Divide by Repeated Subtraction

How to divide by repeated subtraction?

We will learn how to find the quotient and remainder by the method of repeated subtraction a division problem may be solved.


DIVISION AS REPEATED SUBTRACTION

As multiplication is repeated addition, division is repeated subtraction.

Let us see how.

We know that division is equal distribution of objects.

When we divide, we find out how many times we can subtract the given number from the group of objects.

Let us understand this with the help of following examples.


1. 12 pens have to be equally kept in 2 penstands.

So, how many times can 2 be taken away from 12?

Repeated Subtraction

Let us subtract 2 again and again from 12 till we reach 0.



12 - 2 = 10

Repeated Subtraction



10 - 2 = 8

Repeated Subtraction



8 - 2 = 6

Repeated Subtraction



6 - 2 = 4 

Repeated Subtraction



4 - 2 = 2 

Repeated Subtraction



2 - 2 = 0

Repeated Subtraction


How many times 2 has been subtracted from 12 to reach 0? Clearly, 6

Therefore, 12 ÷ 2=6


Solved examples on divide by repeated subtraction:

1. Solve 16 ÷ 8                                                                       

Solution:

8 is subtracted repeatedly from 16 as shown:

Divide by Repeated Subtraction





When 8 is subtracted from 16, 2 times, then we get the remainder zero.

Hence, 16 ÷ 8 = 2, 2 is the quotient. 

2. Divide 20 ÷ 5

5 is subtracted repeatedly from 20 as shown:

Division by Repeated Subtraction












When 5 is subtracted from 20, four times, then we get the remainder zero.

Hence, 20 ÷ 5 = 4, 4 is the quotient.              


3. Solve 12 by 3

Solution:

3 is subtracted repeatedly from 12 as shown:

Repeated Subtraction












When 3 is subtracted from 12, four times, then we get the remainder zero.

Hence, 12 ÷ 3 = 4, 4 is the quotient.              


4. Divide 28 ÷ 7

7 is subtracted repeatedly from 28 as shown:

7 is Subtracted Repeatedly












When 7 is subtracted from 28, four times, then we get the remainder zero.

Hence, 28 ÷ 7 = 4, 4 is the quotient.        

 

5. Divide 32 ÷ 4

4 is subtracted repeatedly from 32 as shown:

4 is Subtracted Repeatedly from 32























When 4 is subtracted from 32, eight times, then we get the remainder zero.

Hence, 32 ÷ 4 = 8, 8 is the quotient.              


6. Solve 18 by 6.

6 is subtracted repeatedly from 18 as shown:

6 is Subtracted Repeatedly from 18










When 6 is subtracted from 18, three times, then we get the remainder zero.

Hence, 18 ÷ 6 = 3, 3 is the quotient.              

 

7. Divide 12 flowers in 3 vases.

We put 1 flower in each of the 3 vases and subtract 3 from 12 each time.

12 – 3 = 9

9 – 3 = 6

6 – 3 = 3

3 – 3 = 0

There are no more flowers left. We subtracted 4 times 3 from 12.


We subtract 3 flowers 4 times from 12 to get 0.


7. Divide 18 ice creams among 6 children by repeated subtraction.

Division by Repeated Subtraction


8. Find 12 ÷ 4 by repeated subtraction.

Example: 

12 - 4 = 8        8 - 4 = 4       4 - 4 = 0

4 can be subtracted 3 times from 12. So, 12 ÷ 4 = 3


The above examples will help us to solve various division problems on 2-digit number by a single digit number using the method of repeated subtraction.


Division by Equal Distribution:

When 8 balls are equally distributed in 2 boys, we write 8 ÷ 2 = 4

Division by Equal Distribution




Questions and Answers on Divide by Repeated Subtraction:

1. Divide using repeated subtraction. One has been done for you.

(i) Divide 16 by 4.

     T     O

     1     6

     -     4

     1    2

     T     O

     1     2

     -     4

           8

     T     O

            8

     -     4

           4

     T     O

            4

     -     4

           0



16 ÷ 4 = 4


(ii) Divide 6 by 2.

     T     O

            6

     -     2

             

     T     O

     

              

              

     T     O

     

              

              

     T     O

     

              

              



6 ÷ 2 = __


(iii) Divide 12 by 3.

     T     O

     1     2

     -     3

             

     T     O

     

              

              

     T     O

     

              

              

     T     O

     

              

              



12 ÷ 3 = __


(iv) Divide 20 by 5.

     T     O

     2     0

     -     5

             

     T     O

     

              

              

     T     O

     

              

              

     T     O

     

              

              



20 ÷ 5 = __


(v) Divide 14 by 7.

     T     O

     1     4

     -     7

             

     T     O

     

              

              

     T     O

     

              

              

     T     O

     

              

              



14 ÷ 7 = __


Answer:

1. (ii)

     T     O

            6

     -      2

            4

     T     O

            4

     -      2

            2

     T     O

            2

     -      2

            0

   



6 ÷ 2 = 3


(ii)

     T     O

     1     2

     -     3

           9

     T     O

            9

     -      3

            6

     T     O

            6

     -      3

            3

     T     O

            3

     -      3

            0



12 ÷ 3 = 4


(iii)

     T     O

     2     0

     -     5

    1     5

     T     O

     1     5

     -     5

    1     0

     T     O

     1     0

     -     5

           5

     T     O

            5

     -      5

            0



20 ÷ 5 = 4


(iv)

     T     O

     1     4

     -     7

           7

     T     O

            7

     -      7

            0

    

    



14 ÷ 7 = 2


2. Write the following subtractions as division facts. One has been done for you.

(i)

Subtractions as Division Facts

(ii)

Subtractions as Division Facts

Division Fact is 

_____ ÷ __________ 

(iii)

Subtractions as Division Facts

Division Fact is 

_____ ÷ __________ 


3. Write the following division facts as repeated subtractions. One has been done for you.

(i) 20 ÷ 5 = 4

Repeated subtraction for the given fact is:

Division Facts as Repeated Subtractions

(ii)

35 ÷ 7 = 5

Repeated subtraction for the given fact is:









(iii)

48 ÷ 6 = 8

Repeated subtraction for the given fact is:









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