Shortcut-5

Shortcut of Multiplication by “9”

Let’s take an example.

1210112 * 9

Step – 1:

Take “0” on left hand side.

The result is:

“01210112”

Step-2:

Now, make pairs of 2 digits of “01210112” and at last write last digit again:

The pairs are:

“01” ... “12” ... “21” ... “10” ... “01” ... “11” ... “12” and the last digit is: “2”

For First pair:

“01”

Subtract “1” from right hand side.

Thus:

“01” = 1 -1 = 0

For middle pairs:

“12” ... “21” ... “10” ... “01” ... “11” ... “12”

Subtract left hand digit from “9” and add the result to right hand side digit:

Thus,

“12” = 9 – 1 = 8 + 2 = 10

“21” = 9 – 2 = 7 + 1 = 8

“10” = 9 – 1 = 8 + 0 = 8

“01” = 9 – 0 = 9 + 1 = 10

“11” = 9 – 1 = 8 + 1 = 9

“12” = 9 – 1 = 8 + 2 = 10

For the last digit: “2”

Subtract “2” from 10:

10 – 2 = 8

Now, write all the results:

(0) (10) (8) (8) (10) (9) (10) (8)

Take carries on left hand side:

(0) (10) (8) (8) (10) (10) (0) (8)

(0) (10) (8) (8) (11) (0) (0) (8)

(0) (10) (8) (9) (1) (0) (0) (8)

(1) (0) (8) (9) (1) (0) (0) (8)

Hence,

Answer is:

1210112 * 9 = 1089108

Lot of practice and examples are required as, you are using this shortcut first time.

Let’s take more examples:

879 * 9

Step – 1:

Take “0” on left hand side.

Result is:

“0879”

Step-2:

Make pairs of 2 digits of “0879” and write last digit “9” also.

We would get:

“08” ... “87” ... “79” ... “9”

For first pair:

Subtract “1” from “8”

8 – 1 = 7

Thus,

“08” = 7

For middle pairs:

Subtract left hand side digit from “9” and add the result to the right hand side digit:

Thus,

“87” = 9 – 8 = 1 + 7 = 8

“79” = 9 – 7 = 2 + 9 = 11

For the last digit: “9”

Subtract it from “10”.

Result is:

10 – 9 = 1

Write the results:

(7) (8) (11) (1)

Take carries on left hand side:

Hence the answer is:

(7) (9) (1) (1)

7911

58 * 9

Step – 1:

Take “0” on left hand side.

Result is:

“058”

Step – 2:

Make pairs of 2 digits of “058” and right “8” at the last.

Thus,

We get:

“05” ... “58” ... “8”

For first pair:

Subtract “1” from right hand digit.

Thus,

“05” = 5 – 1 = 4

For middle pair:

Subtract “9” from left hand digit and add the result to the right:

We would get:

“58” = 9 – 5 = 4 + 8 = 12

For last digit:

Subtract “8” from 10:

Thus,

We get:  

10 – 8 =2

Now,

Write all the results:

(4) (12) (2)

Take carries to the left hand side:

We would get:

(5) (2) (2)

Hence,

Answer is:

522