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vector-toc-level-2"> <a class="vector-toc-link" href="#Multiplication_and_division"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Multiplication and division</span> </div> </a> <ul id="toc-Multiplication_and_division-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Addition_and_subtraction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addition_and_subtraction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Addition and subtraction</span> </div> </a> <ul id="toc-Addition_and_subtraction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples_of_all_rules" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples_of_all_rules"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Examples of all rules</span> </div> </a> <ul id="toc-Examples_of_all_rules-sublist" class="vector-toc-list"> <li id="toc-Example_one" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Example_one"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4.1</span> <span>Example one</span> </div> </a> <ul id="toc-Example_one-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Example_two" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Example_two"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4.2</span> <span>Example two</span> </div> </a> <ul id="toc-Example_two-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Acronyms" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Acronyms"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Acronyms</span> </div> </a> <ul id="toc-Acronyms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_pages" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_pages"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Related pages</span> </div> </a> <ul id="toc-Related_pages-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-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="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" 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Available in 41 languages" > <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-41" 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">41 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B1%D8%AA%D9%8A%D8%A8_%D8%A7%D9%84%D8%B9%D9%85%D9%84%D9%8A%D8%A7%D8%AA_%D8%A7%D9%84%D8%AD%D8%B3%D8%A7%D8%A8%D9%8A%D8%A9" title="ترتيب العمليات الحسابية – Arabic" lang="ar" hreflang="ar" data-title="ترتيب العمليات الحسابية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/I%C3%A1n-s%C7%B9g_s%C5%ABn-s%C5%AB" title="Ián-sǹg sūn-sū – Minnan" lang="nan" hreflang="nan" data-title="Ián-sǹg sūn-sū" 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-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D1%8B%D1%8F%D1%80%D1%8B%D1%82%D1%8D%D1%82_%D0%B0%D1%80%D1%8B%D1%84%D0%BC%D0%B5%D1%82%D1%8B%D1%87%D0%BD%D1%8B%D1%85_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D0%B9" title="Прыярытэт арыфметычных аперацый – Belarusian" lang="be" hreflang="be" data-title="Прыярытэт арыфметычных аперацый" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ordre_de_les_operacions" title="Ordre de les operacions – Catalan" lang="ca" hreflang="ca" data-title="Ordre de les operacions" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Precedence" title="Precedence – Czech" lang="cs" hreflang="cs" data-title="Precedence" 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/Regnearternes_hierarki" title="Regnearternes hierarki – Danish" lang="da" hreflang="da" data-title="Regnearternes hierarki" 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/Operatorrangfolge" title="Operatorrangfolge – German" lang="de" hreflang="de" data-title="Operatorrangfolge" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%81%CE%BF%CF%84%CE%B5%CF%81%CE%B1%CE%B9%CF%8C%CF%84%CE%B7%CF%84%CE%B1_%CF%80%CF%81%CE%AC%CE%BE%CE%B5%CF%89%CE%BD" title="Προτεραιότητα πράξεων – Greek" lang="el" hreflang="el" data-title="Προτεραιότητα πράξεων" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Order_of_operations" title="Order of operations – English" lang="en" hreflang="en" data-title="Order of operations" 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/Orden_de_evaluaci%C3%B3n" title="Orden de evaluación – Spanish" lang="es" hreflang="es" data-title="Orden de evaluación" 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/Rango_de_operacioj" title="Rango de operacioj – Esperanto" lang="eo" hreflang="eo" data-title="Rango de operacioj" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eragiketen_hierarkia" title="Eragiketen hierarkia – Basque" lang="eu" hreflang="eu" data-title="Eragiketen hierarkia" 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%A7%D9%88%D9%84%D9%88%DB%8C%D8%AA_%D8%B9%D9%85%D9%84%DA%AF%D8%B1%D9%87%D8%A7" title="اولویت عملگرها – Persian" lang="fa" hreflang="fa" data-title="اولویت عملگرها" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ordre_des_op%C3%A9rations" title="Ordre des opérations – French" lang="fr" hreflang="fr" data-title="Ordre des opérations" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xerarqu%C3%ADa_das_operaci%C3%B3ns" title="Xerarquía das operacións – Galician" lang="gl" hreflang="gl" data-title="Xerarquía das operacións" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AD%E0%AA%BE%E0%AA%97%E0%AB%81%E0%AA%B8%E0%AA%AC%E0%AA%BE_%E0%AA%A8%E0%AB%8B_%E0%AA%A8%E0%AA%BF%E0%AA%AF%E0%AA%AE" title="ભાગુસબા નો નિયમ – Gujarati" lang="gu" hreflang="gu" data-title="ભાગુસબા નો નિયમ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%B0%EC%82%B0%EC%9D%98_%EC%9A%B0%EC%84%A0%EC%88%9C%EC%9C%84" title="연산의 우선순위 – Korean" lang="ko" hreflang="ko" data-title="연산의 우선순위" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Urutan_operasi" title="Urutan operasi – Indonesian" lang="id" hreflang="id" data-title="Urutan operasi" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Framkv%C3%A6mdar%C3%B6%C3%B0_reiknivirkja" title="Framkvæmdaröð reiknivirkja – Icelandic" lang="is" hreflang="is" data-title="Framkvæmdaröð reiknivirkja" 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/Ordine_delle_operazioni" title="Ordine delle operazioni – Italian" lang="it" hreflang="it" data-title="Ordine delle operazioni" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%93%D7%99%D7%9E%D7%95%D7%AA_%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8%D7%99%D7%9D" title="קדימות אופרטורים – Hebrew" lang="he" hreflang="he" data-title="קדימות אופרטורים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A4%82%E0%A4%9A%E0%A5%87%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A5%81%E0%A4%AC%E0%A5%87%E0%A4%B5_%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AF%E0%A4%BE_%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE" title="कंचेभागुबेव क्रिया क्रम – Marathi" lang="mr" hreflang="mr" data-title="कंचेभागुबेव क्रिया क्रम" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Urutan_pengiraan" title="Urutan pengiraan – Malay" lang="ms" hreflang="ms" data-title="Urutan pengiraan" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bewerkingsvolgorde" title="Bewerkingsvolgorde – Dutch" lang="nl" hreflang="nl" data-title="Bewerkingsvolgorde" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%BC%94%E7%AE%97%E5%AD%90%E3%81%AE%E5%84%AA%E5%85%88%E9%A0%86%E4%BD%8D" title="演算子の優先順位 – Japanese" lang="ja" hreflang="ja" data-title="演算子の優先順位" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Regnerekkef%C3%B8lge" title="Regnerekkefølge – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Regnerekkefølge" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Kolejno%C5%9B%C4%87_wykonywania_dzia%C5%82a%C5%84" title="Kolejność wykonywania działań – Polish" lang="pl" hreflang="pl" data-title="Kolejność wykonywania działań" 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/Ordem_de_opera%C3%A7%C3%B5es" title="Ordem de operações – Portuguese" lang="pt" hreflang="pt" data-title="Ordem de operações" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ordinea_opera%C8%9Biilor" title="Ordinea operațiilor – Romanian" lang="ro" hreflang="ro" data-title="Ordinea operațiilor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%BE%D1%80%D0%B8%D1%82%D0%B5%D1%82_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B8" title="Приоритет операции – Russian" lang="ru" hreflang="ru" data-title="Приоритет операции" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Radha_e_veprimeve_matematikore" title="Radha e veprimeve matematikore – Albanian" lang="sq" hreflang="sq" data-title="Radha e veprimeve matematikore" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/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="Редослед операција – Serbian" lang="sr" hreflang="sr" data-title="Редослед операција" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Laskuj%C3%A4rjestys" title="Laskujärjestys – Finnish" lang="fi" hreflang="fi" data-title="Laskujärjestys" 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/Operatorprioritet" title="Operatorprioritet – Swedish" lang="sv" hreflang="sv" data-title="Operatorprioritet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Ayos_ng_operasyon" title="Ayos ng operasyon – Tagalog" lang="tl" hreflang="tl" data-title="Ayos ng operasyon" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AE%B2%E0%AE%BF%E0%AE%AF%E0%AF%88_%E0%AE%85%E0%AE%AE%E0%AE%B2%E0%AF%8D%E0%AE%AA%E0%AE%9F%E0%AF%81%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AF%81%E0%AE%AE%E0%AF%8D_%E0%AE%B5%E0%AE%B0%E0%AE%BF%E0%AE%9A%E0%AF%88_%E0%AE%AE%E0%AF%81%E0%AE%B1%E0%AF%88" title="செயலியை அமல்படுத்தும் வரிசை முறை – Tamil" lang="ta" hreflang="ta" data-title="செயலியை அமல்படுத்தும் வரிசை முறை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A5%E0%B8%B3%E0%B8%94%E0%B8%B1%E0%B8%9A%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3" title="ลำดับการดำเนินการ – Thai" lang="th" hreflang="th" data-title="ลำดับการดำเนินการ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0%C5%9Flem_s%C4%B1ras%C4%B1" title="İşlem sırası – Turkish" lang="tr" hreflang="tr" data-title="İşlem sırası" 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%A7%D0%B5%D1%80%D0%B3%D0%BE%D0%B2%D1%96%D1%81%D1%82%D1%8C_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%96%D0%B9" title="Черговість операцій – Ukrainian" lang="uk" hreflang="uk" data-title="Черговість операцій" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99_%C6%B0u_ti%C3%AAn_c%E1%BB%A7a_to%C3%A1n_t%E1%BB%AD" title="Độ ưu tiên của toán tử – Vietnamese" lang="vi" hreflang="vi" data-title="Độ ưu tiên của toán tử" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%81%8B%E7%AE%97%E6%AC%A1%E5%BA%8F" title="運算次序 – Chinese" lang="zh" hreflang="zh" data-title="運算次序" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</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/Q845118#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Change links</a></span></div> </div> </div> </div> </header> <div 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class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Simple English Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>The <b>order of operations</b> is a <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> and <a href="/wiki/Algebra" title="Algebra">algebraic</a> set of rules. It is used to evaluate (solve) and <a href="https://simple.wiktionary.org/wiki/simplify" class="extiw" title="wikt:simplify">simplify</a> <a href="/wiki/Equation" title="Equation">expressions and equations</a>. The order of operations is the order that different mathematical operations are done. The standard mathematical operations are <a href="/wiki/Addition" title="Addition">addition</a> (<b>+</b>), <a href="/wiki/Subtraction" title="Subtraction">subtraction</a> (<b>−</b>), <a href="/wiki/Multiplication" title="Multiplication">multiplication</a> (<b>*</b>, <b>×</b>, <b>·</b> or <b>n</b>), <a href="/wiki/Division_(mathematics)" title="Division (mathematics)">division</a> (<b>/</b>, <b>÷</b>, <b>:</b> or <b><style data-mw-deduplicate="TemplateStyles:r7803981">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span role="math" class="sfrac tion"><span class="num">n</span><span class="sr-only">/</span><span class="den">n</span></span></b>), grouping/parenthesizing/bracketing (<b>()</b>, <b>[]</b> or <b>{}</b>)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Exponentiation" title="Exponentiation">exponentiation</a> (<b>^</b> or <b>ⁿ</b>),<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><sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> which includes <a href="/wiki/Nth_root" title="Nth root">root extraction</a> (<b>√</b>). </p><p>Mathematicians have agreed on a correct order to use operations, and it is very important that they know these rules. When people are solving a problem with more than one operation, they will need to know the correct order to solve the problem correctly. Otherwise, the answer will be wrong. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Rules">Rules</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=1" title="Change section: Rules" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=1" title="Edit section's source code: Rules"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Follow all the rules in this order <b>from left to right</b> in the equation. </p> <div class="mw-heading mw-heading3"><h3 id="Brackets_and_parentheses">Brackets and parentheses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=2" title="Change section: Brackets and parentheses" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=2" title="Edit section's source code: Brackets and parentheses"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Use operations inside brackets and solve any indices. You should always solve brackets first when solving an equation. </p><p><b>Example</b>: </p> <dl><dd>2 * 4 + (9 - 8) + 3</dd> <dd>2 * 4 + <b>(9 - 8)</b> + 3</dd> <dd>2 * 4 + 1 + 3</dd> <dd><b>2 * 4</b> + 1 + 3</dd> <dd>8 + 1 + 3</dd> <dd><b>8 + 1</b> + 3</dd> <dd>9 + 3</dd> <dd><b>9 + 3</b></dd> <dd>12</dd></dl> <div class="mw-heading mw-heading4"><h4 id="Exponents">Exponents</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=3" title="Change section: Exponents" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=3" title="Edit section's source code: Exponents"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When seeing an exponent, solve it first after solving the brackets. (5<sup>3</sup> = 5 * 5 * 5 = 125) </p><p><b>Example</b>: </p> <dl><dd>5<sup>3</sup> * 7 + 4</dd> <dd><b>5<sup>3</sup></b> * 7 + 4</dd> <dd>125 * 7 + 4</dd> <dd><b>125 * 7</b> + 4</dd> <dd>875 + 4</dd> <dd><b>875 + 4</b></dd> <dd>879</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Multiplication_and_division">Multiplication and division</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=4" title="Change section: Multiplication and division" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=4" title="Edit section's source code: Multiplication and division"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Solve any multiplication and division in the problem. Note that multiplication does not precede division; this is a common mistake. Both are solved from left to right as they occur. </p><p><b>Example</b>: </p> <dl><dd>5 * 4 - 9 / 3</dd> <dd><b>5 * 4</b> - 9 / 3</dd> <dd>20 - 9 / 3</dd> <dd>20 - <b>9 / 3</b></dd> <dd>20 - 3</dd> <dd><b>20 - 3</b></dd> <dd>17</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Addition_and_subtraction">Addition and subtraction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=5" title="Change section: Addition and subtraction" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=5" title="Edit section's source code: Addition and subtraction"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lastly, solve any addition or subtraction. It always goes from left to right. </p><p><b>Example</b>: </p> <dl><dd>10 - 9 + 4</dd> <dd><b>10 - 9</b> + 4</dd> <dd>1 + 4</dd> <dd><b>1 + 4</b></dd> <dd>5</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Examples_of_all_rules">Examples of all rules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=6" title="Change section: Examples of all rules" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=6" title="Edit section's source code: Examples of all rules"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Example_one">Example one</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=7" title="Change section: Example one" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=7" title="Edit section's source code: Example one"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>(1 + 8) * (4 - 1) + 16 / 2<sup>3</sup></dd> <dd><b>(1 + 8)</b> * (4 - 1) + 16 / 2<sup>3</sup></dd> <dd>9 * <b>(4 - 1)</b> + 16 / 2<sup>3</sup></dd> <dd>9 * 3 + 16 / <b>2<sup>3</sup></b></dd> <dd>9 * 3 + 16 / 8</dd> <dd><b>9 * 3</b> + 16 / 8</dd> <dd>27 + <b>16 / 8</b></dd> <dd>27 + 2</dd> <dd><b>27 + 2</b></dd> <dd><b>29</b></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Example_two">Example two</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=8" title="Change section: Example two" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=8" title="Edit section's source code: Example two"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>(7 + 3) * (6 - 3) + 216 / 3<sup>3</sup></dd> <dd><b>(7 + 3)</b> * (6 - 3) + 216 / 3<sup>3</sup></dd> <dd>10 * <b>(6 - 3)</b> + 216 / 3<sup>3</sup></dd> <dd>10 * 3 + 216 / <b>3<sup>3</sup></b></dd> <dd>10 * 3 + 216 / 27</dd> <dd><b>10 * 3</b> + 216 / 27</dd> <dd>30 + <b>216 / 27</b></dd> <dd>30 + 8</dd> <dd><b>30 + 8</b></dd> <dd>38</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Acronyms">Acronyms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=9" title="Change section: Acronyms" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=9" title="Edit section's source code: Acronyms"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The acronym for the order of standard operations is GEMDAS/PEMDAS/BOMDAS/BIMDAS, which stands for Grouping/Parenthesization/Bracketing, Exponentation, Multiplication, Division, Addition and Subtraction.