# 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.

 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:

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

3. Multiply 687 and 23.

Solution:

 Step I: Arrange the numbers vertically.Step II: Multiply 687 by 3 ones              687 × 3 = 2061Step III: Multiply 687 by 2 tens               687 × 20 = 13740Step 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

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 = __________

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      _________

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 = __________

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       _____________

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 = __________

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

6. (i) 783

(ii) 1372

(iii) 5418

(iv) 12915

(v) 45625

(vi) 5250

(vii) 5670

(viii) 8125

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