Chapter 10 Chapter 3 Arithmetic Operations

The nine-nine table is used for multiplication and division. Both "Guanzi" and Liu Hui talked about Fuxi's ninety-nine skills.The Art of Ninety-Nine is Ninety-Nine Table, which was also extended as a synonym for mathematics during the Tang and Song Dynasties.The ancient nine-nine table started from "nine nine eighty-one" to "two two as four", hence the name.Classics such as "Lushi Chunqiu" at the end of the Warring States period and "Hanshiwaizhuan" at the beginning of the Han Dynasty also recorded the story of Duke Huan of Qi setting up a court to recruit talents. It can be seen that the ninety-nine table was common sense at that time.

As early as the pre-Qin period, people were familiar with the rules of multiplication and division.According to "Sun Tzu's Suan Jing" records, two numbers are multiplied together to make three lines of calculations.Up and down are the multiplication numbers, and the middle is the product.Move the lower number to the left so that the last digit of the lower number is aligned with the first digit of the upper number, and the first digit of the upper number is multiplied by the numbers in the lower row from left to right, and put into the middle row after being added.Remove the first digit in the upper row, move the lower digit to the right by one digit, multiply the digits in the lower row from left to right, add the digits in the middle row, and so on, to get the product.

Division is the inverse operation of multiplication.The dividend is called real, placed in the middle row, the divisor is called dharma, and in the lower row, the process of division is called "real as dharma and one". "Reality" comes from the real things that are divided, and the law means the standard and the standard. The meaning of this sentence is: if there is a number equal to the law in the reality, then there is one. .Make the first place of law and reality equal (if the part that is aligned with the law is less than the law, then move the law to the right by one), discuss the first place of the quotient, put it in the upper row, multiply the numbers from left to right, and then subtract the real.Then move the law to the right by one place, and then discuss the next place, repeat the above steps until the law and the real place are aligned.If the truth is not exhaustive, we will name a fraction with the remainder as the numerator and the law as the denominator.