Get one by one; One two gets two, two two gets four; One three gets three, two three gets six, and three three gets nine; 14 is 4, 24 is 8, 34 12, 446; 15 is five, 25 10, 35 15, 4520, 5525; 16 got 6,262,368,4624,5630,6636;
17 got seven, 274,3721,4728,5735,6742,7749; 18 got 8,286,3824,4832,5840,6848,785168864;
1999, 298, 3927, 4936, 594 15, 6954, 796 13, 8972, 998 1.
Expand knowledge:
The origin of 99 multiplication table
China used the "99 formula" earlier. Sentences such as "3927", "684 18", "483 12" and "6636" can be found in books such as Xunzi, Guanzi, Huainanzi and Warring States Policy. It can be seen that "99 Multiplication Song" has already become popular.
Ancient Greece, ancient Egypt, ancient India, and ancient Rome did not have a carry system. In principle, they needed infinite multiplication tables, and it was impossible to have nine tables. For example, the Greek multiplication table must list 7x8, 70x8, 700 x8, 700x8, 700x8, 700x8, 700x8, 7000x8.
In contrast, because the 999 table is decimal, 7x8=56, 70x8=560, 700x8 = 5600；; 7000x8=56000, only 7x8=56 represents a project. There was no multiplication table in ancient Egypt. Archaeologists found that the ancient Egyptians used iterative addition to calculate the product.
For example, to calculate 5x 13, first get 26 from 13+ 13, then add 26+26=52, and then add 13 to get 65. Babylonian arithmetic had a carry system, which made great progress than Greece and other countries. However, Babylonian arithmetic used a hexadecimal system. In principle, a multiplication table of "59x59" needs 59*60/2= 1770 items;
Because the "59x59" multiplication table is too large, the Babylonians never used a "multiplication table" similar to the Jiujiu table. Archaeologists have never found the multiplication table of "59x59" similar to Jiujiu Table. But archaeologists found that Babylonians used only 1x 1 = 1, 2x2 = 4, 3x3 = 9...7x7 = 49, ... 9x9 = 81...16x/kloc.
To calculate the product of two numbers A and B, the Babylonians relied on their best algebra, axb=((a+b)x(a+b)-axa-bxb)/2. Such as 7x9 = ((7+9) x (7+9)-7x7-9x9)/2 = (256-49-81)/2 =126/2 = 63. The ancient Mayans used the decimal system, which is the closest to the decimal system commonly used in the modern world.
A multiplication table of 19x 19 has 190, which is more than three times larger than the 45 items in the Jiujiu table, but much simpler than the Babylonian method. But archaeologists haven't found any Mayan multiplication tables yet. Multiplication by multiplication table is not the inevitable result of carry system.
Babylon had the carry system, but they didn't invent or use the multiplication table in the form of 99 tables, but invented the square table method to calculate the products. The Mayans' mathematics was the most advanced in the ancient civilization in the Western Hemisphere, and they used the decimal system, but they didn't invent the multiplication table. It can be seen that there has been a lot of progress from the carry system to the multiplication table.
China not only invented the decimal system, but also invented the Jiujiu Watch during the Spring and Autumn Period and the Warring States Period. Later, the East was introduced to Korea and Japan, and then spread to India and Persia in the west through the Silk Road, which became popular all over the world. Decimal system and nine tables are important contributions of ancient China to world culture. Nowadays, countries around the world rarely use multiplication in Greece and other countries.