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 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

10. 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

11. 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

12. 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.

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