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I found another technique of multiplying numbers which respect the following conditions:
- have the same number of digits
- the first digit of both numbers is equal
- the sum of last digit of both numbers is 10
Example for applicable numbers could be: 56 x 54, 21 x 29, 37 x 33, 112 x 118, etc.
The algorithm:
56 x 54:
- the next ordinal number that comes after that 5 is 6; so we multiply 5×6 = 30, so we got the first two digits of our product
- the last step is to multiply the units numbers, I mean: 6 x 4 which is 24; so 24 is the last two digits of our product
This mean that 56 x 54 = 3024.
Another example:
21 x 29:
- the next ordinal number that comes after that 2 is 3; so we multiply 2×3 = 6, so we got the first two digits of our product
- the last step is to multiply the units numbers, I mean: 1 x 9 which is 9; because is small than 10 we write down 09 instead of 9
This mean that 21 x 29 = 609.
Another example:
112 x 118:
- the next ordinal number that comes after that 11 is 12; so we multiply 12×11 = 132, so we got the first two digits of our product
- the last step is to multiply the units numbers, I mean: 2 x 8 which is 16
This mean that 112 x 118 = 13216.
When the above conditions are not meet you can still use the other method explained here and here.
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