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 24Solution: **

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:**

Therefore, take 143
Since 140 < 143, write 5 as first digit of the quotient. Write the product 26 × 5 = 140 below 143 and subtract.
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.
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 13Solution:**

92 > 13, we know that 13 x 7 = 91 We write 7 in the quotient. Subtract 91 from 92.
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. |

**14.** Divide 1749 by 27 and check your answer.

Let us divide 1749 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:**

Therefore, take 156
32 × 4 = 128 < 156 Since 128 < 156, write 4 as first digit of the quotient. Write the product 32 × 4 = 128 below 156 and subtract.
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.
32 × 8 = 256 < 282.
282 – 256 = 26. Since 26 < 32, stop the division. |

**Questions and Answers 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

Answer:

**Related Concept**

● Addition

● Check for Subtraction and Addition

● Word Problems Involving Addition and Subtraction

● Estimating Sums and Differences

● Multiply a Number by a 2-Digit Number

● Multiplication of a Number by a 3-Digit Number

● Word Problems on Multiplication

● 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

● Division by Two-Digit Numbers

**4th Grade Math Activities**

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