Pictures of the multiplication tables are as follows:

I. Brief description

1. The "Little Nine-Nine" mnemonic that elementary school children learn is from "a one to get a" start, to "9981", but in ancient times, it is the reverse, from "9981", to "two two to get four" stop. In ancient times, it was the other way around, starting from "9981" and ending at "2.2.4".

2. Because the first two words of the mnemonic are "九九", people shortened it to "小九九". Around the 13th and 14th centuries, it was reversed like this "a one to get a ...... nine nine eighty-one".

Two, from

1, China used the "nine nine recitation" time is relatively early. In the "Xunzi", "Guanzi", "Huainanzi", "Strategy of the Warring States" and other books can be found in the "thirty-nine twenty-seven", "sixty-eight forty-eight", "forty-eight thirty-two", "Sixty-six thirty-six" and so on. From this, we can see that the "Nine-Nine Multiplication Songs" had already become popular.

2, Ancient Greece, Ancient Egypt, Ancient India, Ancient Rome did not have a rounding system, in principle, the need for an infinite multiplication table, so it is not possible to have a table of ninety-nine. For example, the Greek multiplication table must list 7x8, 70x8, 700x8, 700x8, 7000x8 ....... By contrast, since the 9-9-9 table is based on the decimal system, 7x8=56, 70x8=560, 700x8=5600, 7000x8=56000.

3. Only one representation, 7x8=56, is needed. There were no multiplication tables in ancient Egypt. Archaeologists found that the ancient Egyptians were through the cumulative iterative addition method to calculate the product. For example, to calculate 5x13, first 13 + 13 to get 26, and then iteratively add 26 + 26 = 52, and then add 13 to get 65. Babylonian arithmetic has a system of rounding, a great improvement over Greece and several other countries.

Three, multiplication

Multiplication (multiplication), is a shortcut for adding identical numbers. The result of the operation is called a product, and "x" is the multiplication sign. Philosophically parsed, multiplication is the result of a quantitative change in addition leading to a qualitative change. Multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers is defined by a systematic generalization of this basic definition.