## What Is Repeated Subtraction?

Repeated subtraction is a process of subtracting the same number from a large number until we get 0 or a number less than the number we are subtracting.

Consider a situation where you have to distribute 15 candies among 5 friends. How many candies will each friend get? You can solve this problem using repeated subtraction where you will subtract 5 from 15 “three” times to get 0 in the end. This way each friend will get 3 candies and no candy will be left.

$15\;-\;5 = 10$

$10\;-\;5 = 5$

$5\;-\;5 = 0$

However, if there are 16 sweets and 5 people, you will subtract 5 “three” times; each friend will get 3 candies and you will be left with 1 spare candy.

$16\;-\;5 = 11$

$11\;-\;5 = 6$

$6\;-\;5 = 1$

So, repeated subtraction is a good way to introduce “division” to kids. Division is also known as repeated subtraction. Let us look at the definition and example of the concept to make our understanding more clear.

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## Repeated Subtraction: Definition

Repeated subtraction definition can be given as:

Repeated subtraction is a method of subtracting the same number repeatedly from a large number until we get remainder 0 or less than the number being subtracted. It is also called division.

**Repeated subtraction example:** If 18 strawberries are divided among 6 friends, how many strawberries will each friend get?

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## Division as Repeated Subtraction

Let us look at repeated subtraction as division.

Repeated subtraction is subtracting the same number from a large number until the end result is zero or less than the number being subtracted. This process is also called division. In other words, if a same number is subtracted from a different number until the remainder is zero or less than the actual number. The number of times we subtract the same value is also known as quotient.

Divide 20 stars in 4 groups. How many stars will be in each group?

Let’s understand this using visual representation.

Here, 20 is the dividend. 4 is the divisor.

We will subtract 4 repeatedly from 20 until we get 0 remainder.

This means the 4 is subtracted **five** times to reach 0 and can be written in division form as $20 \div 4 = 5$.

In summary:

Dividend: Large Number

Divisor: Small number being subtracted repeatedly

Quotient: Number of times you subtract the small number from the large number before you get 0 or a smaller number

Remainder: Number left in the end

## How to Divide with Repeated Subtraction

Let’s solve two division problems using repeated subtraction, one where we get 0 remainder and one where the remainder is non-zero.

**Example 1:** $18 \div 3$

$18 \;-\; 3 = 15$

$15 \;-\; 3 = 12$

$12 \;-\; 3 = 9$

$9 \;-\; 3 = 6$

$6 \;-\; 3 = 3$

$3 \;-\; 3 = 0$

Quotient is 6. Remainder is 0.

This implies that the number is subtracted 6 times. It can also be written in division form as:

$18 \div 3 = 6$

**Example 2:** $27 \div 5$

$27\;-\; 5 = 22$

$22 \;-\; 5 = 17$

$17\; -\; 5 = 12$

$12 \;-\; 5 = 7$

$7 \;-\; 5 = 2$

The quotient is 5 and the remainder is 2.

This implies that the number is subtracted 5 times. It can also be written in division form as:

$27 = (5 \times 5) + $Remainder

$27 = (5 \times 5) + 2$

## Repeated Subtraction on Number Line

Repeated subtraction is the same as regular division. A representation is depicted below:

Here, we have solved $15 \div 3$ using repeated subtraction through division.

## Applications of Repeated Subtraction

- Why is repeated subtraction useful? Repeated subtraction is a great way of teaching and introducing division in early grades.

- Using the repeated subtraction activities, it is easy to teach the concepts and terms related to division, like divisor, quotient, remainder, dividend.

- We can also determine the square root of a perfect square using this method.

For example: $4 \;-\; 2 = 2,\; 2 \;-\; 2 = 0$.

Here, quotient = divisor = 2. So, 2 is the square root of 4.

## Properties of Repeated Subtraction

- Repeated subtraction is also known as division. We subtract equal groups or the same number over and over again to find the quotient and remainder.
- Repeated subtraction is a precursor to teaching division. It is an easier way for children to develop the understanding of division.
- Repeated subtraction helps to understand multiplication and division arrays.

## Conclusion

In this article, we talked about repeated subtraction and division as repeated subtraction with the help of interactive examples. Let’s solve a few more examples!

## Solved Examples on Repeated Subtraction

**Solve**$25 \div 5$**using repeated subtraction.**

**Solution:**

We are given to divide the numbers $25 \div 5$ using repeated subtraction.

So,

$25 \;-\;5 = 20$

$20 \;-\; 5 = 15$

$15 \;-\; 5 = 10$

$10 \;-\; 5 = 5$

$5 \;-\; 5 = 0$

We subtracted 5 “five” times.

