What is Repeated Subtraction?
Repeated subtraction is a method of subtracting the equal number of items from a larger group. It is also known as division.
If the same number is repeatedly subtracted from another larger number until the remainder is zero or a number smaller than the number being subtracted, we can write that in the form of division.
For example:
If there are 25 balls and we form a group of 5 balls each.
Here, the number 5 has been repeatedly subtracted 5 times. We can say that the number 5 has been subtracted 5 times from 25. So, we can write this subtraction as 25 ÷ 5 = 5.
Similarly, to solve a division problem through repeated subtraction, we repetitively group and subtract the same number again and again to find the answer.
Here are a few examples of repeated subtraction.
There are 34 stars. How many groups of 4 stars in each can be formed?
In the given image we can see 34 stars. Now, using repeated subtraction, we can group them in smaller groups of 4 stars in each group. We can start to subtract 4 stars repeatedly until we are left with 0 or a number less than 4.
34 - 4 = 30 30 - 4 = 26 26 - 4 = 22 22 - 4 = 18 18 - 4 = 14 14 - 4 = 10 10 - 4 = 6 6 - 4 = 2
We get 8 groups of 4 and with 2 stars remaining.
This example can be mathematically written as 34 ÷ 4. Where 34 is the dividend. The divisor is the number of stars in each group, that is, 4. The number of times 4 is subtracted is the quotient. So, 8 is the quotient and the leftover stars are the remainder. So, 2 is the remainder.
Since repeated subtraction is division, it can be written in 2 ways.
Example: Let’s say there are 18 items. These can be written in 2 ways as shown.
| 18 ÷ 6 | 18 ÷ 3 |
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When the divisor is 6, we make groups of 6. We get, 3 groups of 6. So, 18 ÷ 6 = 3 |
When the divisor is 3, we make groups of 3. We get, 6 groups of 3. So, 18 ÷ 3 = 6 |
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Fun fact:
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18 – 6 = 12 → 12 – 6 = 6 → 6 – 6 = 0
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18 ÷ 6 = 3
