It is impossible to prove when and by whom the abacus was invented. But its use should be very early. Mathematicians in the Eastern Han Dynasty, the legacy of mathematical art, said: "abacus controls the four seasons, and latitude and longitude are three talents." In the Northern Zhou Dynasty, Zhen Luan wrote: "stereotyped writing is three points. There are five beads in each position, and the upper bead is different from the lower four beads. There are five beads with different colors on the top and one on the bottom. " It can be seen that there were abacus in Han dynasty, but its shape was different from today. But as in modern times, one bead above the central beam is five, and each bead below the central beam is one. According to Xu Yue, his teacher, Liu Hong, once asked Mr. Tianmu, a Taoist priest. Mr. Tianmu taught the method of abacus, which shows that abacus appeared in the Eastern Han Dynasty at the latest. Some historians believe that the name of abacus first appeared in the Collected Works of Mr. Jing Xiu written by Liu Yin in Yuan Dynasty (1249- 1293). In Yuan Qu Xuan, the anonymous "Pang Juquan paid off his debts in his next life by mistake" also mentioned the abacus. There is a saying in the play: "Idle hands, go to that abacus and pull out my age." In A.D. 1274, Yang Hui recorded the nine-point method of abacus calculation in his book Multiplication and Division into Treasure, and Zhu Shijie recorded the nine-point method of abacus calculation in his book Arithmetic Enlightenment in 1299. In A.D. 1450, Jason Wu described the usage of abacus in detail in Detailed Notes on Analogy in Chapter 9. Zhang Zeduan drew an abacus in The Riverside Scene at Qingming Festival, which shows that abacus was widely used in China as early as the Northern Song Dynasty.

China's abacus evolved from the ancient "calculation". "Calculation" is to use a bamboo stick as a bargaining chip. The multiplication and division method was improved at the end of the Tang Dynasty, and the formula for calculating division was produced in the Song Dynasty. /kloc-In the middle of the 5th century, Luban Mu Jing had a standard for making abacus. Due to the popularity of abacus, books on abacus came into being. The most popular book of abacus calculation is "Arithmetic Unity" compiled by Cheng Dawei in Ming Dynasty on 1593. Because the abacus formula is easy to remember and calculate, it is widely used in China, and also spread to Japan, Korea, India, the United States, Southeast Asia and other countries and regions. The appearance of abacus, known as a major reform of calculators in human history, still plays its unique role today with the popularization of electronic calculators.

[abacus addition and subtraction]

Abacus addition and subtraction should be aimed at the number of digits, from the high place.

The formula of abacus addition and subtraction is as follows:

Abacus addition formula table

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Abacus subtraction formula table

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The first number in the formula indicates the number to be added (or subtracted), and the following "previous", "previous", "last five", "last one" and "advance one" indicate the plucking action and the number of strokes.

Abacus addition and subtraction can also be done without formulas. Abacus addition and subtraction without formulas are generally divided into three categories.

(1) direct addition and direct subtraction. It's this stall where the number of beads is enough, just add it, and if it's enough, just subtract it. For example, 2+6 and 7-5.

(2) Five plus five breaks, that is, when the beads in this file are not enough to add or subtract, you need to add beads. Together, the beads are dialed by the method of "adding five and subtracting more". The subtraction method adopts the method of "adding more and subtracting five", such as 4+3=4+5-2, 7-4=7+ 1-5.

(3) carry or abdicate. In other words, if this file is not enough to add or subtract, it needs to be carried or abdicated.

Add ten, add, subtract ten. For example, 4+8=4-2+ 10,12-8 =12-10+2.

Abacus addition and subtraction, you can teach addition first, then subtraction; You can also add and subtract. In teaching, (1) you should explain the principle and method of pearl picking clearly. (2) You should guide students to pick pearls according to the rules, and don't change the numbers after oral calculation. If you teach five plus or five minus, you should think of two as soon as you see the addition of three. Pearl picking is "five times and two times". Listening and counting should be used first in abacus practice.

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