Squaring 15, 25, 35, ..., 95

To square a two digit number ending in 5; i.e. 15, 25, 35, ..., 95, first multiply the tens digit by the next whole number and then affix 25 to it.

Example 1:

To square 15 (15^2):

The tens digit of 15 is 1 and the next whole number of 1 is 2. So:
1 * 2 = 2
Now, we affix 25 to 2. The answer is 225.


Example 2:

To square 35 (35^2):

The tens digit of 35 is 3 and the next whole number of 3 is 4. So:
3 * 4 = 12
Now, we affix 25 to 12. The answer is 1225.


Example 3:

To square 95 (95^2):

The tens digit of 95 is 9 and the next whole number of 9 is 10. So:
9 * 10 = 90
Now, we affix 25 to 90. The answer is 9025.

Multiplying by 5, 10, and 15

Multiplying By Five

Multiplying by 5 is just multiplying by 10 and then dividing by 2. Example:

15 * 5 = (15 * 10) / 2 = 150 / 2 = 75


Multiplying By Ten

Everybody knows that to multiply by 10, a zero should be added to the end of the number. Example:

26 * 10 = 260


Multiplying By Fifteen

To multiply by 15, you can use one of these two methods:

1) Multiply by 5 then then add it up with the product of the number and 10. Example:

43 * 15 = (43 * 5) + (43 * 10) = (43 * 10 / 2) + 430 = 215 + 430 = 645

In other words, add half of the product of the number and 10 to the product of the number and 10; i.e.:

43 * 15 = 430 + (1/2 * 430) = 645

2) Multiply by 30 and then divide by 2 (in the next post, a method is presented for "Multiply by 30"). Example:

57 * 15 = (57 * 30) / 2 = 1710 / 2 = 855