" data-title="Аритметика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Malagasy" lang="mg" hreflang="mg" data-title="Aritmetika" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Mirandese" lang="mwl" hreflang="mwl" data-title="Aritmética" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="അങ്കഗണിതം — Malayalam" lang="ml" hreflang="ml" data-title="അങ്കഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अंकगणित — Marathi" lang="mr" hreflang="mr" data-title="अंकगणित" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%82%E1%80%8F%E1%80%94%E1%80%BA%E1%80%B8%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="ဂဏန်းသင်္ချာ — Burmese" lang="my" hreflang="my" data-title="ဂဏန်းသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Tlap%C5%8Dhuall%C5%8Dtl" title="Tlapōhuallōtl — Nahuatl" lang="nah" hreflang="nah" data-title="Tlapōhuallōtl" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Maqusa" title="Maqusa — Fijian" lang="fj" hreflang="fj" data-title="Maqusa" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%99%E0%A5%8D%E0%A4%95_%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अङ्क गणित — Nepali" lang="ne" hreflang="ne" data-title="अङ्क गणित" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rekenen" title="Rekenen — Dutch" lang="nl" hreflang="nl" data-title="Rekenen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="अंकगणित — Newari" lang="new" hreflang="new" data-title="अंकगणित" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://nap.wikipedia.org/wiki/Artemeteca" title="Artemeteca — Neapolitan" lang="nap" hreflang="nap" data-title="Artemeteca" data-language-autonym="Napulitano" data-language-local-name="Neapolitan" class="interlanguage-link-target"><span>Napulitano</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Aritmeetik" title="Aritmeetik — Northern Frisian" lang="frr" hreflang="frr" data-title="Aritmeetik" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Aritmetikk" title="Aritmetikk — Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Aritmetikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Aritmetikk" title="Aritmetikk — Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Aritmetikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Aritmetike" title="Aritmetike — Novial" lang="nov" hreflang="nov" data-title="Aritmetike" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Occitan" lang="oc" hreflang="oc" data-title="Aritmetica" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Lakxii" title="Lakxii — Oromo" lang="om" hreflang="om" data-title="Lakxii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Arifmetika" title="Arifmetika — Uzbek" lang="uz" hreflang="uz" data-title="Arifmetika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A9%B0%E0%A8%95_%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4" title="ਅੰਕ ਗਣਿਤ — Punjabi" lang="pa" hreflang="pa" data-title="ਅੰਕ ਗਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pap mw-list-item"><a href="https://pap.wikipedia.org/wiki/Aritm%C3%A9tika" title="Aritmétika — Papiamento" lang="pap" hreflang="pap" data-title="Aritmétika" data-language-autonym="Papiamentu" data-language-local-name="Papiamento" class="interlanguage-link-target"><span>Papiamentu</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Piedmontese" lang="pms" hreflang="pms" data-title="Aritmética" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Arithmetik" title="Arithmetik — Low German" lang="nds" hreflang="nds" data-title="Arithmetik" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8" title="حساب — Western Punjabi" lang="pnb" hreflang="pnb" data-title="حساب" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Arytmetyka" title="Arytmetyka — Polish" lang="pl" hreflang="pl" data-title="Arytmetyka" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Aritm%C3%A9tica" title="Aritmética — Portuguese" lang="pt" hreflang="pt" data-title="Aritmética" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8" title="حساب — Pashto" lang="ps" hreflang="ps" data-title="حساب" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Aritmitik" title="Aritmitik — Jamaican Creole English" lang="jam" hreflang="jam" data-title="Aritmitik" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Arifmetika" title="Arifmetika — Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Arifmetika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Esap" title="Esap — Crimean Tatar" lang="crh" hreflang="crh" data-title="Esap" data-language-autonym="Qırımtatarca" data-language-local-name="Crimean Tatar" class="interlanguage-link-target"><span>Qırımtatarca</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Aritmetic%C4%83" title="Aritmetică — Romanian" lang="ro" hreflang="ro" data-title="Aritmetică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupa_hap%27ichiy" title="Yupa hap'ichiy — Quechua" lang="qu" hreflang="qu" data-title="Yupa hap'ichiy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D1%80%D1%96%D1%84%D0%BC%D0%B5%D1%82%D1%96%D0%BA%D0%B0" title="Аріфметіка — Rusyn" lang="rue" hreflang="rue" data-title="Аріфметіка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru badge-Q17437796 badge-featuredarticle mw-list-item" title="sjajan članak"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Russian" lang="ru" hreflang="ru" data-title="Арифметика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%85%E0%A4%99%E0%A5%8D%E0%A4%95%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%AE%E0%A5%8D" title="अङ्कगणितम् — Sanskrit" lang="sa" hreflang="sa" data-title="अङ्कगणितम्" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Yakut" lang="sah" hreflang="sah" data-title="Арифметика" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Aritm%C3%A8tica" title="Aritmètica — Sardinian" lang="sc" hreflang="sc" data-title="Aritmètica" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Arithmetic" title="Arithmetic — Scots" lang="sco" hreflang="sco" data-title="Arithmetic" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Albanian" lang="sq" hreflang="sq" data-title="Aritmetika" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Aritmetica" title="Aritmetica — Sicilian" lang="scn" hreflang="scn" data-title="Aritmetica" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Arithmetic" title="Arithmetic — Simple English" lang="en-simple" hreflang="en-simple" data-title="Arithmetic" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Slovak" lang="sk" hreflang="sk" data-title="Aritmetika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Slovenian" lang="sl" hreflang="sl" data-title="Aritmetika" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%DB%8E%D8%B1%DB%95" title="ژمێرە — Central Kurdish" lang="ckb" hreflang="ckb" data-title="ژمێرە" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Serbo-Croatian" lang="sh" hreflang="sh" data-title="Aritmetika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Aritmetiikka" title="Aritmetiikka — Finnish" lang="fi" hreflang="fi" data-title="Aritmetiikka" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Swedish" lang="sv" hreflang="sv" data-title="Aritmetik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="எண்கணிதம் — Tamil" lang="ta" hreflang="ta" data-title="எண்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Aritmetika" title="Aritmetika — Tagalog" lang="tl" hreflang="tl" data-title="Aritmetika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Tatar" lang="tt" hreflang="tt" data-title="Арифметика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="เลขคณิต — Thai" lang="th" hreflang="th" data-title="เลขคณิต" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/S%E1%BB%91_h%E1%BB%8Dc" title="Số học — Vietnamese" lang="vi" hreflang="vi" data-title="Số học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B2%D0%B8%D1%81%D0%BE%D0%B1" title="Ҳисоб — Tajik" lang="tg" hreflang="tg" data-title="Ҳисоб" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Turkish" lang="tr" hreflang="tr" data-title="Aritmetik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика — Ukrainian" lang="uk" hreflang="uk" data-title="Арифметика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8" title="حساب — Urdu" lang="ur" hreflang="ur" data-title="حساب" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-ug mw-list-item"><a href="https://ug.wikipedia.org/wiki/%D8%A6%D8%A7%D8%B1%D9%89%D9%81%D9%85%DB%90%D8%AA%D9%89%D9%83%D8%A7" title="ئارىفمېتىكا — Uyghur" lang="ug" hreflang="ug" data-title="ئارىفمېتىكا" data-language-autonym="ئۇيغۇرچە / Uyghurche" data-language-local-name="Uyghur" class="interlanguage-link-target"><span>ئۇيغۇرچە / Uyghurche</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Aritm%C3%A8tega" title="Aritmètega — Venetian" lang="vec" hreflang="vec" data-title="Aritmètega" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Arifmetik" title="Arifmetik — Veps" lang="vep" hreflang="vep" data-title="Arifmetik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Kalkulav" title="Kalkulav — Volapük" lang="vo" hreflang="vo" data-title="Kalkulav" data-language-autonym="Volapük" data-language-local-name="Volapük" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Arvokunst" title="Arvokunst — Võro" lang="vro" hreflang="vro" data-title="Arvokunst" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Aritmetik%C3%A1" title="Aritmetiká — Waray" lang="war" hreflang="war" data-title="Aritmetiká" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%AE%97%E6%9C%AF" title="算术 — Wu" lang="wuu" hreflang="wuu" data-title="算术" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tinhlayo-tinomboro" title="Tinhlayo-tinomboro — Tsonga" lang="ts" hreflang="ts" data-title="Tinhlayo-tinomboro" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%98%E1%83%97%E1%83%9B%E1%83%94%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="არითმეტიკა — Mingrelian" lang="xmf" hreflang="xmf" data-title="არითმეტიკა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%A8%D7%99%D7%98%D7%9E%D7%A2%D7%98%D7%99%D7%A7" title="אריטמעטיק — Yiddish" lang="yi" hreflang="yi" data-title="אריטמעטיק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%8C%E1%B9%A3%C3%ADr%C3%B2" title="Ìṣírò — Yoruba" lang="yo" hreflang="yo" data-title="Ìṣírò" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zea mw-list-item"><a href="https://zea.wikipedia.org/wiki/Rekenen" title="Rekenen — Zeelandic" lang="zea" hreflang="zea" data-title="Rekenen" data-language-autonym="Zeêuws" data-language-local-name="Zeelandic" class="interlanguage-link-target"><span>Zeêuws</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%AE%97%E6%9C%AF" title="算术 — Chinese" lang="zh" hreflang="zh" data-title="算术" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%AE%97%E8%A1%93" title="算術 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="算術" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%AE%97%E8%A1%93" title="算術 — Cantonese" lang="yue" hreflang="yue" data-title="算術" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Ar%C4%97tmet%C4%97ka" title="Arėtmetėka — Samogitian" lang="sgs" hreflang="sgs" data-title="Arėtmetėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Aritmetik" title="Aritmetik — Iban" lang="iba" hreflang="iba" data-title="Aritmetik" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-tly mw-list-item"><a href="https://tly.wikipedia.org/wiki/Hisob" title="Hisob — Talysh" lang="tly" hreflang="tly" data-title="Hisob" data-language-autonym="Tolışi" data-language-local-name="Talysh" class="interlanguage-link-target"><span>Tolışi</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11205#sitelinks-wikipedia" title="Uredi međujezičke veze" class="wbc-editpage">Uredi veze</a></span></div> </div> </div> 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dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/%D0%94%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:1%2B1%3D2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/1%2B1%3D2.png/250px-1%2B1%3D2.png" decoding="async" width="250" height="94" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0d/1%2B1%3D2.png 1.5x" data-file-width="364" data-file-height="137" /></a><figcaption>Sabiranje je primer aritmetičke operacije</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%94%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Tables_generales_aritmetique_MG_2108.