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**

**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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