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:

1. 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. Multiply 42 by 27

Step I: Write 42 and 27 as shown.

Step II: Multiply 42 by 7 and write the partial product as shown.

Step III: Now, since 2 a at tens place we have to multiply 42 by 20.

Now, Multiply 42 by 20.

Step IV: Add the two partial products.

Hence, 42 × 27 = 1,134

The above procedure can be summarised as:

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

1. Multiply 456 x 43

Solution:

(i) First Method

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

(ii) Second Method

(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.

→ 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

Hence, 687 × 23 = 15801

4. Multiply 624 and 22.

Solution:

We multiply 624 by 2 and 624 by 20 respectively.

Finally add the results to get the required product.

Therefore, 624 × 22 = 13,728

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

1. 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

2. Multiply: 1793 × 25

→ 20 + 5 Multiply by 5 Multiply by 20

Answer: 44,825

We can find the product of two numbers by lattice multiplication algorithm mathematics lab as follows:

Let us find 12413 × 37

Take a white chart paper and prepare a box.

Write 12413 on the top and 37 on the side as shown.

Multiply 3 by 3 and write the product 9 as 09 under the column headed by 3.

Similarly, multiply 1 by 3, 4 by 3, 2 by 3 and 1 by 3 and write the products under respective columns.

The multiply each of the digits 3, 1, 4, 2 and 1 by 7 and write the products under the respective columns.

Starting from the sower most row and the last column add.

The first sum is 1. Next 9 + 2 + 7 = 18

Carry 1 and so on.

Now the product is 0459281.

Hence, 12413 × 37459281 = 459281.

Worksheet 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:

1. (i) 132

(ii) 840

(iii) 3402

(iv) 782

(v) 2596

(vi) 6862

2. Multiply (2-digit by 2-digit) each of the following:

Answer:

2. (i) 871

(ii) 350

3. 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:

3. (i) 2919

(ii) 8448

(iii) 31434

(iv) 41340

(v) 63936

(vi) 77760

4. Multiply 3-digit by 2-digit number:

Answer:

4. (i) 11421

(ii) 9537

(iii) 10672

(iv) 18700

(v) 6160

(vi) 38227

5. 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:

5. (i) 36425

(ii) 54418

(iii) 239239

(iv) 51282

(v) 337716

(vi) 162500

6. Multiply by 2-digit numbers:

(i) 27 by 29

(ii) 28 by 49

(iii) 129 by 42

(iv) 205 by 63

(v) 625 by 73

(vi) 125 by 42

(vii) 405 by 14

(viii) 325 by 25

Answer:

6. (i) 783

(ii) 1372

(iii) 5418

(iv) 12915

(v) 45625

(vi) 5250

(vii) 5670

(viii) 8125

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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