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Tables_generales_aritmetique_MG_2108.jpg/250px-Tables_generales_aritmetique_MG_2108.jpg" decoding="async" width="250" height="375" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Tables_generales_aritmetique_MG_2108.jpg/375px-Tables_generales_aritmetique_MG_2108.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Tables_generales_aritmetique_MG_2108.jpg/500px-Tables_generales_aritmetique_MG_2108.jpg 2x" data-file-width="2691" data-file-height="4038" /></a><figcaption>Aritmetičke tabele za decu, <a href="/wiki/%D0%9B%D0%BE%D0%B7%D0%B0%D0%BD%D0%B0" title="Lozana">Lozana</a>, 1835</figcaption></figure> <p><b>Aritmetika</b> (od <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%BE%D0%B3%D1%80%D1%87%D0%BA%D0%B8_%D1%98%D0%B5%D0%B7%D0%B8%D0%BA" title="Starogrčki jezik">grčkog</a> <a href="https://sr.wiktionary.org/wiki/en:%E1%BC%80%CF%81%CE%B9%CE%B8%CE%BC%CF%8C%CF%82#Ancient_Greek" class="extiw" title="wikt:en:ἀριθμός">ἀριθμός</a> <i>arithmos</i>, "<a href="/wiki/%D0%91%D1%80%D0%BE%D1%98" title="Broj">broj</a>") grana je <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Matematika">matematike</a> koja beleži osnovne osobine određenih operacija sa <a href="/wiki/%D0%91%D1%80%D0%BE%D1%98" title="Broj">brojevima</a>.<sup id="cite_ref-британика_1_1-0" class="reference"><a href="#cite_note-британика_1-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>Aritmetika je elementarni deo <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Teorija brojeva">teorije brojeva</a>, i teorija brojeva se smatra jednim od osnovnih nivoa <a href="/w/index.php?title=%D0%9E%D0%B1%D0%BB%D0%B0%D1%81%D1%82%D0%B8_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5&action=edit&redlink=1" class="new" title="Oblasti matematike (stranica ne postoji)">podele moderne matematike</a>, zajedno sa <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Algebra">algebrom</a>, <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Geometrija">geometrijom</a>, i <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0" title="Matematička analiza">analizom</a>. Termina <i>aritmetika</i> i <i>viša aritmetika</i> su korišteni do početka 20. veka kao sinonimi za <i>teoriju brojevi</i> i ponekad se još uvek koriste kao naziv za širi deo teorije brojeva.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Postoje četiri operacije: <a href="/wiki/%D0%A1%D0%B0%D0%B1%D0%B8%D1%80%D0%B0%D1%9A%D0%B5" title="Sabiranje">sabiranje</a>, <a href="/wiki/%D0%9E%D0%B4%D1%83%D0%B7%D0%B8%D0%BC%D0%B0%D1%9A%D0%B5" title="Oduzimanje">oduzimanje</a>, <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%9A%D0%B5" title="Množenje">množenje</a> i <a href="/wiki/%D0%94%D0%B5%D1%99%D0%B5%D1%9A%D0%B5" title="Deljenje">deljenje</a>, iako se ponekad ovde uvrštavaju i naprednije operacije, kao što su <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82" title="Kvadrat">dizanje na kvadrat</a> (kvadriranje) i <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B8_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD" title="Kvadratni koren">vađenje korena</a> (korenovanje). U aritmetici postoji <a href="/w/index.php?title=%D0%9F%D1%80%D0%B2%D0%B5%D0%BD%D1%81%D1%82%D0%B2%D0%BE_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Prvenstvo operacija (stranica ne postoji)">prvenstvo operacija</a> gde množenje i deljenje imaju prednost nad sabiranjem i oduzimanjem. Stavljanjem u zagrade, koje imaju prednost u odnosu na druge operacije, je moguće promeniti redosled izračunavanja u izrazima. </p><p>Aritmetika <a href="/wiki/%D0%9F%D1%80%D0%B8%D1%80%D0%BE%D0%B4%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Prirodan broj">prirodnih</a>, <a href="/wiki/%D0%A6%D0%B5%D0%BE_%D0%B1%D1%80%D0%BE%D1%98" title="Ceo broj">celih</a>, <a href="/wiki/%D0%A0%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Racionalan broj">racionalnih</a> (u obliku <a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%BB%D0%BE%D0%BC%D0%B0%D0%BA" title="Razlomak">razlomaka</a>) i <a href="/wiki/%D0%A0%D0%B5%D0%B0%D0%BB%D0%B0%D0%BD_%D0%B1%D1%80%D0%BE%D1%98" title="Realan broj">realnih</a> brojeva (koji imaju <a href="/wiki/%D0%94%D0%B5%D1%86%D0%B8%D0%BC%D0%B0%D0%BB%D0%B0" title="Decimala">decimale</a>) obično se uči u osnovnoj školi. Tada se uči i procentni račun, odnosno predstavljanje brojeva pomoću <a href="/wiki/%D0%9F%D1%80%D0%BE%D1%86%D0%B5%D0%BD%D0%B0%D1%82" title="Procenat">postotaka</a>. Ipak, većina odraslih oslanja se na <a href="/wiki/%D0%9A%D0%B0%D0%BB%D0%BA%D1%83%D0%BB%D0%B0%D1%82%D0%BE%D1%80" title="Kalkulator">kalkulatore</a>, <a href="/wiki/%D0%A0%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%80" title="Računar">računare</a> ili <a href="/wiki/%D0%90%D0%B1%D0%B0%D0%BA%D1%83%D1%81_(%D1%80%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%9A%D0%B5)" title="Abakus (računanje)">abakuse</a> da bi izračunala aritmetičke operacije. </p><p>Pojam „aritmetika“ koristi se i za osnovnu <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Teorija brojeva">teoriju brojeva</a>; u tom kontekstu se pojavljuju i <a href="/wiki/%D0%9E%D1%81%D0%BD%D0%BE%D0%B2%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B5" title="Osnovna teorema aritmetike">Osnovna teorema aritmetike</a> i <a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Aritmetička funkcija (stranica ne postoji)">aritmetičke funkcije</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Историја"><span id=".D0.98.D1.81.D1.82.D0.BE.D1.80.D0.B8.D1.98.D0.B0"></span>Istorija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=1" title="Uredite odeljak „Istorija”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=1" title="Edit section's source code: Istorija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Preistorija aritmetike je ograničena na mali broj artefakata koji mogu da indiciraju postojanje koncepata sabiranja i oduzimanja. Najpoznatiji je <a href="/w/index.php?title=Ishango_bone&action=edit&redlink=1" class="new" title="Ishango bone (stranica ne postoji)">Išango kost</a> iz <a href="/wiki/%D0%94%D0%B5%D0%BC%D0%BE%D0%BA%D1%80%D0%B0%D1%82%D1%81%D0%BA%D0%B0_%D0%A0%D0%B5%D0%BF%D1%83%D0%B1%D0%BB%D0%B8%D0%BA%D0%B0_%D0%9A%D0%BE%D0%BD%D0%B3%D0%BE" title="Demokratska Republika Kongo">centralne Afrike</a>, koja potiče i perioda između 20.000 i 18.000 p. n. e, mada je njena interpretacija sporna.<sup id="cite_ref-FOOTNOTERudman200764_3-0" class="reference"><a href="#cite_note-FOOTNOTERudman200764-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Najraniji pisani rekordi indiciraju da su <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%BE%D0%B5%D0%B3%D0%B8%D0%BF%D0%B0%D1%82%D1%81%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Staroegipatska matematika">Egipćani</a> i <a href="/w/index.php?title=Babylonian_mathematics&action=edit&redlink=1" class="new" title="Babylonian mathematics (stranica ne postoji)">Vavilonci</a> koristili sve <a href="/w/index.php?title=Elementary_arithmetic&action=edit&redlink=1" class="new" title="Elementary arithmetic (stranica ne postoji)">elementarne aritmetičke</a> operacije još pre 2000. p. n. e. Ovi <a href="/wiki/%D0%90%D1%80%D1%82%D0%B5%D1%84%D0%B0%D0%BA%D1%82" title="Artefakt">artefakti</a> ne otkrivaju uvek specifičan proces koji je korišten za rešavanje problema, mada karakteristike datog <a href="/wiki/%D0%91%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Brojevni sistem">numeričkog sistema</a> snažno utiču na kompleksnost metoda. Hijeroglifski sistem <a href="/w/index.php?title=%D0%95%D0%B3%D0%B8%D0%BF%D0%B0%D1%82%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8&action=edit&redlink=1" class="new" title="Egipatski brojevi (stranica ne postoji)">Egipatskih brojeva</a>, kao i kasniji <a href="/wiki/%D0%A0%D0%B8%D0%BC%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Rimski brojevi">rimski brojevi</a>, izvedeni su iz <a href="/wiki/%D0%A0%D0%B0%D0%B1%D0%BE%D1%88" title="Raboš">beleški</a> korištenih za prebrojavanje. U oba slučaja, takvo poreklo je dovelo do vrednosti koje se koriste u <a href="/wiki/%D0%94%D0%B5%D0%BA%D0%B0%D0%B4%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Dekadni sistem">decimalnoj</a> osnovi, ali <a href="/wiki/Pozicioni_brojevni_sistem" class="mw-redirect" title="Pozicioni brojevni sistem">poziciona notacija</a> nije obuhvaćena. Kompleksni proračuni sa rimskim ciframa se mogu sprovesti uz pomoć brojčanice ili <a href="/w/index.php?title=%D0%A0%D0%B8%D0%BC%D1%81%D0%BA%D0%B8_%D0%B0%D0%B1%D0%B0%D0%BA%D1%83%D1%81&action=edit&redlink=1" class="new" title="Rimski abakus (stranica ne postoji)">rimskog abakusa</a>. </p><p>Rani brojevni sistemi koji su obuhvatali pozicionu notaciju nisu bili decimalni. Primeri takvih sistema su <a href="/w/index.php?title=%D0%A1%D0%B5%D0%BA%D1%81%D0%B0%D0%B3%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%BD%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Seksagezimalni brojevni sistem (stranica ne postoji)">seksagezimalni</a> (osnova 60) sistem za <a href="/w/index.php?title=%D0%92%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE%D0%BD%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8&action=edit&redlink=1" class="new" title="Vavilonski