# Division by Two-Digit Numbers

In division by two-digit numbers we will practice dividing two, three, four and five digits by two-digit numbers.

Consider the following examples on division by two-digit numbers:

Let us use our knowledge of estimation to find the actual quotient.

1. Divide 94 by 12

Round the number

94 ÷ 12 → 90 ÷ 10

Estimated quotient = 9

In order to find the actual quotient, multiply the divisor 12 by the estimated quotient.

12 × 9 = 108

12 × 8 = 96

12 × 7 = 84

108 > 94

96 > 94

The actual quotient, we find is 7.

Check:

Quotient - 7

Remainder - 10

12 × 7 + 10 = 94

2. Divide 96 by 16

Solution:

16 x 6 = 96, so, 6 will be the quotient.

We search for the possible quotient. The divisor is a number of two digits.

So, 96 is taken as dividend.

Therefore, Quotient = 6

3. Divide 88 by 17

Solution:

17 x 5 = 85 and 17 x 6 = 102,

85 < 88 but 102 > 88

So, 5 will be the quotient

Therefore, Quotient = 5, Remainder = 3

4. Divide 192 by 24

Solution:

19 < 24, so, 192 will be taken as dividend.

24 x 8 = 192. So, 8 will be the quotient.

Therefore, Quotient = 8

5. 510 ÷ 32 ⟶ 500 ÷ 30 ⟶ 50 ÷ 3

Estimated quotient = 16

Try:

32 × 16 = 512

32 × 15 = 480

512 > 510

The actual quotient is 15

6. Divide 275 by 24

Solution:

(a) 27 > 24, 24 x 1 = 24, 24 x 2 = 48

So, 1 will be quotient.

Here, 27 is 27T or, 270

So, 1T or 10 is the quotient.

(b) 275 -240 = 35, 24 x 1. = 24,

So, 1 is the quotient.

24 x 11 + 11 = 264 + 11 = 275

Therefore, result is verified

Therefore, Quotient = 11, Remainder =11

7. Divide 803 by 70

Solution:

(a) 80 > 70,

So, 80T will be taken as dividend

70 x 1 = 70, 70 x 2 = 140

So, 1T will be quotient.

(b) 803 - 700 = 103, 70 x 1 = 70, 70 x 2 = 140

So, 1 will be quotient.

70 x 11 + 33 = 770 + 33 = 803

Therefore, result is verified

Therefore, Quotient =11, Remainder = 33

8. Divide 345 by 49

Solution:

34 < 49, So, 345 will be taken as dividend.

By trial 49 x 7 = 343 which is near to 345

So, 7 will be quotient.

Verification: 49 x 7 + 2 = 343 + 2 = 345

Therefore, Quotient = 7, Remainder = 2

9. Divide 1432 by 28.

Solution:

 I: 1 < 28            14 < 28Therefore, take 143 II: We have 28 × 6 = 168; 28 × 5 = 140 Since 140 < 143, write 5 as first digit of the quotient. Write the product 26 × 5 = 140 below 143 and subtract. III: 143 – 140 = 3; Bring down 2 32 > 28 We have 28 × 1 = 28 < 32. 28 × 2 = 56 > 32 Since 28 < 32, write 1 as the second digit of the quotient. Write the product 28 × 1 = 28 below and subtract. IV: 32 – 28 = 4 Since 4 < 28, stop the division.

10. Divide 4963 by 14

Solution:

(I method)

(a) 14 x 3 = 42 and 14 x 4 = 56, 42 < 49 and 56 > 49

So, 3H will be quotient.

(b) 4963 - 4200 = 763, 14 x 5 = 70 and 14 x 6 = 84

So, 5T will be quotient.

(c) 763 - 700 = 63, 14 x 4 = 56, 14 x 5 = 70

56 < 63, 70 > 63

Therefore, 4 is the quotient.

Verification: 14 x 354 + 7 = 4956 + 7 = 4963

Therefore, Quotient = 354, Remainder = 7

(II method)

(a) 14 x 3 = 42, 14 x 4 = 56,

Therefore, 3H will be quotient.

49 - 42 = 7, 6 is carried down

(b) 14 x 5 = 70, 14 x 6 = 84,

Therefore, 5T will be quotient.

76 - 70 = 6, 3 is carried down.

14 x 4 = 56, 14 x 5 = 70,

Therefore, 4 will be quotient.

63 - 56 = 7 is the remainder

Quotient = 354

Remainder = 7

Verification:

Quotient x divisor + remainder

= 354 x 14 + 7

= 4956 +7

= 4963 (dividend)

So, result is verified

11. Divide 47320 by 35

Solution:

(a) 47 Th is divided by 35, 35 x 1 = 35 < 47,

35 x 2 = 70 > 47, so, 1 Th is quotient.