Here, you can see the remainder is 0 and the quotient is 5.

**2. Solve the numbers **$83 \div 11$** using repeated subtraction.**

**Solution:**

We have to divide the numbers $83 \div 11$** **using repeated subtraction.

$83 \;-\; 11 = 72$

$72 \;-\; 11 = 61$

$61 \;-\; 11 = 50$

$50 \;-\; 11 = 39$

$39 \;-\; 11 = 28$

$28 \;-\; 11 = 17$

$17 \;-\; 11 = 6$

We subtracted 11 “seven” times. Remainder is 6.

So, the quotient is 7.

**3. Alicia bought 52 melons to distribute among her 25 neighbors. How many melons is she left with? **

**Solution:**

Number of melons Alicia has $= 50$

By repeated subtraction,

$53 \;-\; 25 = 28$

$28 \;-\; 25 = 3$

We subtracted 25 twice and got the remainder of 3.

Each neighbor will get 2 watermelons and Alicia is left with 3 melons.

**4. John has 65 pens to arrange on the rack. Each rack can accommodate 13 pens. How many racks does John need in total?**

**Solution:**

Dividend $= 65$

Divisor $= 10$

Using the repeated subtraction method:

$65 \;-\; 13 = 52$

$52\;-\; 13 = 39$

$39\;-\; 13 = 26$

$26\;-\; 13 = 13$

$13\;-\; 13 = 00$

Here, 13 is subtracted 5 times from 65 and the remainder as 0.

Therefore, Sam needs 5 racks which will be fully filled.

**4. What is repeated subtraction?**

**Solution: **

Repeated subtraction is the process of subtracting a number from a large number until the end result is zero.

## Practice Problems on Repeated Subtraction

## Repeated Subtraction - Definition With Examples

### What will be the quotient if we divide $90 \div 45$ by repeated subtraction methods.

Subtract 45 from 90 repeatedly.

$90 \;–\; 45 =45$

$45 \;–\; 45=0$

Here, 45 is subtracted 2 times from 90 and remainder as 0.

Hence, $90 \div 45 = 2;\; 2$ is the quotient.

### What would be the remainder after dividing 8 by 7?

We will solve $8 \div 7$ by repeated subtraction.

$8 \;-\; 7 = 1$

Here, 7 is subtracted only once from 8 and remainder is 1.

The quotient is 1 and the remainder is also 1.

### What will be the quotient if we divide $29 \div 6$ using repeated subtraction?

Dividend $= 29$

Divisor $= 6$

Using the repeated subtraction method,

$29 \;-\; 6 = 23$

$23 \;-\; 6 = 17$

$17 \;-\; 6 = 11$

$11 \;-\; 6 = 5$

Therefore, $29 \div 6 = 4;\; 4$ is the quotient and 5 is the remainder.

### What will be the remainder, if we solve $55 \div 25$ by repeated subtraction method?

Dividend $= 55$

Divisor $= 25$

Subtract 15 from 55 repeatedly.

$55 \;-\;25 = 30$

$30 \;- \;25 = 5$

Here, 25 is subtracted 2 times from 55 and the remainder is 5.

Hence, $55 \div 25 =2;\; 2$ is the quotient and 5 is the remainder.

### What will be the quotient if we divide the number $20000 \div 5000$ using repeated subtraction?

Subtract 5000 from 20000 repeatedly.

$20000\;-\;5000 = 15000$

$15000\;-\;5000 = 10000$

$10000\;-\;5000 = 5000$

$5000\;-\;5000 = 0$

Here, 5000 is subtracted 4 times from 20000 and remainder is 0.

Hence, $20000 \div 5000=4;\; 4$ is the quotient.

## Frequently Asked Questions on Repeated Subtraction

**How to find the square root of a number using repeated subtraction?**

The square root of a number is the number that when multiplied to itself gives the original number as the product. When the divisor and the quotient are the same, leaving no remainder, then when can say that the square root of the dividend is the divisor.

Example: $4\;-\;2 = 2;\; 2\;-\;2 = 0$

Divisor $= 2$, Quotient $= 2$

Thus, square root of $4 = 2$

**What is the difference between subtraction and division?**

Repeated subtraction, also called division, is the process in which a small number is repeatedly subtracted from the large number until the remainder is 0 or less than the small number. Subtraction simply means taking away one number from another.

**What is repeated addition?**

Repeated addition is called multiplication.

Example: 4 times 5 $= 4 5 = 5 + 5 + 5 + 5 = 20$

**What is the quotient in the repeated subtraction?**

The number of times we subtract the same number until we get the remainder 0 or less than the number is the quotient in the repeated subtraction.