brojevi (stranica ne postoji)">vavilonske brojeve</a> i <a href="/w/index.php?title=Vigesimal&action=edit&redlink=1" class="new" title="Vigesimal (stranica ne postoji)">vigezimalni</a> (osnova 20) sistem koji su definisali <a href="/wiki/Majanski_brojevi" title="Majanski brojevi">majanski brojevi</a>. Zahvaljujući konceptu mesta i vrednosti, mogućnost ponovne upotrebe istih cifara za različite vrednosti doprinela je razvoju jednostavnijih i efikasnijih metoda računanja. </p><p>Kontinualni istorijski razvoj moderne aritmetike započeo je sa <a href="/wiki/%D0%A5%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D1%81%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D0%B5%D1%80%D0%B0" title="Helenistička era">Helenističkom civilizacijom</a> antičke Grčke, mada ona potiče iz znatno kasnijeg perioda od Vavilonskih i Egipatskih primera. Pre radova <a href="/wiki/%D0%95%D1%83%D0%BA%D0%BB%D0%B8%D0%B4" title="Euklid">Euklida</a> oko 300 p. n. e, <a href="/wiki/%D0%93%D1%80%D1%87%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" class="mw-redirect" title="Grčka matematika">grčke studije matematike</a> su se preklapale sa filozofskim i mističkim verovanjima. Na primer, <a href="/wiki/%D0%9D%D0%B8%D0%BA%D0%BE%D0%BC%D0%B0%D1%85" title="Nikomah">Nikomah</a> je sumirao gledište ranijeg <a href="/wiki/%D0%9F%D0%B8%D1%82%D0%B0%D0%B3%D0%BE%D1%80%D0%B5%D1%98%D1%86%D0%B8" title="Pitagorejci">pitagorejskog</a> pristupa brojevima, i njihovih međusobnih relacija, u svom radu <i><a href="/w/index.php?title=Introduction_to_Arithmetic&action=edit&redlink=1" class="new" title="Introduction to Arithmetic (stranica ne postoji)">Uvod u aritmetiku</a></i>. </p><p><a href="/wiki/%D0%93%D1%80%D1%87%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Grčki brojevi">Grčke brojeve</a> su koristili <a href="/wiki/%D0%90%D1%80%D1%85%D0%B8%D0%BC%D0%B5%D0%B4" title="Arhimed">Arhimed</a>, <a href="/w/index.php?title=%D0%94%D0%B8%D0%BE%D1%84%D0%B0%D0%BD%D1%82%D1%83%D1%81&action=edit&redlink=1" class="new" title="Diofantus (stranica ne postoji)">Diofantus</a> i drugi u <a href="/wiki/Pozicioni_brojevni_sistem" class="mw-redirect" title="Pozicioni brojevni sistem">pozicionoj notaciji</a> koja se puno ne razlikuje od današnje. Pošto je antičkim Grcima nedostajao simbol za nulu (do Helenističkog perioda), oni su koristili tri zasebna seta simbola. Jedan set za jedinično mesto, jedan za desetično mesto, i jedan za stotine. Zatim za mesto hiljada oni bi ponovo koristili simbole za jedinično mesto, i tako dalje. Njihov algoritam sabiranja je bio identičan današnjem, i njihov algoritam množenja se samo neznatno razlikovao. Njihov algoritam deljenja je bio isti, i algoritam kvadratnog korena, koji se nekad predavao u školama, je bio poznat Arhimedu, a moguće je i da ga je on izumeo. On ga je preferirao u odnosu na <a href="/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4%D0%B5_%D0%B7%D0%B0_%D0%B8%D0%B7%D1%80%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D0%B2%D0%B0%D1%9A%D0%B5_%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%BE%D0%B3_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B0" title="Metode za izračunavanje kvadratnog korena">Heronov metod</a> sukcesivnih aproksimacija zato što kad se jednom izračunaju cifre one se više ne menjaju, i kvadratni koreni perfektnih kvadrata, kao što je 7485696, bi se neposredno završavali, poput 2736. Za brojeve sa frakcionim delom, kao što je 546,934, oni su koristili negativni stepen od 60 umesto negativnog stepena od 10 za frakcioni deo 0,934.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Antički Kinezi su unapredili aritmetičke studije počevši od vremena dinastije Šang i tokom dinastije Tang, od osnovnih brojeva do napredne algebre. Antički Kinezi su koristili pozicionu notaciju sličnu onoj koju su koristili Grci. Pošto im je nedostajao simbol za nulu, oni su imali jedan set simbola za jedinično mesto, i drugi set za mesto desetica. Za mesto stotina oni su ponovo koristili simbole jediničnog mesta, i tako dalje. Njihovi simboli su bili bazirani na drevnim <a href="/w/index.php?title=Counting_rods&action=edit&redlink=1" class="new" title="Counting rods (stranica ne postoji)">brojevnim štapićima</a>. Pitanje tačnog određivanja vremena kada su Kinezi počeli da računaju sa pozicionom reprezentacijom je komplikovano, ali se zna da je to definitivno bilo pre 400. p. n. e.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Antički Kinezi su prvi otkrili, razumeli i primenili negativne brojeve, kao što je objašnjeno u <i><a href="/w/index.php?title=Nine_Chapters_on_the_Mathematical_Art&action=edit&redlink=1" class="new" title="Nine Chapters on the Mathematical Art (stranica ne postoji)">Devet poglavlja o matematičkoj veštini</a></i> (<i>Jiuzhang Suanshu</i>), što je rad autora <a href="/w/index.php?title=Liu_Hui&action=edit&redlink=1" class="new" title="Liu Hui (stranica ne postoji)">Lju Hui</a>. </p><p>Postepenim razvojem <a href="/wiki/%D0%90%D1%80%D0%B0%D0%BF%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Arapski brojevi">hindu–arapskih brojeva</a> nezavisno je razvijen vrednosno pozicioni koncept i poziciona notacija, koji kombinuju jednostavnije metode za računanje sa decimalnom osnovom i upotrebom cifre za <a href="/wiki/0_(%D0%B1%D1%80%D0%BE%D1%98)" title="0 (broj)">0</a>. Time je formiran sistem za konzistentnu reprezentaciju velikih i malih celih brojeva. Taj pristup je vremenom zamenio sve druge sisteme. U ranom 6. veku, indijski matematičar <a href="/wiki/Aryabhata" class="mw-redirect" title="Aryabhata">Arjabhata</a> je inkorporirao postojeću verziju tog sistema u svoj rad, i eksperimentisao je sa različitim notacijama. U 7. veku, <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Bramagupta">Bramagupta</a> je uspostavio upotrebu simbola 0 kao zasebnog broja i utvrdio rezultat množenja, deljenja, sabiranja i oduzimanja nule i svih drugih brojeva, izuzev rezultata <a href="/w/index.php?title=Division_by_zero&action=edit&redlink=1" class="new" title="Division by zero (stranica ne postoji)">deljenja nulom</a>. Njegov savremenik, <a href="/wiki/%D0%A5%D1%80%D0%B8%D1%88%D1%9B%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE_%D1%83_%D0%A1%D0%B8%D1%80%D0%B8%D1%98%D0%B8" title="Hrišćanstvo u Siriji">sirijski</a> episkop <a href="/w/index.php?title=%D0%A1%D0%B5%D0%B2%D0%B5%D1%80%D1%83%D1%81_%D0%A1%D0%B5%D0%B1%D0%BE%D0%BA%D1%85%D1%82&action=edit&redlink=1" class="new" title="Severus Sebokht (stranica ne postoji)">Severus Sebokht</a> (650.) je izjavio, „Indijci poseduju metod računanja koji ni jedna reč ne može dovoljno pohvaliti. Njihov racionalni sistem matematike, ili njihov metod računanja. Mislim da sistem koristi devet simbola.”<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Arapi su isto tako znali za ovaj novi metod i nazivali su ga <i>hesab</i>. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%94%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Leibniz_Stepped_Reckoner.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/250px-Leibniz_Stepped_Reckoner.png" decoding="async" width="250" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/375px-Leibniz_Stepped_Reckoner.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Leibniz_Stepped_Reckoner.png/500px-Leibniz_Stepped_Reckoner.png 2x" data-file-width="1235" data-file-height="803" /></a><figcaption>Lajbnicova <a href="/w/index.php?title=Stepped_Reckoner&action=edit&redlink=1" class="new" title="Stepped Reckoner (stranica ne postoji)">mašina</a> je bila prvi kalkulator koji je mogao da izvodi sve četiri aritmetičke operacije.</figcaption></figure> <p>Mada je <a href="/w/index.php?title=Codex_Vigilanus&action=edit&redlink=1" class="new" title="Codex Vigilanus (stranica ne postoji)">Kodeks Vigilanus</a> opisao jednu ranu formu arapskih brojeva (bez nule) do 976, Leonardo od Pize (<a href="/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4%D0%BE_%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D0%B8" title="Leonardo Fibonači">Fibonači</a>) je prvenstveno odgovoran za širenje njihove upotrebe u Evropi, nakon objavljivanja njegove knjige <i><a href="/w/index.php?title=Liber_Abaci&action=edit&redlink=1" class="new" title="Liber Abaci (страница не постоји)">Liber Abaci</a></i> 1202. godine. On je pisao, „Metod Indijaca (latinski <i>Modus Indoram</i>) prevazilazi bili koji drugi metod računanja. To je izvanredan metod. Oni vrše svoja izračunavanja koristeći devet cifara i simbol <a href="/wiki/0_(%D0%B1%D1%80%D0%BE%D1%98)" title="0 (broj)">nulu</a>”.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> U <a href="/wiki/%D0%A1%D1%80%D0%B5%D0%B4%D1%9A%D0%B8_%D0%B2%D0%B5%D0%BA" title="Srednji vek">srednjem veku</a>, aritmetika je bila jedna od sedam <a href="/wiki/%D0%A1%D0%B5%D0%B4%D0%B0%D0%BC_%D1%81%D0%BB%D0%BE%D0%B1%D0%BE%D0%B4%D0%BD%D0%B8%D1%85_%D0%B2%D0%B5%D1%88%D1%82%D0%B8%D0%BD%D0%B0" title="Sedam slobodnih veština">liberalnih umetnosti</a> predavanih na univerzitetima. </p><p>Napredna <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Algebra">algebra</a> srednjovekovnog <a href="/wiki/%D0%98%D1%81%D0%BB%D0%B0%D0%BC" title="Islam">islamskog</a> sveta i <a href="/wiki/%D0%A0%D0%B5%D0%BD%D0%B5%D1%81%D0%B0%D0%BD%D1%81%D0%B0" title="Renesansa">renesansne</a> <a href="/wiki/%D0%95%D0%B2%D1%80%D0%BE%D0%BF%D0%B0" title="Evropa">Evrope</a> je proistekla iz enormnog pojednostavljenja <a href="/wiki/%D0%A0%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%9A%D0%B5" title="Računanje">računanja</a> primenom <a href="/wiki/%D0%94%D0%B5%D0%BA%D0%B0%D0%B4%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Dekadni sistem">decimalne</a> notacije. Razni tipovi oruđa su izmišljeni i široko korišteni kao pomagala u numeričkim proračunima. Pre renesanse, postojali su različiti tipovi <a href="/wiki/%D0%90%D0%B1%D0%B0%D0%BA%D1%83%D1%81_(%D1%80%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%9A%D0%B5)" title="Abakus (računanje)">abakusa</a>. Primeri iz bliže prošlosti obuhvataju <a href="/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B0%D1%80" title="Logaritmar">logaritmare</a>, <a href="/w/index.php?title=%D0%9D%D0%BE%D0%BC%D0%BE%D0%B3%D1%80%D0%B0%D0%BC&action=edit&redlink=1" class="new" title="Nomogram (stranica ne postoji)">nomograme</a> i <a href="/w/index.php?title=Mechanical_calculator&action=edit&redlink=1" class="new" title="Mechanical calculator (stranica ne postoji)">mehaničke kalkulatore</a>, kao što je <a href="/wiki/%D0%9F%D0%B0%D1%81%D0%BA%D0%B0%D0%BB%D0%B8%D0%BD%D0%B0" title="Paskalina">paskalina</a>. U današnje vreme, svi ti uređaji su zamenjeni elektronskim <a href="/wiki/%D0%9A%D0%B0%D0%BB%D0%BA%D1%83%D0%BB%D0%B0%D1%82%D0%BE%D1%80" title="Kalkulator">kalkulatorima</a> i <a