Multiply a Number by a
2-Digit Numbers

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

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.


I. Example to multiply 2-digit numbers by a 2-digit numbers:

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

Multiply 2-digit by 2-digit Numbers


(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

Multiply 2-digit by 2-digit Numbers


(a) 14 = (10 + 4)

(b) 63 × 4 = 252

(c) 63 × 10 = 630


(iv) Fourth Method

multiply a number by a 2 digit number

(a) 14 = 4 ones + 1 ten

(b) 63 × 4 ones = 252 ones

(c) 63 × 1 ten = 63 tens

(Generally the fourth method is adopted)


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

1. Multiply 456 x 43

Solution:

(i) First Method

Multiply 3-digit by 2-digit Numbers


(a) 43 = 3 + 40

(b) 456 × 3 = 1368

(c) 456 × 40 = 18240

Therefore, 456 × 43 = 19608


(ii) Second Method

Multiply 3-digit by 2-digit Numbers


(a) 43 = 3 ones + 4 tens

(b) 456 × 3 ones = 1368 ones

(c) 456 × 4 tens = 1824 tens

Hence, Product = 19608


2. Find the product of 165 and 45.

Multiply 3-digit by 2-digit Numbers

→ 40 + 5 

Multiply by 5

Multiply by 40

Add the two products

Answer: 7290


3. Multiply 687 and 23.

Solution:

Step I: Arrange the numbers vertically.

Step II: Multiply 687 by 3 ones

              687 × 3 = 2061

Step III: Multiply 687 by 2 tens

               687 × 20 = 13740

Step IV: Add 2061 and 13740

              2061 + 13740 = 15801

Multiply 3-digit Numbers by a 2-digit Numbers

Hence, 687 × 23 = 15801



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

1. Multiply 3157 x 56

Solution:

(i) First Method

Multiply 4-digit by 2-digit Numbers


(a) 56 = 6 + 50

(b) 3157 × 6 = 18942

(c) 3157 × 50 = 157850

(ii) Second Method

Multiply 4-digit by 2-digit Numbers


(a) 56 = 6 ones + 5 tens

(b) 3157 × 6 ones = 18942 ones

(c) 3157 × 5 tens = 15785 tens

Hence, Product = 176792


2. Multiply: 1793 × 25

Multiply 4-digit by 2-digit Numbers

→ 20 + 5

Multiply by 5

Multiply by 20

Answer: 44825


Questions and Answers on Multiply a Number by a 2-Digit Number:

1. Multiplication of 2-Digit Numbers by 2-Digit Numbers by column method.

(i) 12 × 11 = __________

(ii) 24 × 35 = __________

(iii) 42 × 81 = __________

(iv) 17 × 46 = __________

(v) 44 × 59 = __________

(vi) 73 × 94 = __________


Answers:

(i) 132

(ii) 840

(iii) 3402

(iv) 782

(v) 2596

(vi) 6862


2. Multiplication of 3-Digit Numbers by 2-Digit Numbers by column method.

(i) 139 × 21 = __________

(ii) 256 × 33 = __________

(iii) 507 × 62 = __________

(iv) 780 × 53 = __________

(v) 864 × 74 = __________

(vi) 972 × 80 = __________


Answers:

(i) 2919

(ii) 8448

(iii) 31434

(iv) 41340

(v) 63936

(vi) 77760


3. Multiplication of 4-Digit Numbers by 2-Digit Numbers by column method.

(i) 1457 × 25 = __________

(ii) 1183 × 46 = __________

(iii) 3107 × 77 = __________

(iv) 4662 × 11 = __________

(v) 9381 × 36 = __________

(vi) 6500 × 25 = __________


Answers:

(i) 36425

(ii) 54418

(iii) 239239

(iv) 51282

(v) 337716

(vi) 162500

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