Repeated Subtraction

Repeated subtraction is the process of subtracting a number from a large number until the end result is zero. This process is usually seen and used while numbers are divided and is a good way to introduce division to smaller grades. Let us learn more about repeated subtraction, ways to divide using repeated subtraction, and solve a few examples to understand the concept better.

Repeated subtraction is defined as the process of subtracting the same number from the large number until the end result or remainder is zero or smaller than the number being subtracted. This process is also called division. In other words, when the same number is subtracted from the other number until the remainder is zero or until it is smaller than the actual number is called repeated subtraction and this process can also be expressed in the division form. For example, 25 - 5 = 20, 20 - 5 = 15, 15 - 5 = 10, 10 - 5 = 5, 5 - 5 = 0. This means the number is subtracted 5 times and can be written in division form as 25 ÷ 5 = 5.

Division Definition

Division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. The process is also called repeated subtraction. Division is used in multiplication or long division or short division or repeated subtraction. There are four parts of the division, which are dividend, divisor, quotient, and remainder.

Repeated subtraction can be a useful method to teach younger students the process of basic division. There are two simple methods of using this process, they are:

1. Repeated subtraction can be considered as a process of jumping backward from the actual number until we get the required answer. And the number of times the same number is subtracted is the remainder when it is used in division form. For example, let us subtract 12 - 3 using the number line. The number of times 3 is subtracted to obtain zero is the remainder when divided. 12 - 3 = 9, 9 - 3 = 6, 6 - 3 = 3, 3 - 3 = 0. 12 ÷ 3 = 4. Look at the image below to understand it better.

2. Repeated subtraction in division is also used when the remainder is less than the actual number and does not necessarily have to be zero. For example, 16 - 3 = 13, 13 - 3 = 10, 10 - 3 = 7, 7 - 3 = 4, 4 -3 = 1. Here, the remainder or end result is 1. Since it is lesser than 3, we can stop repeated subtraction.

Repeated subtraction can be used in solving division problems just as how repeated addition is used to solve multiplication problems. While dividing any numbers, the four parts of division is taken under consideration i.e. dividend, divisor, quotient, and remainder. The steps used in division by repeated subtraction are:

• Identify the dividend and divisor. The dividend is the number that is divided by the divisor and the divisor is the number by which divided is to be divided.
• Start subtracting the divisor from the dividend.
• Once the difference is obtained, subtract the divisor again with that number.
• Repeat the subtraction process until you get a number that is less than the divisor or obtain zero.
• The number of times the subtraction process is completed is called the quotient.
• The number that is left at the end of subtraction is called the remainder.

Let us look at an example to understand this better.

Example: Divide 120 ÷ 15 by repeated subtraction method.

Solution:

Dividend = 120
Divisor = 15
Subtract 15 from 120 repeatedly.
120 – 15 = 105
105 – 15 = 90
90 – 15 = 75
75 – 15 = 60
60 – 15 = 45
45 – 15 = 30
30 – 15 = 15
15 – 15 = 0
Here, 120 is subtracted 8 times from 15 with remainder as 0. Hence, 120 ÷ 15 = 8, 8 is the quotient.

Related Topics

Listed below are a few topics related to repeated subtraction, take a look!

• Multiplication
• Addition and Subtraction
• Subtraction With Regrouping
• Binary Subtraction
• Dividend Divisor Quotient Remainder Formula

What is Repeated Subtraction Called?

Repeated subtraction is also called division. It is the method that subtracts the entire number from a group.

What is Repeated Subtraction with Example?

Repeated subtraction is the process of subtracting a number continuously from the large number until the remainder is zero or lesser than the actual number. For example, 20 - 4 = 16, 16 - 4 = 12, 12 - 4 = 8, 8 - 4 = 4, 4 - 4 = 0. Hence, 20 is subtracted 5 times with the remainder as zero.

How to Do Repeated Subtraction?

Repeated subtraction is done by subtracting the divisor by the dividend continuously until the remainder is zero or lesser than the dividend. This process can also be used while dividing numbers and the number of times the same number is subtracted is the remainder when it is used in division form. For example, 32 - 4 = 28, 28 - 4 = 24, 24 - 4 = 20, 20 - 4 = 16, 16 - 4 = 12, 12 - 4 = 8, 8 - 4 = 4, 4 - 4 = 0. Here, 32 is subtracted 8 times from 4 with remainder as 0. Hence, in the division form it is written as 32 ÷ 4 = 8.

Why is Repeated Subtraction Important?

Repeated subtraction is important in teaching the method of division to younger students. It acts as the introductory to division that can be understood in a simpler and easy manner. Repeated subtraction is used to solve division problems by subtracting the divisor from the dividend until the remainder is less than the divisor.

How to Find Square Root by Repeated Subtraction?

The square root of a number is the number that when multiplied to itself gives the original number as the product. We can also say that sum of the first n odd natural numbers is n². One of the methods to find the square root of a number is by repeated subtraction. Let us look at an example, square root of 169. Start from 169 and keep subtracting the successive odd numbers till we obtain zero. The total numbers we subtract is the square root of 169.

• 169 - 1 = 168
• 168 - 3 = 165
• 165 - 5 = 160
• 160 - 7 = 153
• 153 - 9 = 144
• 144 -11 = 133
• 133 -13 = 120
• 120 -15 = 105
• 105 - 17 = 88
• 88 - 19 = 69
• 69 - 21 = 48
• 48 - 23 = 25
• 25 - 25 = 0

Thus starting from 169, we have subtracted 13 times to obtain 0. Thus, the square root of 169 is 13.