href="/wiki/%D0%A0%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%80" title="Računar">računarima</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Аритметичке_операције"><span id=".D0.90.D1.80.D0.B8.D1.82.D0.BC.D0.B5.D1.82.D0.B8.D1.87.D0.BA.D0.B5_.D0.BE.D0.BF.D0.B5.D1.80.D0.B0.D1.86.D0.B8.D1.98.D0.B5"></span>Aritmetičke operacije</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=2" title="Uredite odeljak „Aritmetičke operacije”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=2" title="Edit section's source code: Aritmetičke operacije"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r24414138">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">Vidi još: <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D0%B0%D1%80%D1%81%D0%BA%D0%B5_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B5&action=edit&redlink=1" class="new" title="Algebarske operacije (stranica ne postoji)">Algebarske operacije</a></div> <p>Osnovne aritmetičke operacije su sabiranje, oduzimanje, množenje i deljenje, mada ovaj predmet obično obuhvata i naprednije operacije, kao što je manipulacija <a href="/wiki/%D0%9F%D1%80%D0%BE%D1%86%D0%B5%D0%BD%D0%B0%D1%82" title="Procenat">procentima</a>, <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D0%B8_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD" title="Kvadratni koren">kvadratnim korenima</a>, <a href="/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BE%D0%B2%D0%B0%D1%9A%D0%B5" title="Stepenovanje">stepenovanje</a>, i <a href="/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Logaritam">logaritamske funkcije</a>. Aritmetika se izvodi u skladu sa <a href="/wiki/%D0%A0%D0%B5%D0%B4%D0%BE%D1%81%D0%BB%D0%B5%D0%B4_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Redosled operacija">redosledom operacija</a>. Bilo koji set objekata na kome se sve četiri aritmetičke operacije (izuzev deljenja nulom) mogu izvršiti, i gde su te operacije podložne uobičajenim zakonima, naziva se <a href="/wiki/%D0%9F%D0%BE%D1%99%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Polje (matematika)">polje</a>.<sup id="cite_ref-Oxford_8-0" class="reference"><a href="#cite_note-Oxford-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Сабирање"><span id=".D0.A1.D0.B0.D0.B1.D0.B8.D1.80.D0.B0.D1.9A.D0.B5"></span>Sabiranje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=3" title="Uredite odeljak „Sabiranje”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=3" title="Edit section's source code: Sabiranje"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sabiranje je osnovna računska operacija aritmetike. U svom najjednostavnijem obliku, sabrati dva broja znači naći broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a+b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a+b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2391acf09244b9dba74eb940e871a6be7e7973a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.068ex; height:2.343ex;" alt="{\displaystyle a+b}"></span> </p> <dl><dt>Primeri</dt></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2+2=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2+2=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb6a3bbd9401d92584246527beee883714954a41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.426ex; height:2.343ex;" alt="{\displaystyle 2+2=4}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3+5=8}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>8</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3+5=8}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2f26bb33f785c904f8efe68093e92d105cc532" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.426ex; height:2.343ex;" alt="{\displaystyle 3+5=8}"></span> </p><p>Mogu se sabrati više od 2 broja. To uključuje sabiranje beskonačno mnogo brojeva. Sabiranje broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> s nekim brojem je najosnovniji oblik brojanja. </p><p>Sabiranjem broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> i nekog broja dobijamo taj broj. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5+0=5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>+</mo> <mn>0</mn> <mo>=</mo> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5+0=5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6b733fb3358586126ccd49c2c64c545bf56d5a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.426ex; height:2.343ex;" alt="{\displaystyle 5+0=5}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> je neutralni element za sabiranje </p><p>Sabiranjem 2 suprotna broja dobijamo broj 0. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 8+(-8)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>8</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>8</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 8+(-8)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c297a9c75f64cbf90f856275fa818407d7978a9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.044ex; height:2.843ex;" alt="{\displaystyle 8+(-8)=0}"></span> </p><p>To je inverzan element za sabiranje. </p><p>Važi zakon komutacije </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}3+4=7\\4+3=7tj\\3+4=4+3=7\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>=</mo> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> <mo>+</mo> <mn>3</mn> <mo>=</mo> <mn>7</mn> <mi>t</mi> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>=</mo> <mn>4</mn> <mo>+</mo> <mn>3</mn> <mo>=</mo> <mn>7</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}3+4=7\\4+3=7tj\\3+4=4+3=7\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/716f86e7422867c22b5d1643a6f86bc1ee6736e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:20.507ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}3+4=7\\4+3=7tj\\3+4=4+3=7\end{cases}}}"></span> </p><p>Važi zakon asocijacije </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}(2+3)+5=5+5=10\\2+(3+5)=2+8=10tj\\(2+3)+5=2+(3+5)=10\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>5</mn> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>10</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mn>8</mn> <mo>=</mo> <mn>10</mn> <mi>t</mi> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>10</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}(2+3)+5=5+5=10\\2+(3+5)=2+8=10tj\\(2+3)+5=2+(3+5)=10\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b7deff3774a69f2dea5248992f132641b42d3ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:33.294ex; height:8.843ex;" alt="{\displaystyle {\begin{cases}(2+3)+5=5+5=10\\2+(3+5)=2+8=10tj\\(2+3)+5=2+(3+5)=10\end{cases}}}"></span> </p><p>Sabrati se može i geometrijski, kao u sledećem primeru: </p><p>Ako postoje dva štapića dužine <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29483407999b8763f0ea335cf715a6a5e809f44b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 5}"></span> i ako se stave jedan za drugim, tako da se kraj prvog poklapa sa početkom drugog štapića, dobija se štap čija je dužina </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2+5=7}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>+</mo> <mn>5</mn> <mo>=</mo> <mn>7</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2+5=7}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f13c2cc3632e995ba4ba4ebec919767b83cc002a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.426ex; height:2.343ex;" alt="{\displaystyle 2+5=7}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="Одузимање"><span id=".D0.9E.D0.B4.D1.83.D0.B7.D0.B8.D0.BC.D0.B0.D1.9A.D0.B5"></span>Oduzimanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=4" title="Uredite odeljak „Oduzimanje”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=4" title="Edit section's source code: Oduzimanje"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oduzimanje je inverzna operacija od sabiranja. Rezultat ove operacije je razlika. Oduzeti broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> od broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> znači naći broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a-b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>−</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a-b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b80866c2bf2f1bc1f2e4c97e7937f5663150ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.068ex; height:2.343ex;" alt="{\displaystyle a-b}"></span> odnosno znači naći zbir brojeva <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (-b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (-b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48827b58299886483952c6fcf3f8f55948ab2fc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.615ex; height:2.843ex;" alt="{\displaystyle (-b)}"></span>. To se zapisuje sa </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a-b=a+(-b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a-b=a+(-b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f03e1ad2ad4d5dbbd763ad4c40a0d7bf250cd208" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.851ex; height:2.843ex;" alt="{\displaystyle a-b=a+(-b)}"></span> </p><p>Postoje sledeći slučajevi </p> <ul><li>Ako je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a<b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo><</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a<b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91a7698e4c7401bb321f97888b872b583a9e4642" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a<b}"></span>, onda je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a-b<0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo><</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a-b<0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1edbca11d21d22ddf092c16957400d467aba505" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.976ex; height:2.509ex;" alt="{\displaystyle a-b<0,}"></span></li> <li>Ako je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a>b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>></mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a>b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/83fc0063781fb9bf4ec7608b2fd11ed6d5b05a13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a>b}"></span>, onda je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a-b>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a-b>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/339d548bacc61bd395f85d85a587ea0bd5b9f85d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.329ex; height:2.343ex;" alt="{\displaystyle a-b>0}"></span></li> <li>Ako je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1956b03d1314c7071ac1f45ed7b1e29422dcfcc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a=b}"></span>, onda