Division of Two-Digit by a
One-Digit Numbers
In division of two-digit by a one-digit numbers are discussed here step by step.
How to divide 2-digit numbers by single-digit numbers?
Let us follow the examples to learn to divide 2-digit numbers by one-digit numbers.
I: Dividing a 2-digit Number by a 1-Digit Number without Remainder:
1. Divide the following and verify the result
(i) 42 ÷ 6
(ii) 85 ÷ 5
Solution:
(i) 42 ÷ 6
Since, 6 sevens are 42, i.e., 6 × 7 = 42
So, 7 will be quotient
6 × 7 + 0 = 42, the dividend
So, quotient 7 is verified
Therefore, 7 is quotient
(ii) 85 ÷ 5
(a) 8 > 5 so first 8 will be divided. 8T ÷ 5 = 1T so quotient will be 1 ten
(b) 8T - 5T = 3T, 3T + 5 = 35 for 35 ÷ 5, 5 × 7 = 35.
So 7 is quotient
(c) 5 × 17 = 85 (dividend)
So, result is verified.
Therefore, Quotient = 17, remainder = 0
2. Divide 77 by 7
We proceed as follows:
Step I: Arrange the two given numbers as shown.
Step II: Divide the tens by 7.
We know 7 × 1 = 7.
Write 1 in tens place of the quotient and 7 below 7.
Subtract 7 from 7 to get 0.
Step III: Bring down 7 ones and divide it by 7.
We know 7 × 1 = 7.
Write 1 in the ones place of the quotient and 7 bellow 7.
Subtract 7 from 7 to get 0.
Thus, 77 ÷ 7 = 11
II: Dividing a 2-digit Number by a 1-Digit Number with Remainder:
1. Divide the following and verify the result
76 ÷ 6
(a) 7 > 6, so 7T will be divided by 6,
6 one is 6, so 1T is quotient
(b) 7 – 6 = 1, 6 is carried down, so 16 will, be divided by 6.
6 twos are 12, 6 threes are 18, so quotient will be 2.
(c) 16 - 12 = 4 is the remainder
(d) 6 × 12 + 4 = 72 + 4 = 76 (dividend)
Therefore, result is verified.
The quotient = 12
Remainder = 4
2. Divide 89 by 4.
We proceed as follows:
Step I: Arrange the two given numbers as shown.
Step II: Divide the tens by 4.
Start by looking at the first number (tens place) in the dividend.
Find a number in the table of 4 less than or equal to 8
4 × 1 = 4,
4 × 2 = 8,
So, 2 is the required number.
4 × 2 = 8, write 2 in tens place of the quotient and 8 below 8.
Subtract the number you got by multiplying the divisor. from the number in the dividend.
Subtract 8 from 8 to get 0.
Step III: Divide the ones by 4.
Bring down the next digit (ones place), from the number in the dividend.
i.e., Bring down 9 ones and divide it by 4.
Repeat the same process again.
Find a number in the table of 4 less than or equal to 9
4 × 1 = 4,
4 × 2 = 8,
So, 2 is the required number.
4 × 2 = 8, write 2 in ones place of the quotient and 8 below 9.
Subtract 8 from 9 to get 1.
So, the quotient = 22 and remainder = 1.
3. Divide 66 by 5 and verify the result.
We proceed as follows:
Step I: Arrange the two given numbers.
Step II: Divide the tens by 5.
Start by looking at the first number (tens place) in the dividend.
Find a number in the table of 5 less than or equal to 6
5 × 1 = 5,
So, 1 is the required number.
5 × 1 = 5, write 1 in tens place of the quotient and 5 below 6.
Subtract the number you got by multiplying the divisor. from the number in the dividend.
Subtract 5 from 6 to get 1.
Step III: Bring down the next digit (ones place), from the number in the dividend.
i.e., Bring down 6 ones
The number is 16
Now and divide 16 by 5.