<sup id="cite_ref-:0_3-1" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>When solving 8 - 7 + 5, some people say that 7 + 5 must take precedence, but this is incorrect. Instead, one should look from left to right to find the correct answer. This rule also applies to multiplication and division. </p> <div class="mw-heading mw-heading2"><h2 id="Related_pages">Related pages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=10" title="Change section: Related pages" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=10" title="Edit section's source code: Related pages"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Associativity" title="Associativity">Associativity</a></li> <li><a href="/wiki/Commutative_property" title="Commutative property">Commutativity</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Order_of_operations&veaction=edit&section=11" title="Change section: References" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Order_of_operations&action=edit&section=11" title="Edit section's source code: References"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r9724332">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mathvault.ca/hub/higher-math/math-symbols/">"Compendium of Mathematical Symbols"</a>. <i>Math Vault</i>. 2020-03-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Math+Vault&rft.atitle=Compendium+of+Mathematical+Symbols&rft.date=2020-03-01&rft_id=https%3A%2F%2Fmathvault.ca%2Fhub%2Fhigher-math%2Fmath-symbols%2F&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AOrder+of+operations" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite id="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Precedence.html">"Precedence"</a>. <i>mathworld.wolfram.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mathworld.wolfram.com&rft.atitle=Precedence&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FPrecedence.html&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AOrder+of+operations" class="Z3988"></span></span> </li> <li id="cite_note-:0-3"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-:0_3-0">3.0</a></sup> <sup><a href="#cite_ref-:0_3-1">3.1</a></sup></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r9724332"><cite id="CITEREFStapel" class="citation web cs1">Stapel, Elizabeth. <a rel="nofollow" class="external text" href="https://www.purplemath.com/modules/orderops.htm">"The Order of Operations: PEMDAS"</a>. <i>Purplemath</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-08-22</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Purplemath&rft.atitle=The+Order+of+Operations%3A+PEMDAS&rft.aulast=Stapel&rft.aufirst=Elizabeth&rft_id=https%3A%2F%2Fwww.purplemath.com%2Fmodules%2Forderops.htm&rfr_id=info%3Asid%2Fsimple.wikipedia.org%3AOrder+of+operations" class="Z3988"></span></span> </li> </ol>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://simple.wikipedia.org/w/index.php?title=Order_of_operations&oldid=9866608">https://simple.wikipedia.org/w/index.php?title=Order_of_operations&oldid=9866608</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Category</a>: <ul><li><a href="/wiki/Category:Arithmetics" title="Category:Arithmetics">Arithmetics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden category: <ul><li><a href="/wiki/Category:Pages_using_the_JsonConfig_extension" title="Category:Pages using the JsonConfig extension">Pages using the JsonConfig extension</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last changed on 5 November 2024, at 20:04.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> and the <a href="/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License" title="Wikipedia:Text of the GNU Free Documentation License">GFDL</a>; additional terms may apply. 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