# Speed Multiplying by 21, 31, 41 and so on

There are times when the multiplication algorithm gives you some shortcut multiplications if you just inspect what you are doing. Here is a neat little multiplication shortcut to perform various multiplications with the numbers 21, 31, 41, 51 and so on.

To multiply by 21: Double the number, append a ‘0’ after that and add the original number.

For example: To multiply 37 by 21,

Double 37 yields 74, append a 0 to get 740; and then add the original number 37 to get 777.

To multiply by 31: Triple the number, attach a ‘0’ after that and add the original number.

For example: To multiply 43 by 31,

Triple 43 yields 129, attach a 0 to get 1,290; and then add the original number 43 to get 1,333.

To multiply by 41: Quadruple the number, put a ‘0’ after that and add the original number.

For example: To multiply 47 by 41,

Quadruple 47 yields 188, put a 0 to get 1,880; and then add the original number 47 to get 1,927.

Extend the rule further to other numbers.

If the multiplicand is a big one and to multiply mentally follow the below method:

Multiplying by 21

Rule: The units (right) digit of the answer is the units digit of the given number. The tens (2nd from right) digit of the answer will be twice the units digit plus the 2nd -right digit of the given number. The 3rd-right digit of the answer will be twice the second digit plus the 3rd-right digit of the given number. Continue the process for the rest of digits of the given number. For the leftmost digit(s) of the answer simply double the leftmost digit of the given number. Whenever a sum is a two-digit number, record its units digit and add the tens digit to the left answer digit.

This rule is very much like the one for multiplying by 11. In fact, since 21 is the sum of 11 and 10, it does belong to the same family of short cuts.

As an example, we shall multiply 5,392 by 21.

The unit’s digit of the answer is the unit’s digit of the given number, 2.

The tens digit of the answer is obtained by adding the tens digit of the given number to twice the units digit of the given number.
(2 x 2) + 9 = 13

Record the 3; carry the 1 to the left.

The next digit is obtained by adding 3 to twice 9 plus carried 1.
(2 x 9) + 3 + 1 = 22

Record the 2 and carry the 2 to the left.

Next, add the first digit of the given number, 5, to twice the second digit, 3 plus carried 2.
(2 x 3) + 5 + 2 = 13

Record the 3 and carry the 1 to the left.

The leftmost digit(s) of the answer will be equal to twice the first digit of the given number plus carried 1.

(5 x 2) + 1 = 11. The product is therefore, 5,392 x 21 = 113,232

Extend the rule further to other numbers i.e. 31, 41, 51 and so on.