This article is posted by reader Ankit Mundra

Multiplication by 12:

Rule: “double each number and add it to its neighbor”

Eg:

4452 x 12 = 04452 x 12

“Double rightmost digit and add it to its previous neighbor”

So, double of 2 =4 no carry

double of 5=10 +2(neighbor)+0(carry)=12 ,carry =1

double of 4+5(neighbor)+1(carry)=14 ,carry 1

double of 4+4(neighbor)+1(carry)=13, carry 1

double of 0+4(neighbor)+1(carry)=5, carry 0

so, answer = 53424

0 4 4 5 2

x 1 2

5*3*4*2 4

*= carry

Multiplication by 11:

Rule:” Add the neighbor to the digit”

Eg:

7859 x 11 = 07859 x 11

0 7 8 5 9

X 1 1

9 (9 is copied as it is as no digit to add on right)

0 7 8 5 9

X 1 1

*49 (5+9=14)

0 7 8 5 9

X 1 1

*4*4 9 (8+5+1(carry)=14)

 

0 7 8 5 9

X 1 1

*6*4*4 9 (7+8+1=16)

0 7 8 5 9

X 1 1

8*6*4*4 9 (7+1=8)

Multiplication by 10:

Rule : “just append the number by 0”

Eg: 2345 x 10 = 23450

Multiplication by 9:

Rule 1: subtract rightmost from 10

Rule 2: subtract other digit from 9 and add neighbor

Rule 3: copy leftmost digit -1 as most significant digit

Eg:

0789 x 9

0 7 8 9

x 9

1 (10-9=1)

0 7 8 9

x 9

*0 1 (9-8+9(neighbor)=10)

0 7 8 9

x 9

*1*0 1 (9-7+8(neighbor)+1(carry)=11)

0 7 8 9

x 9

7*1*0 1 (7-1+1(carry)=7)

Multiplication by 8:

Rule 1: subtract rightmost from 10 and double

Rule 2: subtract other digit from 9 and double and add neighbor

Rule 3: copy leftmost digit -2 as most significant digit

Eg:

0789 x 8

0 7 8 9

x 8

2 ((10-9)*2=2)

0 7 8 9

x 8

*1 2 ((9-8)*2+9(neighbor)=11)

0 7 8 9

x 8

*3*1 2 ((9-7)*2+8(neighbor)+1(carry)=13)

0 7 8 9

x 8

6*3*1 2 (7-2+1(carry)=7)

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Multiplication by 7:

Rule : “Double the number add half neighbor and add 5 if number is odd”

0687 x 7

7 is odd = 2*7+5=19 , carry 1

8 is even=2*8+3(7/2)+1=20, carry 2

6 is even=2*6+4+2=18,carry 1

Now , just add half of 6 i.e. 3 + carry=4

Answer: 4809

Multiplication by 6:

Rule : “to each number add half neighbor and add 5 if number is odd”

0687 x 6

7 is odd = 7+5=12 , carry 1

8 is even=8+3(7/2)+1=12, carry 1

6 is even=6+4+1=11,carry 1

Now , just add half of 6 i.e. 3 + carry=4

Answer: 4122

Multiplication by 5:

Rule: “half neighbor and add 5 if number is odd”

0687 x 5

7 is odd = 0(no neighbor)+5=5 , carry 0

8 is even=3(7/2)+0=3, carry 0

6 is even=4+0=4,carry

Now, just take half of neighbor (that is 6) = 3

Answer: 3435

Others are easy and you can verify the rules:

Multiplication by 4:

Rule 1: subtract rightmost from 10 and add 5 if digit is odd

Rule 2: subtract other digit from 9 and add half of neighbor and add 5 if digit is odd

Rule 3: half of leftmost digit -1 as most significant digit

Multiplication by 3:

Rule 1: subtract rightmost from 10 and double it, add 5 if digit is odd

Rule 2: subtract other digit from 9 and double it, then add half of neighbor and add 5 if digit is odd

Rule 3: half of leftmost digit -2 as most significant digit

Multiplication by 2:

Rule: “Double each number without using neighbor at all”

0786 x 2 = __*2

0786 x 2 = _*72

0786 x 2 = *572

0786 x 2 = 1572

Multiplication by 1:

Rule: “Copy as it is”

Multiplication by 0:

Rule: “Answer is zero”

By Ankit Mundra (OxyGyan Reader)

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