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/></span></span></td> <td style="color:black; text-align:left; vertical-align:middle; padding:0.5em; padding-left:0em; border:none;"> <p>This book is intended for <b><a href="/wiki/Wikibooks:Reading_Levels" title="Wikibooks:Reading Levels">advanced</a></b> readers. </p> </td></tr></tbody></table> <table class="plainlinks noprint messagebox notice" style="width:250px; float:right; clear:right; margin:0px; margin-left:10px;"> <tbody><tr style="vertical-align:middle;"><td style="padding:0.1em; text-align:center; vertical-align:middle; width:45px; border:none;"> <span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Warning_icon_WikiBooks.svg/40px-Warning_icon_WikiBooks.svg.png" decoding="async" width="40" height="33" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Warning_icon_WikiBooks.svg/60px-Warning_icon_WikiBooks.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Warning_icon_WikiBooks.svg/80px-Warning_icon_WikiBooks.svg.png 2x" data-file-width="600" data-file-height="500" /></span></span></td> <td style="color:black; text-align:left; vertical-align:middle; padding:0.5em; padding-left:0em; border:none;"> <p>This book requires that you first read <b><a href="/wiki/Using_an_Abacus" title="Using an Abacus">Using an Abacus</a></b>. </p> </td></tr></tbody></table> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:The_lone_goose_returns_to_its_flock.png" class="mw-file-description"><img alt="Allegory of a traditional division exercise" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/The_lone_goose_returns_to_its_flock.png/450px-The_lone_goose_returns_to_its_flock.png" decoding="async" width="450" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/2c/The_lone_goose_returns_to_its_flock.png 1.5x" data-file-width="624" data-file-height="308" /></a><figcaption>孤雁歸隊 (<i>Gūyàn guīduì</i>) <i>The lone geese return to flock</i>. Allegory of a traditional division exercise with abacus (998001/999)</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg/220px-Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg" decoding="async" width="220" height="119" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg/330px-Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg/440px-Traditional_Chinese_abacus_illustrating_the_suspended_bead_use.jpg 2x" data-file-width="1801" data-file-height="978" /></a><figcaption>Traditional Chinese abacus illustrating the suspended bead use</figcaption></figure><p>This textbook is an introduction to the <a href="https://en.wikipedia.org/wiki/Chinese_Zhusuan" class="extiw" title="w:Chinese Zhusuan">Traditional Beads Arithmetic</a> (珠算; <i>zhūsuàn</i> in Chinese, <i>shuzan</i> in Japanese), or the use of the eastern fixed-bead abacus (算盤, <a href="https://en.wikipedia.org/wiki/Suanpan" class="extiw" title="w:Suanpan"><i>suanpan</i></a> in Chinese, <a href="https://en.wikipedia.org/wiki/Soroban" class="extiw" title="w:Soroban"><i>soroban</i></a> in Japanese) as practiced in China, Japan, Korea, Vietnam, etc. for at least four centuries. </p><p>Chinese beads arithmetic has been inscribed in 2013 on the <a href="https://en.wikipedia.org/wiki/UNESCO_Intangible_Cultural_Heritage_Lists" class="extiw" title="w:UNESCO Intangible Cultural Heritage Lists">UNESCO Representative List of the Intangible Cultural Heritage of Humanity</a>, however, the information available in English on this subject is scant and scattered, so it is worth the effort of trying to gather it somewhere, for instance, in this book. </p><p>This text is aimed at those who already have a basic level in the use of the abacus following the <i>Modern Method</i> currently taught and who wish to delve into the history of their favorite instrument and mathematics in the Far East. After studying this text and practicing its content, the reader should be able to perform calculations according to the <i>Traditional Method</i> using any type of eastern abacus and understand (whenever possible) why they were done that way. </p> <div class="mw-heading mw-heading2"><h2 id="Table_of_content">Table of content</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Traditional_Abacus_and_Bead_Arithmetic&veaction=edit&section=1" title="Edit section: Table of content" class="mw-editsection-visualeditor"><span>edit</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Traditional_Abacus_and_Bead_Arithmetic&action=edit&section=1" title="Edit section's source code: Table of content"><span>edit source</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint" style="float:right; clear:right; margin:0 0 1em 1em; width:250px;"> <table> <tbody><tr> <td style="width:50px;"> </td> <td style="width:385px;"> <div class="mw-inputbox-centered" style=""><form name="searchbox" class="searchbox mw-inputbox-form" action="/wiki/Special:Search"><div class="cdx-text-input"><input class="mw-inputbox-input mw-searchInput searchboxInput cdx-text-input__input" name="search" placeholder="" size="13" dir="ltr" /></div><input type="hidden" value="Traditional Abacus and Bead Arithmetic/" name="prefix" /><br /><input type="submit" name="fulltext" value="Search this book" class="cdx-button" /><input type="hidden" value="Search" name="fulltext" /></form></div> </td></tr></tbody></table> </div> <ul><li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Introduction" title="Traditional Abacus and Bead Arithmetic/Introduction">Introduction</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Addition_and_subtraction" title="Traditional Abacus and Bead Arithmetic/Addition