Multiply a Number by a 2-Digit Number

How to multiply a number by a 2-digit number?

We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of 3-digit, 4-digit, etc., numbers by a 2-digit multiplier.

1. Example to multiply 2-digit numbers by a 2-digit number:

Multiply 63 by 14

Solution:

(i) First Method

63 x 14

= (60 + 3) × (10 + 4)                    63 = 60 + 3
14 = 10 + 4
= (60 + 3) × 10 + (60 + 3) × 4

= (600 + 30) + (240 + 12)

= 630 + 252

= 882

or, 63 × 14 = (60 + 3) (10 + 4)

= (60 + 3) x 4 + (60 + 3) x l0

= (240 +12) + (600 + 30)

= 252 + 630

= 882

(ii) Second Method

 (a) 4 × 3 ones = 12 ones (b) 4 × 6 tens = 24 tens = 240 ones (c) 1 ten × 3 ones = 3 tens = 30 ones (d) 1 ten = 10 × 6 tens = 10 × 60 ones = 600 ones

(iii) Third Method

 (a) 14 = (10 + 4) (b) 63 × 4 = 252 (c) 63 × 10 = 630

(iv) Fourth Method

 (a) 14 = 4 ones + 1 ten (b) 63 × 4 ones = 252 ones (c) 63 × 1 ten = 63 tens (Generally the fourth method is adopted)

2. Example to multiply 3-digit numbers by a 2-digit number:

Multiply 456 x 43

Solution:

(i) First Method

 (a) 43 = 3 + 40 (b) 456 × 3 = 1368 (c) 456 × 40 = 18240
Therefore, 456 × 43 = 19608

(ii) Second Method

 (a) 43 = 3 ones + 4 tens (b) 456 × 3 ones = 1368 ones (c) 456 × 4 tens = 1824 tens

Hence, Product = 19608

Multiplication by 2 and 3 digit numbers

A. Find the product of 165 and 45.

 → 40 + 5 Multiply by 5 Multiply by 40 Add the two products

B. Multiply: 1793 × 25

 → 20 + 5 Multiply by 5 Multiply by 20

3. Example to multiply 4-digit numbers by a 2-digit number:

Multiply 3157 x 56

Solution:

(i) First Method

 (a) 56 = 6 + 50 (b) 3157 × 6 = 18942 (c) 3157 × 50 = 157850

(ii) Second Method

 (a) 56 = 6 ones + 5 tens (b) 3157 × 6 ones = 18942 ones (c) 3157 × 5 tens = 15785 tens

Hence, Product = 176792

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