Fraction operation in ancient China, how to represent fractions in ancient China

1. Two ways to express fractions in ancient China:

1. Chinese character notation.

In China, fractions have been used for a long time, and the world's earliest study of fractions appeared in the Nine Chapters of Arithmetic, in which fractions and their operations were systematically discussed. ("Nine Chapters of Arithmetic" "Fang Tian" and chapter "Da Guangtian Shu" point out: "Denominator.")

Multiply the rest, and the molecule follows. This formally gives the concept of denominator and numerator.

And one of the counting methods specifically mentioned is the kanji notation"....Divide it....”。

2. Calculation and notation.

When calculating division with arithmetic, the quotient is above, real (i.e., the dividend.

The column is in the middle, and the method (i.e., the divisor) is below, and when the whole division is completed, there may be a surplus in the middle, as shown in the figure, which represents the fraction. In the third century AD, the Chinese used this notation to represent fractions.

2. Introduction to the score.

Fractions (from Latin.

Broken") represents a part of the whole, or more generally, any part of an equal number. The fraction is an integer a and a positive integer.

b is not equal to the ratio of integers.

A fraction indicates that a number is a fraction of another number, or the ratio of one event to all events. Dividing the unit "1" into several equal parts, indicating that the comma number of such a part or several parts is called a fraction. The numerator is on top and the denominator is on the bottom.

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The method of expressing fractions in ancient countries.

In fact, fractions have been produced for a long time, and the cultures of various ancient civilizations also record the knowledge of fractions. The ancient Egyptians and Babylonians also had fraction marks, while the ancient Greeks used l"Indicates , for example: l"=1， βl"=2, and l"= 3 etc.

Adding a dot to the upper right corner of a number means 'one of the number.

Ancient India. The notation of human fractions is very similar to that of Chinese arithmetic, for example. In the 12th century AD, Arabia.

Renheiser was the first to use the score line. He has since said. And Fibonacci.

He was the first to introduce the score line to Europe.

It was not until the 15th century that the modern fractional algorithm was gradually formed. In 1530, the German Rudolf calculated + in the form of a fraction that was gradually adopted later.

In 1845, in one of his essays, The Calculus of Functions, he proposed a slash to represent the fractional line. Because the fraction is represented by a b, which is conducive to typographic layout, some printed books now also use this kind of slash score notation.

1. Two ways to express fractions in ancient China:

1. Chinese character notation.

In China, fractions have been used for a long time, and the world's earliest study of fractions appeared in the "Nine Chapters of Early Arithmetic", in which fractions and their operations were systematically discussed. ("Nine Chapters of Arithmetic" "Fang Tian" and chapter "Da Guangtian Shu" point out: "The denominator is multiplied by the rest, and the numerator follows it.")

This formally gives the concept of denominator and numerator.

And one of the counting methods specifically mentioned is the kanji notation"....Divide it....”。

2. Calculation and notation.

When calculating division with arithmetic, where the quotient is above, real (i.e., the dividend) is listed in the middle, and the method (i.e., the divisor) is below, when the whole division is completed, there may be a surplus in the middle, as shown in the figure, which represents the fraction. In the third century AD, the Chinese used this notation to represent fractions.

2. Introduction to the score.

Fractions (from Latin, "broken") represent a part of a whole, or more generally, any part of an equal number. The fraction is the ratio of an integer a to a positive integer b that is not equal to the integer.

A fraction represents a fraction of a number that is another number, or the ratio of an event to all the events that are carried by the Know. The unit "1" is divided into several parts, and the number of such parts or parts is called a fraction. The numerator is on top and the denominator is on the bottom.

There are many ways to express fractions in ancient Chinese, the main ones are:

1. "Denominator + Fraction + + Numerator". For example, "Historical Records and Biography of Goods and Colonies": "Therefore, the land in the middle of the pass is one-third of the world." ”

2. "Denominator + Minute + Noun + + Numerator". For example, "Historical Records: The Biography of the King of Hengshan in Huainan": "The soldiers of the king of Fangjin cannot be one of Wu Chu." ”

3. "Denominator + noun + of + numerator". For example, "Zuo Chuan Yin Gong Gong": "The system of the first king, most of them are only one of the participating countries. ”

4. "Denominator + + numerator". For example, "Zuo Chuan Yin Gong Gong": "Most of them are only one of the participating countries; Form 5 1, Primary 9 1. ”

5. "Denominator + Minute + Numerator". For example, in the "Book of Historical Records": "The son is one point, the ugly is three points two, the Yin is nine points eight, and the Mao is twenty-seven points sixteen." ”

6. "Denominator + numerator". For example, "Historical Records of the Huns": "It will be cold, and the soldiers will fall into the finger two or three out of ten."

1. Indicates multiplication. k

Old Chinese. , the multiple expression is generally in the cardinal number word.

After adding the word "times", if it is a double finch, it is only represented by "times", and "one" is omitted. For example, "Therefore, the law of using soldiers, ten rules surround it."

Five will attack, the double will be divided, the enemy will be able to fight, the less can escape, if not, it can be avoided. Among them, the word "times" after "ten" and "five" is omitted; "Times" means "double". (ffmf?

In ancient Chinese, if there are two parallel numbers, then they are counted by their products. Such as "on the night of the third and fifth day, the bright moon is half a wall." (Xiang Zhixuan Zhi).

The product of "35" is 15, and "35 night" refers to the night of the full moon on the fifteenth day of the lunar month. Similarly, "Twenty-Eight", "Twenty-Eight" is the age of sixteen years old. 3a

Second, it means that the pretense is removed. my)

Most of the expressions of scores in ancient Chinese appear in the context of table comparison, and they are summarized in combination with the context, and there are the following types. %ylk2

a) Completion type. Such as "Qindi, the world is three."

One in one. The fractional form of "one part of three hectares missing" has been preserved since ancient times. x#*q

ii) Abbreviation. Such as "cover to go, than the good traveler can not eleven." (You Bao Zen Mountain.)

"Ten" is the denominator.

"One" is the numerator, and "eleven" is one-tenth. bx`

iii) Embedded. 1. "Denominator + Fraction + + Numerator". For example, "The crowd of the kings of Fang Jin cannot be one of the very Wu Chu."

Historical Records: The Biography of the King of Hengshan in Huainan) "can't be 'tenth' of Wu Chu'", that is, less than one-tenth of Wu Chu. (2) The denominator of the noun "of" numerator. For example, "Dadu is only one of the Three Kingdoms" ("Zuo Chuan: Yin Gong Gong") and "one of the Three Kingdoms", that is, one-third of the national capital.

3) The numerator of the denominator "of". For example, "However, only 12 out of 10 people are unfortunate by floods, droughts, diseases, and epidemics." "12 out of 10", that is, "1/10" to "2/10".

The ancients had brains to calculate!