Instant multiplication

Some tricks of abbreviated calculations know very useful. In addition, these techniques are often curious in and of themselves. Therefore, I consider it a good idea to introduce Habr readers to them.

so…

Multiplication by 15

Any, especially a small number (well, for example, not more than 200), you can easily learn to multiply by 15 almost instantly.
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To do this, take half of the multiplicand, add to the multiplied number and add 0 to the sum (i.e., multiply it by 10).

For example:
38 * 15 = 570 (since 38 + 19 = 57)
164 * 15 = 2460 (because 164 + 82 = 246)

In these examples, even numbers were taken for multiplication.

If by 15 you have to multiply an odd number, then you need to use the same rule, but at the end you should not attribute 0, but the number 5.

For example:
43 * 15 = 645 (because 43 + 21 = 64)
157 * 15 = 2355 (since 157 + 78 = 235)

Note: An odd number, of course, cannot be divided by 2 without a residue. Therefore, the remainder of the division should be discarded. Thus, half of the number 43 should be considered 21, half of the number 157 should be considered 78 and so on.

Multiplying a two-digit number by 11

To do this, it is only necessary to add the digits of this number and insert the sum between the digits of the given two-digit number.
For example, you need 54 times 11; 5 + 4 = 9, therefore 54 * 11 = 594.

Another example: 85 * 11 = 935, because 8 + 5 = 13 = 10 + 3 (in this case it is necessary to add 1 to 8).

The multiplication of a two-digit number that ends in 5, on itself

To do this, you need to multiply the number of tens by a digit, which is 1 more, and then add to the product 25.

For example:
35 * 35 = 1225 (since 3 * 4 = 12 and 25 are attributed to this number)

The multiplication of numbers whose tens digits are the same (43 and 47), and the digits of the units add up to 10

To do this, you need to multiply the number of tens by a number that is 1 more, and assign the product of the number of units to the resulting product.

For example:
It is required to multiply 53 by 57. Multiply by 5 by 6 we get 30 and in this number we assign the product 3 * 7 = 21, so 53 * 57 = 3021.

One more example:
81 * 89 = 7209 (since 8 * 9 = 72 and 1 * 9 = 09, here pay attention to the fact that if a one-digit number is obtained by multiplying the digits of the units, then you should put 0 in front of it)

The multiplication of a three-digit number, the average digit of which is 0 (507, 605), by itself

So let's start right away with an example:
507 * 507 = 257049; Considering the product 25 70 49, it is not difficult to notice that

• 25 = 5 * 5 (i.e. the first digit of our number, multiplied by itself);
• 49 = 7 * 7 (i.e. the last digit of our number, multiplied by itself);
• 70 = (5 * 7) * 2 (i.e., the two middle digits of the work represent the double product of the extreme digits of a given number)

Note that if you have the middle part of the work in the form of a three-digit number, then the number of hundreds should be added to the first part of the work;

For example:
807 * 807 = (64 + 1) 12 49 (8 * 8 = 64; 8 * 7 * 2 = 112; 7 * 7 = 49), the final product is 651249.

This material was taken from the newspaper "For Children and Youth" from 1914.