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

Related Concept

Addition

Word Problems on Addition

Subtraction

Check for Subtraction and Addition

Word Problems Involving Addition and Subtraction

Estimating Sums and Differences

Find the Missing Digits

Multiplication

Multiply a Number by a 2-Digit Number

Multiplication of a Number by a 3-Digit Number

Multiply a Number

Estimating Products

Word Problems on Multiplication

Multiplication and Division

Terms Used in Division

Division of Two-Digit by a One-Digit Numbers

Division of Four-Digit by a One-Digit Numbers

Division by 10 and 100 and 1000

Dividing Numbers

Estimating the Quotient

Division by Two-Digit Numbers

Word Problems on Division






4th Grade Math Activities

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