Multiply a Number by a 2-Digit Number

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

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

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:

4-Digit by 2-Digit Multiplication Video

Subscribe to our YouTube channel for the latest videos, updates, and tips.

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

Multiplying 4-Digit by 2-Digit Numbers Video

Subscribe to our YouTube channel for the latest videos, updates, and tips.

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

From Multiply a Number by a 2-Digit Number to HOME PAGE