Multiplication by regrouping

Mutiplication of a number with other number can be done in the following ways.

(i) Dot multiplication

(ii) Repeated addition

(iii) Regrouping

(iv) Standard multiplication algorithm

(v) Lattice multiplication

Multiplication by regrouping:

This method can be used by multiplying a two digit number.

Consider the following multiplication

53 × 7

53 can be regroup into 5 tens and 3 ones.

Hence, 53 × 7 can be written as (50 + 3) × 7

= (50 × 7) + (3 × 7)

= 350 + 21

= 371.

Example

14 × 2 = ?

That is 2 Times 14

14 × 2 = 2 × 1 Ten + 2 × 4 Ones

 = 2 × 10 + 2 × 4 = 20 + 8

 = 14 × 2 = 28

Exercise

1. Multiply the following numbers by regrouping

(i) 75 × 8

= (70 + 8 ) × 8

= (70 × 8) + (5 × 8)

= 560 + 40

= 600

(ii) 26 × 5

= (26 + 6) × 5

= (20 × 5) + (6 × 5)

= 100 + 30

= 130

(iii) 372 × 6

= (370 + 2 ) × 6

= (370 × 6) + (2 × 6)

= 2220 + 12

= 2232

 (iv) 402 × 7

= ( 400 + 2) × 7

= ( 400 × 7) + (2 × 7)

= 2800 + 14

= 2814

(v) 752 × 3

= ( 750 + 2) × 3

= (750 × 3 ) + (2 × 3)

= 2250 + 6

= 2256