and subtraction">Addition and subtraction</a> <ul><li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="100% developed"><img alt="100% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/9px-100_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/14px-100_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/18px-100_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Addition_and_subtraction/Use_of_the_5th_lower_bead" title="Traditional Abacus and Bead Arithmetic/Addition and subtraction/Use of the 5th lower bead">Use of the 5th lower bead</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="100% developed"><img alt="100% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/9px-100_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/14px-100_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/18px-100_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Addition_and_subtraction/Extending_the_123456789_exercise" title="Traditional Abacus and Bead Arithmetic/Addition and subtraction/Extending the 123456789 exercise">Extending the 123456789 exercise</a></li></ul></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="50% developed"><img alt="50% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/9px-50_percents.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/14px-50_percents.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/18px-50_percents.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division" title="Traditional Abacus and Bead Arithmetic/Division">Division</a> <ul><li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Modern_and_traditional_division;_close_relatives" title="Traditional Abacus and Bead Arithmetic/Division/Modern and traditional division; close relatives">Modern and traditional division; close relatives</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Guide_to_traditional_division_(%E5%B8%B0%E9%99%A4%E6%B3%95)" title="Traditional Abacus and Bead Arithmetic/Division/Guide to traditional division (帰除法)">Guide to traditional division (帰除法)</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="100% developed"><img alt="100% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/9px-100_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/14px-100_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/18px-100_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Learning_the_division_table" title="Traditional Abacus and Bead Arithmetic/Division/Learning the division table">Learning the division table</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Dealing_with_overflow" title="Traditional Abacus and Bead Arithmetic/Division/Dealing with overflow">Dealing with overflow</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Traditional_division_examples" title="Traditional Abacus and Bead Arithmetic/Division/Traditional division examples">Traditional division examples</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="50% developed"><img alt="50% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/9px-50_percents.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/14px-50_percents.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/18px-50_percents.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Special_division_tables" title="Traditional Abacus and Bead Arithmetic/Division/Special division tables">Special division tables</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Division/Division_by_powers_of_two" title="Traditional Abacus and Bead Arithmetic/Division/Division by powers of two">Division by powers of two</a></li></ul></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="50% developed"><img alt="50% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/9px-50_percents.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/14px-50_percents.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/50_percents.svg/18px-50_percents.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Multiplication" title="Traditional Abacus and Bead Arithmetic/Multiplication">Multiplication</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Roots" title="Traditional Abacus and Bead Arithmetic/Roots">Roots</a> <ul><li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Roots/Square_root" title="Traditional Abacus and Bead Arithmetic/Roots/Square root">Square root</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Roots/Cube_root" title="Traditional Abacus and Bead Arithmetic/Roots/Cube root">Cube root</a></li></ul></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Appendix:_Abbreviated_operations" title="Traditional Abacus and Bead Arithmetic/Appendix: Abbreviated operations">Appendix: Abbreviated operations</a></li> <li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="75% developed"><img alt="75% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/9px-75_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/14px-75_percent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/75_percent.svg/18px-75_percent.svg.png 2x" data-file-width="9" data-file-height="9" /></a></span></span> <a href="/wiki/Traditional_Abacus_and_Bead_Arithmetic/Bibliography" title="Traditional Abacus and Bead Arithmetic/Bibliography">Bibliography</a></li></ul> <hr /> <ul><li><span class="noprint"><span typeof="mw:File"><a href="/wiki/Help:Development_stages" title="100% developed"><img alt="100% developed" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/100_percent.svg/9px-100_percent.svg.png" decoding="async" width="9" height="9" class="mw-file-element" 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