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DIVISION BY REPEATED SUBTRACTION

Repeated subtraction can also be used for division.

Anil has 6 marbles. He wants to put 2 marbles
into a bowl. How many bowls will he need?

He puts 2 marbles into one bowl.

6– 2 = 4 1

He puts 2 marbles into another bowl.

4– 2 = 2 2

Finally, he puts the remaining 2 marbles into a third bowl.

2– 2 = 0 3

Here, 2 is subtracted 3 times from 6.

Thus, division is actually repeated subtraction.

We can write “subtracting 2 repeatedly 3 times” as 6 ÷ 2 = 3.

We can show division as repeated subtraction on a number line also.

Observe the following examples.

Example 1. Find: 15 ÷ 3 = _______ 1 5

Solution. –3 1
1 2
Start from 15. –3 2

Take jumps towards the left. In each jump, cover 9
3 numbers. –3 3
6
You will take 5 jumps to reach zero. –3 4

3
5 4 3 2 1 –3 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0
Here we see that 3 has been subtracted 5 times from 15 to reach zero.

Therefore, 15 ÷ 3 = 5.

104 Mathematics 2