je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a-b=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>−</mo> <mi>b</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a-b=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca5e58f4c89d9995717017f3efb3f8712c146045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.329ex; height:2.343ex;" alt="{\displaystyle a-b=0}"></span></li></ul> <p>Za oduzimanje ne važi zakon komutacije, a ni asocijacije. </p> <div class="mw-heading mw-heading3"><h3 id="Множење"><span id=".D0.9C.D0.BD.D0.BE.D0.B6.D0.B5.D1.9A.D0.B5"></span>Množenje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=5" title="Uredite odeljak „Množenje”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=5" title="Edit section's source code: Množenje"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Množenje je druga osnovna računska operacija aritmetike. Pomnožiti 2 broja znači naći broj </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a*b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>∗</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a*b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4baddb0eb2fc85a456316d026699d38f5166a27c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.422ex; height:2.176ex;" alt="{\displaystyle a*b}"></span>, a to je </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\times b=\underbrace {b+\cdots +b} _{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>=</mo> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mi>b</mi> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mi>b</mi> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </munder> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\times b=\underbrace {b+\cdots +b} _{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3e246c3315cb4665c5c9fe6a2b362ae470822d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; margin-right: -0.028ex; width:18.593ex; height:5.676ex;" alt="{\displaystyle a\times b=\underbrace {b+\cdots +b} _{a}}"></span> </p> <dl><dt>Primer</dt></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3*4=4+4+4=12}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>∗</mo> <mn>4</mn> <mo>=</mo> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo>=</mo> <mn>12</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3*4=4+4+4=12}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a8d9db3cd13cb12f2e04180b168a37d70bf359" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:22.21ex; height:2.343ex;" alt="{\displaystyle 3*4=4+4+4=12}"></span> </p><p>Za množenje važi zakon komutacije </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}2*6=6+6=12\\6*2=2+2+2+2+2+2=12tj\\2*6=6*2=12\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>2</mn> <mo>∗</mo> <mn>6</mn> <mo>=</mo> <mn>6</mn> <mo>+</mo> <mn>6</mn> <mo>=</mo> <mn>12</mn> </mtd> </mtr> <mtr> <mtd> <mn>6</mn> <mo>∗</mo> <mn>2</mn> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>2</mn> <mo>=</mo> <mn>12</mn> <mi>t</mi> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> <mo>∗</mo> <mn>6</mn> <mo>=</mo> <mn>6</mn> <mo>∗</mo> <mn>2</mn> <mo>=</mo> <mn>12</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}2*6=6+6=12\\6*2=2+2+2+2+2+2=12tj\\2*6=6*2=12\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cfbb768e918dd0f0c152be0c908a350ddbdc552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:38.833ex; height:8.509ex;" alt="{\displaystyle {\begin{cases}2*6=6+6=12\\6*2=2+2+2+2+2+2=12tj\\2*6=6*2=12\end{cases}}}"></span> </p><p>i asocijacije </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}(2*3)*4=6*4=24\\*(3*4)=2*12=24tj\\(2*3)*4=2*12=24\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>∗</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>∗</mo> <mn>4</mn> <mo>=</mo> <mn>6</mn> <mo>∗</mo> <mn>4</mn> <mo>=</mo> <mn>24</mn> </mtd> </mtr> <mtr> <mtd> <mo>∗</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>∗</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mo>∗</mo> <mn>12</mn> <mo>=</mo> <mn>24</mn> <mi>t</mi> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>∗</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mo>∗</mo> <mn>4</mn> <mo>=</mo> <mn>2</mn> <mo>∗</mo> <mn>12</mn> <mo>=</mo> <mn>24</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}(2*3)*4=6*4=24\\*(3*4)=2*12=24tj\\(2*3)*4=2*12=24\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/228b227d759dd33d3f38ae6b630238eb5e22ba3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:26.707ex; height:8.843ex;" alt="{\displaystyle {\begin{cases}(2*3)*4=6*4=24\\*(3*4)=2*12=24tj\\(2*3)*4=2*12=24\end{cases}}}"></span> </p><p>Ako se broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> pomnoži sa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> (neutralni element), dobija se broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 6*1=6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>6</mn> <mo>∗</mo> <mn>1</mn> <mo>=</mo> <mn>6</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 6*1=6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d3b7945779d2966b6fdd14ede53ad0a14baf658" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.781ex; height:2.176ex;" alt="{\displaystyle 6*1=6}"></span> </p><p>Ako se broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> pomnoži sa recipročnom vrednosti broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, dobija se broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span>. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 6*6^{-1}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>6</mn> <mo>∗</mo> <msup> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 6*6^{-1}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1edf81bb7b31837045831f7769ce4f6186760bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.113ex; height:2.676ex;" alt="{\displaystyle 6*6^{-1}=1}"></span> </p><p>Ovo je inverzan broj. </p><p>Bilo koji broj može imati recipročnu vrednost osim <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span>. </p> <div class="mw-heading mw-heading4"><h4 id="Таблица_множења"><span id=".D0.A2.D0.B0.D0.B1.D0.BB.D0.B8.D1.86.D0.B0_.D0.BC.D0.BD.D0.BE.D0.B6.D0.B5.D1.9A.D0.B0"></span>Tablica množenja</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=6" title="Uredite odeljak „Tablica množenja”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=6" title="Edit section's source code: Tablica množenja"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440192">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <table class="wikitable" style="text-align:center"> <tbody><tr style="height:30px"> <th width="30">×</th> <th width="30">1</th> <th width="30">2</th> <th width="30">3</th> <th width="30">4</th> <th width="30">5</th> <th width="30">6</th> <th width="30">7</th> <th width="30">8</th> <th width="30">9</th> <th width="30">10</th> <th width="30">11</th> <th width="30">12</th> <th width="30">13</th> <th width="30">14</th> <th width="30">15</th> <th width="30">16</th> <th width="30">17</th> <th width="30">18</th> <th width="30">19</th> <th width="30">20</th> <th width="30">21</th> <th width="30">22</th> <th width="30">23</th> <th width="30">24</th> <th width="30">25 </th></tr> <tr style="height:30px"> <th>1 </th> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>11</td> <td>12</td> <td>13</td> <td>14</td> <td>15</td> <td>16</td> <td>17</td> <td>18</td> <td>19</td> <td>20</td> <td>21</td> <td>22</td> <td>23</td> <td>24</td> <td>25 </td></tr> <tr style="height:30px"> <th>2 </th> <td>2</td> <td>4</td> <td>6</td> <td>8</td> <td>10</td> <td>12</td> <td>14</td> <td>16</td> <td>18</td> <td>20</td> <td>22</td> <td>24</td> <td>26</td> <td>28</td> <td>30</td> <td>32</td> <td>34</td> <td>36</td> <td>38</td> <td>40</td> <td>42</td> <td>44</td> <td>46</td> <td>48</td> <td>50 </td></tr> <tr style="height:30px"> <th>3 </th> <td>3</td> <td>6</td> <td>9</td> <td>12</td> <td>15</td> <td>18</td> <td>21</td> <td>24</td> <td>27</td> <td>30</td> <td>33</td> <td>36</td> <td>39</td> <td>42</td> <td>45</td> <td>48</td> <td>51</td> <td>54</td> <td>57</td> <td>60</td> <td>63</td> <td>66</td> <td>69</td> <td>72</td> <td>75 </td></tr> <tr style="height:30px"> <th>4 </th> <td>4</td> <td>8</td> <td>12</td> <td>16</td> <td>20</td> <td>24</td> <td>28</td> <td>32</td> <td>36</td> <td>40</td> <td>44</td> <td>48</td> <td>52</td> <td>56</td> <td>60</td> <td>64</td> <td>68</td> <td>72</td> <td>76</td> <td>80</td> <td>84</td> <td>88</td> <td>92</td> <td>96</td> <td>100 </td></tr> <tr style="height:30px"> <th>5 </th> <td>5</td> <td>10</td> <td>15</td> <td>20</td> <td><b>25</b></td> <td>30</td> <td>35</td> <td>40</td> <td>45</td> <td><b>50</b></td> <td>55</td> <td>60</td> <td>65</td> <td>70</td> <td><b>75</b></td> <td>80</td> <td>85</td> <td>90</td> <td>95</td> <td><b>100</b></td> <td>105</td> <td>110</td> <td>115</td> <td>120</td> <td>125 </td></tr> <tr style="height:30px"> <th>6 </th> <td>6</td> <td>12</td> <td>18</td> <td>24</td> <td>30</td> <td>36</td> <td>42</td> <td>48</td> <td>54</td> <td>60</td> <td>66</td> <td>72</td> <td>78</td> <td>84</td> <td>90</td> <td>96</td> <td>102</td> <td>108</td> <td>114</td> <td>120</td> <td>126</td> <td>132</td> <td>138</td> <td>144</td> <td>150 </td></tr> <tr style="height:30px"> <th>7 </th> <td>7</td> <td>14</td> <td>21</td> <td>28</td> <td>35</td> <td>42</td> <td>49</td> <td>56</td> <td>63</td> <td>70</td> <td>77</td> <td>84</td> <td>91</td> <td>98</td> <td>105</td> <td>112</td> <td>119</td> <td>126</td> <td>133</td> <td>140</td> <td>147</td> <td>154</td> <td>161</td> <td>168</td> <td>175 </td></tr> <tr style="height:30px"> <th>8 </th> <td>8</td> <td>16</td> <td>24</td> <td>32</td> <td>40</td> <td>48</td> <td>56</td> <td>64</td> <td>72</td> <td>80</td> <td>88</td> <td>96</td> <td>104</td> <td>112</td> <td>120</td> <td>128</td> <td>136</td> <td>144</td> <td>152</td> <td>160</td> <td>168</td> <td>176</td> <td>184</td> <td>192</td> <td>200 </td></tr> <tr style="height:30px"> <th>9 </th> <td>9</td> <td>18</td> <td>27</td> <td>36</td> <td>45</td> <td>54</td> <td>63</td> <td>72</td> <td>81</td> <td>90</td> <td>99</td> <td>108</td> <td>117</td> <td>126</td> <td>135</td> <td>144</td> <td>153</td> <td>162</td> <td>171</td> <td>180</td> <td>189</td> <td>198</td> <td>207</td> <td>216</td> <td>225 </td></tr> <tr style="height:30px"> <th>10 </th> <td>10</td> <td>20</td> <td>30</td> <td>40</td> <td><b>50</b></td> <td>60</td> <td>70</td> <td>80</td> <td>90</td> <td><b>100</b></td> <td>110</td> <td>120</td> <td>130</td> <td>140</td> <td><b>150</b></td> <td>160</td> <td>170</td> <td>180</td> <td>190</td> <td><b>200</b></td> <td>210</td> <td>220</td> <td>230</td> <td>240</td> <td>250 </td></tr> <tr style="height:30px"> <th>11 </th> <td>11</td> <td>22</td> <td>33</td> <td>44</td> <td>55</td> <td>66</td> <td>77</td> <td>88</td> <td>99</td> <td>110</td> <td>121</td> <td>132</td> <td>143</td> <td>154</td> <td>165</td> <td>176</td> <td>187</td> <td>198</td> <td>209</td> <td>220</td> <td>231</td> <td>242</td> <td>253</td> <td>264</td> <td>275 </td></tr> <tr style="height:30px"> <th>12 </th> <td>12</td> <td>24</td> <td>36</td> <td>48</td> <td>60</td> <td>72</td> <td>84</td> <td>96</td> <td>108</td> <td>120</td> <td>132</td> <td>144</td> <td>156</td> <td>168</td> <td>180</td> <td>192</td> <td>204</td> <td>216</td> <td>228</td> <td>240</td> <td>252</td> <td>264</td> <td>276</td> <td>288</td> <td>300 </td></tr> <tr style="height:30px"> <th>13 </th> <td>13</td> <td>26</td> <td>39</td> <td>52</td> <td>65</td> <td>78</td> <td>91</td> <td>104</td> <td>117</td> <td>130</td> <td>143</td> <td>156</td> <td>169</td> <td>182</td> <td>195</td> <td>208</td> <td>221</td> <td>234</td> <td>247</td> <td>260</td> <td>273</td> <td>286</td> <td>299</td> <td>312</td> <td>325 </td></tr> <tr style="height:30px"> <th>14 </th> <td>14</td> <td>28</td> <td>42</td> <td>56</td> <td>70</td> <td>84</td> <td>98</td> <td>112</td> <td>126</td> <td>140</td> <td>154</td> <td>168</td> <td>182</td> <td>196</td> <td>210</td> <td>224</td> <td>238</td> <td>252</td> <td>266</td> <td>280</td> <td>294</td> <td>308</td> <td>322</td> <td>336</td> <td>350 </td></tr> <tr style="height:30px"> <th>15 </th> <td>15</td> <td>30</td> <td>45</td> <td>60</td> <td><b>75</b></td> <td>90</td> <td>105</td> <td>120</td> <td>135</td> <td><b>150</b></td> <td>165</td> <td>180</td> <td>195</td> <td>210</td> <td><b>225</b></td> <td>240</td> <td>255</td> <td>270</td> <td>285</td> <td><b>300</b></td> <td>315</td> <td>330</td> <td>345</td> <td>360</td> <td>375 </td></tr> <tr style="height:30px"> <th>16 </th> <td>16</td> <td>32</td> <td>48</td> <td>64</td> <td>80</td> <td>96</td> <td>112</td> <td>128</td> <td>144</td> <td>160</td> <td>176</td> <td>192</td> <td>208</td> <td>224</td> <td>240</td> <td>256</td> <td>272</td> <td>288</td> <td>304</td> <td>320</td> <td>336</td> <td>352</td> <td>368</td> <td>384</td> <td>400 </td></tr> <tr style="height:30px"> <th>17 </th> <td>17</td> <td>34</td> <td>51</td> <td>68</td> <td>85</td> <td>102</td> <td>119</td> <td>136</td> <td>153</td> <td>170</td> <td>187</td> <td>204</td> <td>221</td> <td>238</td> <td>255</td> <td>272</td> <td>289</td> <td>306</td> <td>323</td> <td>340</td> <td>357</td> <td>374</td> <td>391</td> <td>408</td> <td>425 </td></tr> <tr style="height:30px"> <th>18 </th> <td>18</td> <td>36</td> <td>54</td> <td>72</td> <td>90</td> <td>108</td> <td>126</td> <td>144</td> <td>162</td> <td>180</td> <td>198</td> <td>216</td> <td>234</td> <td>252</td> <td>270</td> <td>288</td> <td>306</td> <td>324</td> <td>342</td> <td>360</td> <td>378</td> <td>396</td> <td>414</td> <td>432</td> <td>450 </td></tr> <tr style="height:30px"> <th>19 </th> <td>19</td> <td>38</td> <td>57</td> <td>76</td> <td>95</td> <td>114</td> <td>133</td> <td>152</td> <td>171</td> <td>190</td> <td>209</td> <td>228</td> <td>247</td> <td>266</td> <td>285</td> <td>304</td> <td>323</td> <td>342</td> <td>361</td> <td>380</td> <td>399</td> <td>418</td> <td>437</td> <td>456</td> <td>475 </td></tr> <tr style="height:30px"> <th>20 </th> <td>20</td> <td>40</td> <td>60</td> <td>80</td> <td><b>100</b></td> <td>120</td> <td>140</td> <td>160</td> <td>180</td> <td><b>200</b></td> <td>220</td> <td>240</td> <td>260</td> <td>280</td> <td><b>300</b></td> <td>320</td> <td>340</td> <td>360</td> <td>380</td> <td><b>400</b></td> <td>420</td> <td>440</td> <td>460</td> <td>480</td> <td>500 </td></tr> <tr style="height:30px"> <th>21 </th> <td>21</td> <td>42</td> <td>63</td> <td>84</td> <td>105</td> <td>126</td> <td>147</td> <td>168</td> <td>189</td> <td>210</td> <td>231</td> <td>252</td> <td>273</td> <td>294</td> <td>315</td> <td>336</td> <td>357</td> <td>378</td> <td>399</td> <td>420</td> <td>441</td> <td>462</td> <td>483</td> <td>504</td> <td>525 </td></tr> <tr style="height:30px"> <th>22 </th> <td>22</td> <td>44</td> <td>66</td> <td>88</td> <td>110</td> <td>132</td> <td>154</td> <td>176</td> <td>198</td> <td>220</td> <td>242</td> <td>264</td> <td>286</td> <td>308</td> <td>330</td> <td>352</td> <td>374</td> <td>396</td> <td>418</td> <td>440</td> <td>462</td> <td>484</td> <td>506</td> <td>528</td> <td>550 </td></tr> <tr style="height:30px"> <th>23 </th> <td>23</td> <td>46</td> <td>69</td> <td>92</td> <td>115</td> <td>138</td> <td>161</td> <td>184</td> <td>207</td> <td>230</td> <td>253</td> <td>276</td> <td>299</td> <td>322</td> <td>345</td> <td>368</td> <td>391</td> <td>414</td> <td>437</td> <td>460</td> <td>483</td> <td>506</td> <td>529</td> <td>552</td> <td>575 </td></tr> <tr style="height:30px"> <th>24 </th> <td>24</td> <td>48</td> <td>72</td> <td>96</td> <td>120</td> <td>144</td> <td>168</td> <td>192</td> <td>216</td> <td>240</td> <td>264</td> <td>288</td> <td>312</td> <td>336</td> <td>360</td> <td>384</td> <td>408</td> <td>432</td> <td>456</td> <td>480</td> <td>504</td> <td>528</td> <td>552</td> <td>576</td> <td>600 </td></tr> <tr style="height:30px"> <th>25 </th> <td>25</td> <td>50</td> <td>75</td> <td>100</td> <td>125</td> <td>150</td> <td>175</td> <td>200</td> <td>225</td> <td>250</td> <td>275</td> <td>300</td> <td>325</td> <td>350</td> <td>375</td> <td>400</td> <td>425</td> <td>450</td> <td>475</td> <td>500</td> <td>525</td> <td>550</td> <td>575</td> <td>600</td> <td><b>625</b> </td></tr></tbody></table> </div> <div class="mw-heading mw-heading3"><h3 id="Дељење"><span id=".D0.94.D0.B5.D1.99.D0.B5.D1.9A.D0.B5"></span>Deljenje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=7" title="Uredite odeljak „Deljenje”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=7" title="Edit section's source code: Deljenje"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Deljenje je inverzna računska operacija množenju. Nije definisano deljenje brojem <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span>. Podeliti dva broja znači naći broj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a:b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>:</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a:b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3149b4f815ad9e8b3e8cdd29adcd02a42c22e5ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.165ex; height:2.176ex;" alt="{\displaystyle a:b}"></span> odnosno naći proizvod broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> i recipročne vrednosti broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. </p><p>To znači </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a:b=a*b^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>:</mo> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mo>∗</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a:b=a*b^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a37abf910b541513d4de88094fed71d4f1ac0363" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.018ex; height:2.676ex;" alt="{\displaystyle a:b=a*b^{-1}}"></span> </p><p>Postoje slučajevi </p> <ul><li>Za <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a>b=>a:b>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>></mo> <mi>b</mi> <mo>=></mo> <mi>a</mi> <mo>:</mo> <mi>b</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a>b=>a:b>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e81b8335d4f8174001ee02315563c8e51edb931" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.658ex; height:2.176ex;" alt="{\displaystyle a>b=>a:b>1}"></span></li> <li>Za <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a<b=>a:b<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo><</mo> <mi>b</mi> <mo>=></mo> <mi>a</mi> <mo>:</mo> <mi>b</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a<b=>a:b<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9ebffef8ff6772a87a06df6fa1ca9dd956e4b02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.658ex; height:2.176ex;" alt="{\displaystyle a<b=>a:b<1}"></span></li> <li>Za <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=b=>a:b=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mi>b</mi> <mo>=></mo> <mi>a</mi> <mo>:</mo> <mi>b</mi> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=b=>a:b=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50702491a8061556ce7a7abe3847dec08c141563" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.658ex; height:2.176ex;" alt="{\displaystyle a=b=>a:b=1}"></span></li></ul> <p>Ne važi zakon komutacije, a ni asocijacije. Za deljenje napisano kao proizvod važe sve osobine koje važe za množenje. </p> <div class="mw-heading mw-heading2"><h2 id="Децимална_аритметика"><span id=".D0.94.D0.B5.D1.86.D0.B8.D0.BC.D0.B0.D0.BB.D0.BD.D0.B0_.D0.B0.D1.80.D0.B8.D1.82.D0.BC.D0.B5.D1.82.D0.B8.D0.BA.D0.B0"></span>Decimalna aritmetika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=8" title="Uredite odeljak „Decimalna aritmetika”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=8" title="Edit section's source code: Decimalna aritmetika"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sve vrste zapisa brojeva mogu se zapisati decimalnim zapisom. Na primer zapis broja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 507,36}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>507</mn> <mo>,</mo> <mn>36</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 507,36}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96a52a07f1d7c434cafa1e2f5a4afa17e2089bfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.846ex; height:2.509ex;" alt="{\displaystyle 507,36}"></span> je: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (507,36)_{10}=5*10^{3}+0*10^{2}+7*10+3*10^{-1}+6*10^{-2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>507</mn> <mo>,</mo> <mn>36</mn> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>=</mo> <mn>5</mn> <mo>∗</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>0</mn> <mo>∗</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>7</mn> <mo>∗</mo> <mn>10</mn> <mo>+</mo> <mn>3</mn> <mo>∗</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mn>6</mn> <mo>∗</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (507,36)_{10}=5*10^{3}+0*10^{2}+7*10+3*10^{-1}+6*10^{-2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3f8dbb5f83b483516f6b1114628d87910b87594" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:60.176ex; height:3.176ex;" alt="{\displaystyle (507,36)_{10}=5*10^{3}+0*10^{2}+7*10+3*10^{-1}+6*10^{-2}}"></span>. Ovaj zapis brojeva obuhvata sva pravila aritmetičkih operacija: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>+</mo> <mn>5.67</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>6</mn> </mrow> </msup> <mo>=</mo> <mn>2.34</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>+</mo> <mn>0.567</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>=</mo> <mn>2.907</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5023254d2a7df1e9cff7a47d8bbea37de3167602" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:72.364ex; height:2.843ex;" alt="{\displaystyle 