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 < 28 Therefore, 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 = 91 We 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. |
14. Divide 1749 by 27 and check your answer.
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 < 32 Therefore, take 156 II: We have 32 × 5 = 160 > 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. 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 > 282 32 × 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. |
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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