Multiplication of whole numbers is equivalent to a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the *multiplicand*, as the value of the other one, the *multiplier*.

Normally, the multiplier is written first and multiplicand second, though this can vary, as the distinction is not very meaningful:

**SHORTCUTS IN MULTIPLICATION:**

Multiplication using multiples

12 x 15

= 12 x 5 x 3

= 60 x 3

= 180

Multiplication by “giving and taking”

12 x 47

= 12 x (50 – 3)

= (12 x 50) – (12 x 3)

= 600 – 36

= 564

Multiplication by 5 –> take the half(0.5) then multiply by 10

428 x 5

= (428 x 1/2) x 10 = 428 x 0.5 x 10

= 214 x 10

= 2140

Multiplication by 10 —> just move the decimal point one place to the right

14 x 10

= 140 —> added one zero

Multiplication by 50 —> take the half(0.5) then multiply by 100

18 x 50

= (18/2) x 100 = 18 x 0.5 x 100

= 9 x 100

= 900

Multiplication by 100 —> move the decimal point two places to the right

42 x 100

= 4200 —> added two zeroes

Multiplication by 25 —> use the analogy Rs1 = 4 x 25 cents

25 x 14

= (25 x 10) + (25 x 4) —> 250 + 100 —> $2.50 + $1

= 350

Multiplication by 25 —> divide by 4 then multiply by 100

36 x 25

= (36/4) x 100

= 9 x 100

= 900

Multiplication by 11 if sum of digits is greater than 10

87 x 11

= 8_7 —> the middle term = 8 + 7 = 15

because the middle term is greater than 10, use 5 then

add 1 to the first term 8, which leads to the answer of

= 957

Multiplication of 37 by the 3, 6, 9 until 27 series of numbers –> the “triple effect”

solve 37 x 3

multiply 7 by 3 = 21, knowing the last digit (1), just combine two more 1’s giving the triple digit answer 111

solve 37 x 9

multiply 7 by 9 = 63, knowing the last digit (3), just combine two more 3’s giving the triple digit answer 333

solve 37 x 21

multiply 7 by 21 = 147, knowing the last digit (7), just combine two more 7’s giving the triple digit answer 777

Multiplication of the “dozen teens” group of numbers —

(i.e. 12, 13, 14, 15, 16, 17, 18, 19) by ANY of the numbers within the group:

solve 14 x 17

4 x 7 = 28; remember 8, carry 2

14 + 7 = 21

add 21 to whats is carried (2)

giving the result 23

form the answer by combinig 23 to what is remembered (8)

giving the answer 238

Multiplication of numbers ending in 5 with difference of 10

45 x 35

first term = [(4 + 1) x 3] = 15; (4 is the first digit of 45 and 3 is the first digit of 35 –> add 1 to the higher first digit which is 4 in this case, then multiply the result by 3, giving 15)

last term = 75

combining the first term and last term,

= 1575

75 x 85

first term = (8 + 1) x 7 = 63

last term = 75

combining first and last terms,

= 6375

Multiplication of numbers ending in 5 with the same first terms (square of a number)

25 x 25

first term = (2 + 1) x 2 = 6

last term = 25

answer = 625 —> square of 25

**Examples:**

A chair costs Rs 12. What is the cost of 3 such chairs?

12 × 3 = 36

*Answer:*

The cost of 3 such chairs is Rs 36.

**Problems:**

1.Multiplication by distribution

12 x 17

= (12 x 10) + (12 x 7) —> 12 is multiplied to both 10 & 7

= 120 + 84

= 204

2.Multiplication by distribution

75 x 75 = first term = (7 + 1) x 7 = 56

last term = 25

answer = 5625 —> 75 squared

3.Multiplication by 11 if sum of digits is less than 10

72 x 11

= 7_2 —> the middle term = 7 + 2 = 9

= place the middle term 9 between 7 & 2

= 792

4.Multiplication by 500 —> take the half(0.5) then multiply by 1000

21 x 500

= 21/2 x 1000

= 10.5 x 1000

= 10500

/aptitude-shortcuts-addition-subtraction/