2.34\times 10^{-5}+5.67\times 10^{-6}=2.34\times 10^{-5}+0.567\times 10^{-5}=2.907\times 10^{-5}}"></span> </p><p><a href="/w/index.php?title=%D0%94%D0%B5%D1%86%D0%B8%D0%BC%D0%B0%D0%BB%D0%BD%D0%B0_%D1%80%D0%B5%D0%BF%D1%80%D0%B5%D0%B7%D0%B5%D0%BD%D1%82%D0%B0%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Decimalna reprezentacija (stranica ne postoji)">Decimalna reprezentacija</a> se ekskluzivno odnosi, u običnoj upotrebi, na pisani <a href="/wiki/%D0%91%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Brojevni sistem">numerički sistem</a> koji koristi <a href="/wiki/%D0%90%D1%80%D0%B0%D0%BF%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Arapski brojevi">arapske cifre</a> kao <a href="/wiki/Numerical_digit" class="mw-redirect" title="Numerical digit">brojeve</a> sa osnovom <a href="/wiki/%D0%94%D0%B5%D0%BA%D0%B0%D0%B4%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Dekadni sistem">10 („decimalnom”)</a> <a href="/wiki/Pozicioni_brojevni_sistem" class="mw-redirect" title="Pozicioni brojevni sistem">pozicione notacije</a>; međutim, svaki <a href="/wiki/%D0%91%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Brojevni sistem">numerički sistem</a> baziran na stepenu od 10, e.g., <a href="/wiki/%D0%93%D1%80%D1%87%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Grčki brojevi">grčki</a>, <a href="/wiki/%D0%8B%D0%B8%D1%80%D0%B8%D0%BB%D0%B8%D1%87%D0%BD%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Ćirilični brojevi">ćirilični</a>, <a href="/wiki/%D0%A0%D0%B8%D0%BC%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Rimski brojevi">rimski</a>, ili <a href="/wiki/%D0%9A%D0%B8%D0%BD%D0%B5%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Kineski brojevi">kineski brojevi</a> mogu konceptualno biti opisani kao „decimalna notacija” ili „decimalna reprezentacija”. </p><p>Moderne metode za četiri fundamentalne operacije (sabiranje, oduzimanje, množenje i deljenje) je prvi je izmislio <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" title="Bramagupta">Bramagupta</a> u Indiji. To je bilo poznato u srednjovekovnoj Evropi kao <i>Modus Indoram</i> ili metod Indusa. Poziciona notacija (takođe poznata kao „notacija mesta i vrednosti”) odnosi se na predstavljanje i kodiranje <a href="/wiki/%D0%91%D1%80%D0%BE%D1%98" title="Broj">brojeva</a> koristeći isti simbol za različite <a href="/wiki/%D0%A0%D0%B5%D0%B4_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B5" title="Red veličine">redove veličine</a> (npr., „mesto jedinica”, „mesto desetica”, „mesto stotina”) i, sa <a href="/w/index.php?title=Radix_point&action=edit&redlink=1" class="new" title="Radix point (stranica ne postoji)">radijskom tačkom</a>, koristeći te iste simbole za predstavljanje <a href="/wiki/%D0%A0%D0%B0%D0%B7%D0%BB%D0%BE%D0%BC%D0%B0%D0%BA" title="Razlomak">frakcija</a> (npr., „mesto desetih delova”, „mesto stotih delova”). Na primer, 507,36 označava 5 stotina (10<sup>2</sup>), plus 0 desetica (10<sup>1</sup>), plus 7 jedinica (10<sup>0</sup>), plus 3 desetine (10<sup>−1</sup>), plus 6 stotine (10<sup>−2</sup>). </p><p>Koncept <a href="/wiki/0_(%D0%B1%D1%80%D0%BE%D1%98)" title="0 (broj)">0</a> kao broja uporedivog sa drugim osnovnim ciframa je esencijalan za ovu notaciju, kao što je i koncept upotrebe nule za rezervisanje mesta, i definicija množenja i sabiranja sa nulom. Upotreba nule za rezervisanje mesta i stoga upotreba pozicione notacije je prvi put zabeležena u <a href="/wiki/%D0%82%D0%B0%D0%B8%D0%BD%D0%B8%D0%B7%D0%B0%D0%BC" class="mw-redirect" title="Đainizam">đainizanskom</a> tekstu iz <a href="/wiki/%D0%98%D0%BD%D0%B4%D0%B8%D1%98%D0%B0" title="Indija">Indije</a> sa naslovom <i><a href="/w/index.php?title=Lokavibh%C3%A2ga&action=edit&redlink=1" class="new" title="Lokavibhâga (stranica ne postoji)">Lokavibhaga</a></i>, iz 458. godine i tek je ranom 13. veku ovaj koncept, prenet preko <a href="/wiki/%D0%98%D1%81%D0%BB%D0%B0%D0%BC%D1%81%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Islamska matematika">učenjaka arapskog sveta</a>. U Evropu ga je uveo <a href="/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4%D0%BE_%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D0%B8" title="Leonardo Fibonači">Fibonači</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> koristeći <a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&redlink=1" class="new" title="Hindu–Arabic numeral system (stranica ne postoji)">indusko–arapski brojevni sistem</a>. </p><p><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D0%B7%D0%B0%D0%BC&action=edit&redlink=1" class="new" title="Algorizam (stranica ne postoji)">Algorizam</a> se sastoji od pravila za izvođenje aritmetičkih proračuna koristeći ovaj tip pisanih cifara. Na primer, sabiranje proizvodi sumu dva arbitrarna broja. Rezultat se izračunava ponavljanjem dodavanja pojedinačnih cifara iz svakog broja koje zauzimaju istu poziciju, idući zdesna nalevo. Tabela dodavanja sa deset redova i deset kolona prikazuje sve moguće vrednosti svih suma. Ako jedna individualna suma premaši vrednost 9, rezultat se predstavlja sa dve cifre. Cifra s desne strane je vrednost za trenutnu poziciju, a rezultat naknadnog dodavanja cifara s leve strane se povećava za vrednost druge (leve) cifre, koja je uvek jednaka jedinici. Ovo prilagođavanje se naziva <i>prenošenjem</i> vrednosti 1. </p><p>Proces množenja dva arbitrarna broja je sličan procesu sabiranja. Tabela množenja sa deset redova i deset kolona navodi rezultate za svaki par cifara. Ako jedan individualni proizvod para cifara premaši 9, <i>prenosno</i> podešavanje povećava rezultat svakog narednog množenja cifara na levoj strani za vrednost koja je jednaka drugoj (levoj) cifri, što može da bude bilo koja vrednost u opsegu od 1 do 8 (<span class="texhtml">9 × 9 = 81</span>). Dodatni koraci definišu finalni rezultat. Slične tehnike postoje za oduzimanje i deljenje. </p><p>Kreiranje korektnog procesa za množenje se oslanja na odnose između vrednosti susednih cifara. Vrednost bilo koje pojedinačne cifre broja zavisi od njene pozicije. Isto tako, svaka pozicija sa leve strane predstavlja vrednost koja je deset puta veća od date pozicije. U matematičkom smislu, <a href="/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BE%D0%B2%D0%B0%D1%9A%D0%B5" title="Stepenovanje">eksponent</a> za <a href="/w/index.php?title=Radix&action=edit&redlink=1" class="new" title="Radix (stranica ne postoji)">bazu</a> od 10 se povećava za 1 (nalevo) i smanjuje za 1 (nadesno). Stoga je vrednost bilo koje arbitrarne cifre pomnožena vrednošću oblika 10<sup><i>n</i></sup> pri čemu je <i>n</i> <a href="/wiki/%D0%A6%D0%B5%D0%BE_%D0%B1%D1%80%D0%BE%D1%98" title="Ceo broj">ceo broj</a>. Lista vrednosti koje korespondiraju svim mogućim pozicijama pojedinačnih cifri se piše kao <span class="nowrap"> {..., 10<sup>2</sup>, 10, 1, 10<sup>−1</sup>, 10<sup>−2</sup>, ...}.</span> </p><p>Ponovljeno množenje bilo koje vrednosti u ovoj listi sa 10 proizvodi drugu vrednost na listi. U matematičkoj terminologiji, ova karakteristika se definiše kao <a href="/wiki/%D0%97%D0%B0%D1%82%D0%B2%D0%BE%D1%80%D0%B5%D0%BD%D0%BE%D1%81%D1%82_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Zatvorenost (matematika)">zatvorenost</a>, i prethodna lista se opisuje kao <b>zatvorena pod množenjem</b>. Ovo je osnova za korektno nalaženje rezultata množenja koristeći prethodne tehnike. Ovaj ishod je jedan od primera upotrebe <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Teorija brojeva">teorije brojeva</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Референце"><span id=".D0.A0.D0.B5.D1.84.D0.B5.D1.80.D0.B5.D0.BD.D1.86.D0.B5"></span>Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=9" title="Uredite odeljak „Reference”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=9" title="Edit section's source code: Reference"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440201">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-британика_1-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-британика_1_1-0">^</a></b></span> <span class="reference-text"><cite class="citation book">Mišić, Milan, ur. (2005). <i>Enciklopedija Britanika. A-B</i>. Beograd: Narodna knjiga : Politika. str. 67. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/86-331-2075-5" title="Posebno:Štampani izvori/86-331-2075-5">86-331-2075-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.btitle=%D0%95%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0+%D0%91%D1%80%D0%B8%D1%82%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0.+%D0%90-%D0%91&rft.date=2005&rft.genre=book&rft.isbn=86-331-2075-5&rft.pages=67&rft.place=%D0%91%D0%B5%D0%BE%D0%B3%D1%80%D0%B0%D0%B4&rft.pub=%D0%9D%D0%B0%D1%80%D0%BE%D0%B4%D0%BD%D0%B0+%D0%BA%D1%9A%D0%B8%D0%B3%D0%B0+%3A+%D0%9F%D0%BE%D0%BB%D0%B8%D1%82%D0%B8%D0%BA%D0%B0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation book"><a href="/w/index.php?title=Harold_Davenport&action=edit&redlink=1" class="new" title="Harold Davenport (stranica ne postoji)">Davenport, Harold</a> (1999). <i>The Higher Arithmetic: An Introduction to the Theory of Numbers</i> (7th izd.). Cambridge, UK: Cambridge University Press. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-521-63446-5" title="Posebno:Štampani izvori/978-0-521-63446-5">978-0-521-63446-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.aufirst=Harold&rft.aulast=Davenport&rft.btitle=The+Higher+Arithmetic%3A+An+Introduction+to+the+Theory+of+Numbers&rft.date=1999&rft.edition=7th&rft.genre=book&rft.isbn=978-0-521-63446-5&rft.place=Cambridge%2C+UK&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-FOOTNOTERudman200764-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTERudman200764_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFRudman2007">Rudman 2007</a>, str. 64.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><i>The Works of Archimedes</i>, Chapter IV, <i>Arithmetic in Archimedes</i>, edited by T.L. Heath, Dover Publications Inc, New York, 2002.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Joseph Needham, <i>Science and Civilization in China</i>, Vol. 3. pp. 9, Cambridge University Press, 1959.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Reference: Revue de l'Orient Chretien by François Nau pp. 327-338. (1929)</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Reference: Sigler, L., "Fibonacci's Liber Abaci", Springer, 2003.