Multiplication by 11

Multiplication by 11 with a 2 digit number:

Simply add both the digits of the multiplicand and insert the result in between both the digits.

Example 1: 72 x 11 = (7) (7+2) (2) = 7 9 2.

Multiplication by 11 where multiplicand has more than 2 digits:

1. Prefix a zero to the multiplicand.

2. Write down the right most digit as it is as the unit's place of the answer.

3. Starting from the right, make pairs and add them to get a quick answer.

Example 2: 3214 x 11 = 03214 x 11 

                                  =  (3+0) (2+3) (1+2) (4+1) (4) = 3 5 3 5 4.

Example 3: 257 x 11 = 0257 x 11 

                                = (2+0) ((5+2) + 1 --> Carry) (7+5 = 12, Write 2, Carry 1) (7) = 2 8 2 7.

Example 4: 17.38 x 11 (Decimal = Before 2 digits from right)

Follow the same procedure, lastly place the decimal.

= 017.38 x 11

= (1+0) ((7+1) +1) ((3+7) + 1 =11, Write 1, Carry 1) (8+3 = 11, Write 1, Carry 1) (8)

= 1 9 1 . 1 8

Example 5: 49.39 x 110 (Decimal = Before 1 digit from right)

Same Procedure, Just the decimal will shift one place to the right as its multiplied by 110

= 049.39 x 11

= ((4+0) +1 = 5) ((9+4) +1 = 14, Write 4, Carry 1) ((3+9) +1 = 13, Write 3, Carry 1) (9+3 =12, Write 2, Carry 1) (9)

= 5 4 3 2 . 9

Example 6: 2432 x 0.011 (Decimal = Before 3 digits from right)

= 02432 x 0.011

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

= 2 6 . 7 5 2

Example 7: 57.4 x 0.0011 (Decimal = Before 5 digits from right)

= 057.4 x 0.011

= ((5+0) +1 = 6) ((7+5) +1 = 13, Write 3, Carry 1) (4+7 = 11, Write 1, Carry 1) (4)

= 0 . 0 6 3 1 4 

Example 8: 220 x 12

Does this trick help in 220 x 12 ? - Yes ! Let's see how to use this trick when we have multiples of 11 ...

220 x 12 can be written as:

= ((2 x 11) x 10) x 12

The above can be rearranged to:

= ((12 x 2) x 10) x 11

= 240 x 11

= 0240 x 11 (Applied the same trick again) ... :-)

= (2+0) (4+2) (0+4) (0)

= 2 6 4 0.

Example 9: 2123 x 220

= 2123 x ((2 x 11) x 10) --- Used multiple of 11

= ((2123 x 2) x 10) x 11 --- Re-arranged

= 42460 x 11

= 042460 x 11 --- Applied the same trick again

= (4+0) (2+4) ((4+2) + 1 = 7) (6+4 = 10, Write 0, Carry 1) (0+6) (0)

= 4 6 7 0 6 0

Example 10: 141 x 330 

= 141 x ((3 x 11) x 10) --- Used multiple of 11

= ((141 x 3) x 10) x 11 --- Re-arranged

= 4230 x 11

= 04230 x 11 --- Applied the same trick again

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

= 4 6 5 3 0

Example 11: 225 x 44

= 225 x (4 x 11) --- Used multiple of 11

= (225 x 4) x 11 --- Re-arranged

= 900 x 11

= 0900 x 11 --- Applied the same trick again

=  (9+0) (0+9) (0+0) (0)

= 9 9 0 0

Example 12: 32.8 x 5.5 (Decimal = Before 2 digits from right)

= 328 x (5 x 11) --- Used multiple of 11, Ignored Decimals

= (328 x 5) x 11 --- Re-arranged

= 1640 x 11

= 01640 x 11 --- Applied the same trick again

= (1+0) ((6+1) + 1 = 8) (4+6 = 10, Write 0, Carry 1) (0+4) (0)

= 1 8 0 . 4 0

= 180.4

Example 13: 1.82 x 2200 (Decimal = Before 2 digits from right)

= 182 x ((2 x 11) x 100) --- Used multiple of 11, Ignored Decimal

= (182 x 2) x 100) x 11 --- Re-arranged

= 36400 x 11

= 036400 x 11 --- Applied the same trick again

= ((3+0) +1) ((6+3) +1 - 10, Write 0, Carry 1) (4+6 = 10, Write 0, Carry 1) (0+4) (0+0) (0)

= 4 0 0 4 . 0 0

= 4004

Well to understand this method, you may have to read this whole page of explanation but while solving, it won't take much time. It is much faster than the conventional method... Happy Learning! .. :)