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

Division of two-digit by a one-digit numbers

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

Divide and verify the result

(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.

Division of a Two-Digit by a One-Digit Numbers


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.

Dividing 2-digit by 1-digit Numbers


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.

Divide 2-Digit Number by 1-Digit Number

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

Division of Two-Digit by a One-Digit

(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.

Divide Two Digits by One Digit


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.

Divide Two Digits by One Digit


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.

Divide 2-Digit Number by 1-Digit Number

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.

Divide 2-Digit by 1-Digit Number

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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