</span> </li> <li id="cite_note-Oxford-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Oxford_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTapson1996">Tapson 1996</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.britannica.com/eb/article-4153/Leonardo-Pisano">Leonardo Pisano - pp. 3: "Contributions to number theory"</a>. <i><a href="/wiki/%D0%95%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0_%D0%91%D1%80%D0%B8%D1%82%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Enciklopedija Britanika">Encyclopædia Britannica</a></i> Online, 2006. Pristupljeno 18 September 2006.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Литература"><span id=".D0.9B.D0.B8.D1.82.D0.B5.D1.80.D0.B0.D1.82.D1.83.D1.80.D0.B0"></span>Literatura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=10" title="Uredite odeljak „Literatura”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=10" title="Edit section's source code: Literatura"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r28440192"><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><cite id="CITEREFDavenport1999" class="citation book"><a href="/w/index.php?title=Harold_Davenport&action=edit&redlink=1" class="new" title="Harold Davenport (stranica ne postoji)">Davenport, Harold</a> (1999). <i>The Higher Arithmetic: An Introduction to the Theory of Numbers</i> (7th izd.). Cambridge, UK: Cambridge University Press. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-521-63446-5" title="Posebno:Štampani izvori/978-0-521-63446-5">978-0-521-63446-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.aufirst=Harold&rft.aulast=Davenport&rft.btitle=The+Higher+Arithmetic%3A+An+Introduction+to+the+Theory+of+Numbers&rft.date=1999&rft.edition=7th&rft.genre=book&rft.isbn=978-0-521-63446-5&rft.place=Cambridge%2C+UK&rft.pub=Cambridge+University+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFRudman2007" class="citation book">Rudman, Peter Strom (2007). <a rel="nofollow" class="external text" href="https://archive.org/details/howmathematicsha0000rudm_m4o0"><i>How Mathematics Happened: The First 50,000 Years</i></a>. Prometheus Books. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-1-59102-477-4" title="Posebno:Štampani izvori/978-1-59102-477-4">978-1-59102-477-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.aufirst=Peter+Strom&rft.aulast=Rudman&rft.btitle=How+Mathematics+Happened%3A+The+First+50%2C000+Years&rft.date=2007&rft.genre=book&rft.isbn=978-1-59102-477-4&rft.pub=Prometheus+Books&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhowmathematicsha0000rudm_m4o0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFTapson1996" class="citation book">Tapson, Frank (1996). <a rel="nofollow" class="external text" href="https://archive.org/details/oxfordmathematic0000taps_q1d1"><i>The Oxford Mathematics Study Dictionary</i></a>. <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-19-914551-5" title="Posebno:Štampani izvori/978-0-19-914551-5">978-0-19-914551-5</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.aufirst=Frank&rft.aulast=Tapson&rft.btitle=The+Oxford+Mathematics+Study+Dictionary&rft.date=1996&rft.genre=book&rft.isbn=978-0-19-914551-5&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foxfordmathematic0000taps_q1d1&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li>Cunnington, Susan, <i>The Story of Arithmetic: A Short History of Its Origin and Development</i>, Swan Sonnenschein, London, 1904</li> <li><a href="/w/index.php?title=Leonard_Eugene_Dickson&action=edit&redlink=1" class="new" title="Leonard Eugene Dickson (страница не постоји)">Dickson, Leonard Eugene</a>, <i><a href="/w/index.php?title=History_of_the_Theory_of_Numbers&action=edit&redlink=1" class="new" title="History of the Theory of Numbers (страница не постоји)">History of the Theory of Numbers</a></i> (3 volumes), reprints: Carnegie Institute of Washington, Washington, 1932; Chelsea, New York, 1952, 1966</li> <li><a href="/wiki/%D0%9B%D0%B5%D0%BE%D0%BD%D0%B0%D1%80%D0%B4_%D0%9E%D1%98%D0%BB%D0%B5%D1%80" title="Леонард Ојлер">Euler, Leonhard</a>, <i><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110413234352/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/">Elements of Algebra</a></i>, Tarquin Press, 2007</li> <li><a href="/w/index.php?title=Henry_Burchard_Fine&action=edit&redlink=1" class="new" title="Henry Burchard Fine (страница не постоји)">Fine, Henry Burchard</a> (1858–1928), <i>The Number System of Algebra Treated Theoretically and Historically</i>, Leach, Shewell & Sanborn, Boston, 1891</li> <li><a href="/w/index.php?title=Louis_Charles_Karpinski&action=edit&redlink=1" class="new" title="Louis Charles Karpinski (страница не постоји)">Karpinski, Louis Charles</a> (1878–1956), <i>The History of Arithmetic</i>, Rand McNally, Chicago, 1925; reprint: Russell & Russell, New York, 1965</li> <li><a href="/w/index.php?title=%C3%98ystein_Ore&action=edit&redlink=1" class="new" title="Øystein Ore (страница не постоји)">Ore, Øystein</a>, <i>Number Theory and Its History</i>, McGraw–Hill, New York, 1948</li> <li><a href="/w/index.php?title=Andr%C3%A9_Weil&action=edit&redlink=1" class="new" title="André Weil (страница не постоји)">Weil, André</a>, <i>Number Theory: An Approach through History</i>, Birkhauser, Boston, 1984; reviewed: <a href="/w/index.php?title=Mathematical_Reviews&action=edit&redlink=1" class="new" title="Mathematical Reviews (страница не постоји)">Mathematical Reviews</a> 85c:01004</li> <li>"<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170811133911/http://math.coe.uga.edu/tme/issues/v10n2/5ross.pdf">Subtraction in the United States: An Historical Perspective</a>", Susan Ross, Mary Pratt-Cotter, <i>The Mathematics Educator</i>, Vol. 8, No. 1.</li> <li>Browell, W.A. (1939). <i>Learning as reorganization: An experimental study in third-grade arithmetic</i>, Duke University Press.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Спољашње_везе"><span id=".D0.A1.D0.BF.D0.BE.D1.99.D0.B0.D1.88.D1.9A.D0.B5_.D0.B2.D0.B5.D0.B7.D0.B5"></span>Spoljašnje veze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&veaction=edit&section=11" title="Uredite odeljak „Spoljašnje veze”" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&action=edit&section=11" title="Edit section's source code: Spoljašnje veze"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="width:23em;float:right;clear:right;font-size:90%;margin-bottom:7px;margin-left:14px;"><div role="navigation" aria-labelledby="sister-projects" class="metadata plainlinks plainlist mbox-small" style="border:1px solid #aaa; padding:0.75em; background:#f9f9f9;"> <div style="padding-bottom: 0.75em; text-align: center;">Više informacija o članku<b style="display:block;">Aritmetika</b>pronađite na <a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0" title="Vikipedija">Vikipedijinim</a><br /><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%91%D1%80%D0%B0%D1%82%D1%81%D0%BA%D0%B8_%D0%BF%D1%80%D0%BE%D1%98%D0%B5%D0%BA%D1%82%D0%B8" title="Vikipedija:Bratski projekti"><span id="sister-projects">sestrinskim projektima</span></a>: </div> <ul style="border-top:1px solid #aaa; padding-top: 0.75em;margin:auto 2em auto 2em;"> <div><span style="white-space:nowrap"><span style="display: inline-block; width: 31px; line-height: 31px; vertical-align: middle; text-align: center;"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></span><span style="display: inline-block; margin-left: 4px; width: 182px; vertical-align: middle;"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Arithmetic?uselang=sr">Mediji</a> na Ostavi</span></span></div><div><span style="white-space:nowrap"><span style="display: inline-block; width: 31px; line-height: 31px; vertical-align: middle; text-align: center;"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/WiktionarySr_-_DP_Derivative.svg/22px-WiktionarySr_-_DP_Derivative.svg.png" decoding="async" width="22" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/WiktionarySr_-_DP_Derivative.svg/34px-WiktionarySr_-_DP_Derivative.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/WiktionarySr_-_DP_Derivative.svg/45px-WiktionarySr_-_DP_Derivative.svg.png 2x" data-file-width="512" data-file-height="620" /></span></span></span><span style="display: inline-block; margin-left: 4px; width: 182px; vertical-align: middle;"><a href="https://sr.wiktionary.org/wiki/%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" class="extiw" title="wikt:Aritmetika">Definicije</a> iz Vikirečnika</span></span></div><div><span style="white-space:nowrap"><span style="display: inline-block; width: 31px; line-height: 31px; vertical-align: middle; text-align: center;"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/27px-Wikidata-logo.svg.png" decoding="async" width="27" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/41px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/54px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></span></span></span><span style="display: inline-block; margin-left: 4px; width: 182px; vertical-align: middle;"><a class="external text" href="https://www.wikidata.org/wiki/Special:ItemByTitle/srwiki/Аритметика?uselang=sr">Podaci</a> na Vikipodacima</span></span></div> </ul> </div></div> <ul><li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Arithmetic.html">MathWorld article about arithmetic</a></li> <li><a href="https://sr.wikisource.org/wiki/The_New_Student%27s_Reference_Work/Arithmetic" class="extiw" title="s:The New Student's Reference Work/Arithmetic">The New Student's Reference Work/Arithmetic</a> (historical)</li> <li><a rel="nofollow" class="external text" href="http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1293&bodyId=1422">The Great Calculation According to the Indians, of Maximus Planudes</a> – an early Western work on arithmetic at <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070713083148/http://mathdl.maa.org/convergence/1/">Convergence</a></li> <li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> <cite class="citation encyclopaedia">Weyde, P. H. Vander (1879). „<a href="https://sr.wikisource.org/wiki/The_American_Cyclop%C3%A6dia_(1879)/Arithmetic" class="extiw" title="s:The American Cyclopædia (1879)/Arithmetic">Arithmetic</a>”. <i><a href="/w/index.php?title=The_American_Cyclop%C3%A6dia&action=edit&redlink=1" class="new" title="The American Cyclopædia (stranica ne postoji)">The American Cyclopædia</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%90%D1%80%D0%B8%D1%82%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0&rft.atitle=Arithmetic&rft.aufirst=P.+H.+Vander&rft.aulast=Weyde&rft.btitle=The+American+Cyclop%C3%A6dia&rft.date=1879&rft.genre=bookitem&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><a rel="nofollow" class="external text" href="http://www.wdl.org/en/item/2863">"A Friendly Gift on the Science of Arithmetic"</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r25469611">.mw-parser-output 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