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

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)


2. Multiply 42 by 27

Step I: Write 42 and 27 as shown.

4

2

×

2

7


 

 

 



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

4

2

×


7


2

9

4



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

Now, Multiply 42 by 20.

4

2

×

2

7


2

9

4

  ←  42 × 7

8

4

0

  ←  42 × 20



Step IV: Add the two partial products.

4

2

×

2

7


2

9

4

+

8

4

0


1

1

3

4



Hence, 42 × 27 = 1,134


The above procedure can be summarised as:

Multiply 2-Digit Numbers by a 2-Digit Numbers



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


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.

Multiply 3-Digit Numbers by a 2-Digit Numbers

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

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: 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:

(i)

              6     7

        ×   1      3

      _________

(ii)

              2     5

        ×   1      4

      _________


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:

(i)

              4     2     3

         ×         2      7

       _____________

(ii)

              2     8     9

         ×         3      3

       _____________

(iii)

              4     6     4

         ×         2      3

       _____________

(iv)

              8     5     0

         ×         2      2

       _____________

(v)

              1     7     6

         ×         3      5

       _____________

(vi)

              8     8     9

         ×         4      3

       _____________

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

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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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