Repeat the same process again.
Find a number in the table of 5 less than or equal to 16
5 × 1 = 5,
5 × 2 = 10,
5 × 3 = 15,
So, 3 is the required number.
5 × 3 = 15, write 3 in ones place of the quotient and 15 below 16.
Subtract 15 from 16 to get 1.
So, the quotient = 13 and remainder = 1.
So, 66 is dividend,
5 is divisor,
3 is quotient,
1 is remainder.
Check: Dividend = Quotient × Divisor - Remainder
= 13 × 5 + 1
= 65 + 1
= 66 = Dividend
The same method is used when dividing larger numbers.
Worksheet on Division of Two-Digit by a One-Digit Numbers:
1. Find the quotient and the remainder, using long division method:
(i) 40 ÷ 4
(ii) 36 ÷ 6
(iii) 54 ÷ 6
(iv) 50 ÷ 9
(v) 63 ÷ 8
answer:
1. (i) Quotient: 10; Remainder: 0
(ii) Quotient: 6 ; Remainder: 0
(iii) Quotient: 9 ; Remainder: 0
(iv) Quotient: 5 ; Remainder: 5
(v) Quotient: 7 ; Remainder: 7
2. Divide the following and check your answer using division algorithm:
(i) 46 ÷ 7
(ii) 89 ÷ 9
(iii) 65 ÷ 8
(iv) 35 ÷ 4
(v) 52 ÷ 6
Answer:
2. (i) Quotient: 6; Remainder: 4
(ii) Quotient: 9; Remainder: 8
(iii) Quotient: 8; Remainder: 1
(iv) Quotient: 8; Remainder: 3
(v) Quotient: 8; Remainder: 4
3. Divide the following:
(i) 89 ÷ 4
(ii) 99 ÷ 9
(iii) 92 ÷ 7
(iv) 82 ÷ 2
(v) 66 ÷ 6
(vi) 46 ÷ 7
(vii) 89 ÷ 9
(viii) 65 ÷ 8
(ix) 35 ÷ 4
(x) 52 ÷ 6
(xi) 46 ÷ 7
(xii) 89 ÷ 9
(xiii) 65 ÷ 8
(xiv) 35 ÷ 4
(xv) 52 ÷ 6
Answer:
3. (i) Quotient: 22; Remainder: 1
(ii) Quotient: 11; Remainder: 0
(iii) Quotient: 13; Remainder: 1
(iv) Quotient: 41; Remainder: 0
(v) Quotient: 11; Remainder: 0
(vi) Quotient: 6; Remainder: 4
(vii) Quotient: 9; Remainder: 8
(viii) Quotient: 8; Remainder: 1
(ix) Quotient: 8; Remainder: 3
(x) Quotient: 8; Remainder: 4
(xi) Quotient: 6; Remainder: 4
(xii) Quotient: 9; Remainder: 8
(xiii) Quotient: 8; Remainder: 1
(xiv) Quotient: 8; Remainder: 3
(xv) Quotient: 8; Remainder: 4
4. Divide and check your answer:
(i) 89 ÷ 8
(ii) 45 ÷ 2
(iii) 92 ÷ 3
(iv) 64 ÷ 4
(v) 88 ÷ 5
(vi) 55 ÷ 7
(vii) 65 ÷ 8
(viii) 61 ÷ 6
(ix) 82 ÷ 6
(x) 94 ÷ 6
Answer:
4. (i) Quotient: 11; Remainder: 1
(ii) Quotient: 22; Remainder: 1
(iii) Quotient: 30; Remainder: 2
(iv) Quotient: 16; Remainder: 0
(v) Quotient: 17; Remainder: 3
(vi) Quotient: 7; Remainder: 6
(vii) Quotient: 8; Remainder: 1
(viii) Quotient: 10; Remainder: 1
(ix) Quotient: 13; Remainder: 4
(x) Quotient: 15; Remainder: 4
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