Chinese multiplication table

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The Tsinghua Bamboo Slips, containing the world's earliest decimal multiplication table, dated 305 BC during the Warring States period Qinghuajian, Suan Biao.jpg
The Tsinghua Bamboo Slips, containing the world's earliest decimal multiplication table, dated 305 BC during the Warring States period

The Chinese multiplication table is the first requisite for using the Rod calculus for carrying out multiplication, division, the extraction of square roots, and the solving of equations based on place value decimal notation. It was known in China as early as the Spring and Autumn period, and survived through the age of the abacus; pupils in elementary school today still must memorise it. [1]

Contents

The Chinese multiplication table consists of eighty-one terms. It was often called the nine-nine table, or simply nine-nine, because in ancient times, the nine nine table started with 9 × 9: [2] nine nines beget eighty-one, eight nines beget seventy-two ... seven nines beget sixty three, etc. two ones beget two. In the opinion of Wang Guowei, a noted scholar, the nine-nine table probably started with nine because of the "worship of nine" in ancient China; the emperor was considered the "nine five supremacy" in the Book of Change. See also Numbers in Chinese culture § Nine.

It is also known as nine-nine song (or poem), [2] as the table consists of eighty-one lines with four or five Chinese characters per lines; this thus created a constant metre and render the multiplication table as a poem. For example, 9 × 9 = 81 would be rendered as "九九八十一", or "nine nine eighty one", with the world for "begets" "得" implied. This makes it easy to learn by heart. [1] A shorter version of the table consists of only forty-five sentences, as terms such as "nine eights beget seventy-two" are identical to "eight nines beget seventy-two" so there is no need to learn them twice. When the abacus replaced the counting rods in the Ming dynasty, many authors[ who? ] on the abacus advocated the use of the full table instead of the shorter one. They claimed that memorising it without needing ag a moment of thinking makes abacus calculation much faster.[ citation needed ]

The existence of the Chinese multiplication table is evidence of an early positional decimal system: otherwise a much larger multiplication table would be needed with terms beyond 9×9.

The Nine-nine song text in Chinese

It can be read in either row-major or column-major order.

九九乘法口诀表 (The Nine-nine multiplication table)
1 一 yī2 二 èr3 三 sān4 四 sì5 五 wǔ6 六 liù7 七 qī8 八 bā9 九 jiǔ
1 一 yī一一得一
2 二 èr一二得二二二得四
3 三 sān一三得三二三得六三三得九
4 四 sì一四得四二四得八三四十二四四十六
5 五 wǔ一五得五二五一十三五十五四五二十五五二十五
6 六 liù一六得六二六十二三六十八四六二十四五六三十六六三十六
7 七 qī一七得七二七十四三七二十一四七二十八五七三十五六七四十二七七四十九
8 八 bā一八得八二八十六三八二十四四八三十二五八四十六八四十八七八五十六八八六十四
9 九 jiǔ一九得九二九十八三九二十七四九三十六五九四十五六九五十四七九六十三八九七十二九九八十一
Nine-nine multiplication table
1 One yī2 Two èr3 Three sān4 Four sì5 Five wǔ6 Six liù7 Seven qī8 Eight bā9 Nine jiǔ
1 One yīOne times one equals one
2 Two èrOne times two equals twoTwo times two equals four
3 Three sānOne times three equals threeTwo times three equals sixThree times three equals nine
4 Four sìOne times four equals fourTwo times four equals eightThree times four equals twelveFour times four equals sixteen
5 Five wǔOne times five equals fiveTwo times five equals tenThree times five equals fifteenFour times five equals twentyFive times five equals twenty-five
6 Six liùOne times six equals sixTwo times six equals twelveThree times six equals eighteenFour times six equals twenty-fourFive times six equals thirtySix times six equals thirty-six
7 Seven qīOne times seven equals sevenTwo times seven equals fourteenThree times seven equals twenty-oneFour times seven equals twenty-eightFive times seven equals thirty-fiveSix times seven equals forty-twoSeven times seven equals forty-nine
8 Eight bāOne times eight equals eightTwo times eight equals sixteenThree times eight equals twenty-fourFour times eight equals thirty-twoFive times eight equals fortySix times eight equals forty-eightSeven times eight equals fifty-sixEight times eight equals sixty-four
9 Nine jiǔOne times nine equals nineTwo times nine equals eighteenThree times nine equals twenty-sevenFour times nine equals thirty-sixFive times nine equals forty-fiveSix times nine equals fifty-fourSeven times nine equals sixty-threeEight times nine equals seventy-twoNine times nine equals eighty-one

The Nine-nine table in Chinese literature

Nine nine song in Ming dynasty Cheng Dawei Suanfa tongzong Volume II Ming suanpan.JPG
Nine nine song in Ming dynasty Cheng Dawei Suanfa tongzong Volume II

Many Chinese classics make reference to the nine-nine table:

Archeological artifacts

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References

  1. 1 2 Prado, Jerome; Lu, Jiayan; Dong, Xi; Zhou, Xinlin; Booth, James R (May 2013). "The neural bases of the multiplication problem-size effect across countries". Frontiers in Human Neuroscience. 7: 52. doi: 10.3389/fnhum.2013.00189 . ISBN   9782889198160. PMC   3651960 . PMID   23717274 . Retrieved 12 April 2019.
  2. 1 2 3 Lam Lay Yong; Ang Tian Se (2004). Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in ancient China. World Scientific. pp. 73–77. ISBN   9789814483605.