47 - 35 = 12, 3 is carried down

(b) 123H is divided by 35, 35 x 3 = 105 < 123

35 x 4 = 140 > 123, so, 3 H is quotient

123 - 105 = 18, 2 is carried down.

(c) 182 T is divided by 35, 35 x 5 = 175 < 182

35 x 6 = 210 > 182, therefore, 5T is quotient.

182 - 175 = 7, 0 is carried down.

(d) 70 is divided by 35, 35 x 2 = 70,

2 is the quotient

70 - 70 = 0

Verification: 35 x 1352 + 0 = 47320.

So verified.

Therefore, Quotient = 1352 Remainder = 0

12. Divide 50360 by 43

Solution:

(a) 50Th is divided by 43, 43 x 1 = 43 < 50.

So, 1 Th is quotient, 50 - 43 = 7,3 is taken down.

(b) 73 H is divided by 43, 43 x 1 = 43 < 73

43 x 2 = 86 > 73.

So, 1H is quotient, 73 - 43 = 30, 6 is taken down.

(c) 306 T is divided by 43, 43 x 7 = 301 < 306

7 T is quotient, 306 - 301 = 5, 0 is taken down

(d) 50 is divided by 43, 1 is quotient

50 - 43 = 7 is remainder

Verification: 1171 x 43 + 7 = 50353 + 7 = 50360.

Result is verified.

Quotient =1171 Remainder = 7

13. Divide 923 by 13

Solution:

 Let us divide 923 by 13.Step I: Since, the divisor is a 2-digit number, we consider 92 the 2-digit number on the extreme left of the dividend.92 > 13, we  know that 13 x 7 = 91We write 7 in the quotient.Subtract 91 from 92.Step II: Bring down 3 and write on the right side of the remainder. 13 is the new dividend.Step III: Divide 13 by 13.We know 13 x 1 = 13. Write 1 in the quotient. Subtract 13 from 13. The remainder is 0. Hence, quotient = 71 and remainder = 0.

 Solution:Let us divide 1749 by 27.Step I: The divisor 27 is greater than the 2-digit number on the extreme left of the dividend. So, we take the 3-digit number which is 174 and divide by 27. Write 6 in the quotient and subtract 162 from 174.Step II: Bring down 9 and write on the right side of the remainder. 129 is the new dividend.Step III: Divide 129 by 27.Write 4 in the quotient and subtract 108 from 129. Remainder is 21 Hence, quotient = 64 and remainder = 21

Verification:

We know that

Dividend = Quotient x Divisor + Remainder

= 64 x 27 + 21

= 1728 + 21

= 1749

1749 is the dividend as given in the question.

15. Divide 15642 by 32

Solution:

 I: 1 < 32             15 < 32Therefore, take 156II: We have 32 × 5 = 160 > 15632 × 4 = 128 < 156Since 128 < 156, write 4 as first digit of the quotient. Write the product 32 × 4 = 128 below 156 and subtract.III: 156 – 128 = 28. Bring down 4.284 > 32. We have 32 × 9 = 288 > 284.32 × 8 = 256 < 284.Since 256 < 284, write 8 as the second digit of the quotient. Write the product 32 × 8 = 256 below 284 and subtract.IV: 284 - 256 = 28. Bring down 2. 282 > 32. We have 32 × 9 = 288 > 28232 × 8 = 256 < 282.V: Write 8 as the third digit of the quotient. Write the product 32 × 8 = 256 below 282 and subtract.282 – 256 = 26.Since 26 < 32, stop the division.

Division Activity

Objective: Dividing a 2-digit number by 9 using short cut method.

Materials Required: Pen and paper only.

Procedure/Demonstration: We can divide any 2-digit number by 9 quickly.

Type 1: When the sum of the digits is less than 9.

In this case, the tens digit of the dividend gives quotient and the sum of the two digits gives remainder.

Type 2: When the sum of the digits is greater than or equal of 9 but less than 18. In this case, 1 more than the tens digit of the dividend gives quotient. To get the remainder, subtract 9 from the sum of the digits of the dividend.

75 ÷ 9 gives quotient = 7 + 1 = 8 and remainder = 12 - 9 = 3

63 ÷ 9 gives quotient = 6 + 1 = 7 and remainder = 9 - 9 = 0

Worksheet on Division by 2-Digit Numbers:

1. Divide the following:

(i) 8629 ÷ 12

(ii) 38245 ÷ 32

(iii) 16928 ÷ 11

(iv) 28724 ÷ 33

(v) 86458 ÷ 15

(v) 7542 ÷ 19

1. (i) Quotient: 719; Remainder: 1

(ii) Quotient: 1195; Remainder: 5

(iii) Quotient: 1538; Remainder: 10

(iv) Quotient: 870; Remainder: 14

(v) Quotient: 5763; Remainder: 13

(v) Quotient: 396; Remainder: 18

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