Multiplication by 12

The method is called “Doubling & then adding to the neighbor”

This rule has to be remembered whenever we multiply a number by 12.The right most digit has to be doubled and then right most neighboring digit has to be again added. This will be clear with an e.g.

234 x 12 = 2808

Put 0 in the beginning and at the end of number.
02340

• As the original no. is 234 so we start with 4 and not 0.

Double of 4 is 8
8 + 0 (0 is the first neighbor to it’s right) is 8
So the first digit of the answer at the unit place is 8.

• Next we take 3

Double of 3 is 6
6 + 4 is 10 (4 is the first neighbor to it’s right)
So the second digit of the answer is 0 (1 is carried over).

• Next we take 2

Double of 2 is 4
4 + 3 is 7 (3 is the first neighbor to it’s right)
So the third digit of the answer is 8 (7 + 1 (carried forward from the previous step ) = 8 )

• Next we take 0

Double of 0 is 0
0 + 2 is 2 (2 is the first neighbor to it’s right)
So the forth digit of the answer is 2

Therefore  234 x 12 = 2808

Time for you to try

Three digit Number Multiplied by 11

Whenever a three digit number or more is to be multiplied by 11, then apply the rule “Put 0 and add the neighbor”

Have fun with the trick

234 x 11 = 2574

Put 0 at the beginning and end of the number.
0 2 3 4 0

Now add the neighbor starting from right.
0 2 3 4 0
4 (0 + 4 = 4)

0 2 3 4 0
7 4 (4 + 3 = 7)

0 2 3 4 0
5 7 4 (3 + 2 = 5)

0 2 3 4 0
2 5 7 4 (2 + 0 = 2)

Answer 234 x 11 = 2574

Little Variation

578 x 11= 6358

Put 0 in the beginning and at the end of the number

0 5 7 8 0

Now add the neighbor starting from right

0 5 7 8 0
8 ( 0 + 8 )

0 5 7 8 0

158 (8 + 7= 15) (1 is carried to next digit to your right)

0 5 7 8 0

1358 (5 + 7 = 12) (1 carried from the previous step gets added to 12 which becomes 13. 1 of 13 is carried to next digit to your right)

0 5 7 8 0 x 11

6 3 5 8 (0 + 5 = 5) (1 carried from the previous step gets added to 5 which becomes 6)

Answer = 578 x 11 = 6358

Time for you to try

Two digit number multiplied by 11

Have fun with the trick

You can multiply a two digit number by 11 mentally. it is very easy once you know the trick. Consider a problem:

72 x 11 = ??

To solve this problem, simply add the digits, 7 and 2 and put the answer in between these two digits.

7 + 2 = 9

72 x 11 = 792

62 x 11 = ??

To solve this problem, simply add the digits, 6 and 2 and put the answer in between these two digits.

6 + 2 = 8

62 x 11 = 682

49 x 11 = ??

4  ₁3  9 = 539

In such a case, 3 of 13 goes in between 4 and 9 and 1 gets added to 4 to get 539 as the answer.

Time for you to try

Want to practice again?

This trick is used for multiplying numbers where the first digits add up to 10. Last digits are the same.

Just opposite to what we just practiced.

Have fun with the trick

34 x 74 = 2516
First digits here add up to 10 (3 and 7). Last digits are same.

So we just multiply 3 and 7 and add 4 (the last digit of the number) to get 25 first part of the answer.

3 x 7 = 21 + 4 = 25

And we multiply the last digits: 4 x 4 = 16 to get the last part of the answer.

Let’s try another one

65 x 45 = 2925

First digits here add up to 10 (6 and 4). Last digits are same.

So we just multiply 6 and 4 and add 5 (the last digit of the number) to get 29 for the first part of the answer.

6 x 4 = 24 + 5 = 29

And we multiply the last digits: 5 x 5 = 25 to get the last part of the answer.

Little Variation

81 x 21 = 1701

First digits here add up to 10 (8 and 2). Last digits are same.
So we just multiply 8 and 2 and add 1 (the last digit of the number) to get 17 for the first part of the answer.

8 x 2 = 16 + 1 = 17

And we multiply the last digits: 1 x 1 = 01 to get the last part of the answer.

Here we write 01, as the answer of last part should be a double digit number.

Time for you to try

This trick is used for multiplying numbers where the first digits are the same and the last digits add up to 10.

Let’s learn to multiply fast.

32 x 38 = 1216
Both numbers here start with 3 and the last
digits ( 2 and 8 ) add up to 10.

So we just multiply 3 and 4 (first digit + 1)
to get 12 for the first part of the answer.

And we multiply the last digits: 2 x 8 = 16 to
get the last part of the answer.

45 x 45 = 2025

Both numbers here start with 4 and the last
digits (5 + 5) add up to 10.

So we just multiply 4 and 5 (first digit + 1)
to get 20 for the first part of the answer.

And we multiply the last digits: 5 x 5 = 25 to get the last
part of the answer.

31 x 39 = 1209

Both numbers here start with 3 and the last digits (1 and 9) add up to 10.

So we just multiply 3 and 4 (first digit + 1) to get 12 for the first part of the answer.

And we multiply the last digits: 9 x 1 = 09 to get the last part of the answer. Here we write 09 as the answer, as the last part should be a double digit numbers.

Time for you to try