Subtraction of Fractions

Subtraction of Fractions :

Subtraction of fractions is an arithmetic operation to be performed where fractions are involved in the expression. To subtract two like fractions we have to subtract their numerators, while to subtract two unlike fractions, we have to first convert them into like fractions by taking the LCM of the denominators. We can subtract a whole number and fraction too by writing the whole number in fractional form, for example, 3 = 3/1.

How to Subtract Fractions?

Fractions are referred as a part of a whole. We can find the difference between two like fractions, unlike fractions and fractions and whole numbers. Before moving to the subtraction of fractions, let us revise about fractions here first.

We can easily add or subtract two fractions. There are two cases that come up while learning subtraction of fractions and those are subtracting like fractions and unlike fractions. Let’s learn about each in detail.

Subtracting Fractions with Like Denominators

The fractions with like denominators can be subtracted by subtracting their numerators. The steps to subtract the fractions with like denominators are:

Subtract the numerators.
Write the common denominator as the denominator of the resultant fraction.
Now, the obtained answer can be reduced to its lowest form, if needed.

Let us subtract the fractions 4/5 and 2/5 using rectangular models. We represent 4/5 in this model by shading 4 out of 5 parts. We will further shade out 2 parts from our shaded parts of the model to represent removing 2/5.

We are now left with 2 parts in the shaded parts of the model.Thus the subtraction of the fractions is given as (4/5 – 2/5) = 2/5.

Subtract Fractions with Different Denominators

The steps to approach the problem of subtraction of unlike fractions are,

First we take the LCM of the denominators.
We convert the given fractions to equivalent fractions with the denominator as the LCM.
Now we subtract the numerators.

Let us understand how to subtract unlike fractions using the area model.
(2/5 – 1/3)
This indicates that we have to remove (1/3)^rd part from 2/5. We can represent

As our model is divided into 15 parts, this is our denominator. This is the LCM of the denominators of the given fraction. As we need to remove 1/3 from 2/5, we will move the selected three parts which are not part of the 2/5, to remove it from 2/5. We see that there is only 1 part of the remaining which is not shaded out. Thus, the answer is given as, 2/5 – 1/3 = 1/15.

Subtracting Fractions With Whole Numbers :

Similar to subtracting two fractions, we can also subtract a fraction from a whole number and vice-versa. Every whole number can be written in the fractional form by writing 1 as the denominator, for example, we can write 7 as 7/1. So, to subtracting a fraction and a whole number we first make them write in fractional form, then we can easily find the difference by applying the same rules as subtracting two unlike fractions. To subtract a fraction from a whole number, consider the following example: 2 – 1/4

We convert the whole number to a fractional form as, 2 = 2/1
Now we subtract them like unlike fraction

2/1 – 1/4 = (2/1 × 4/4) – (1/4)
= 8/4 – 1/4 = 7/4 = 134134

Tips to Remember

Recall the steps to subtracting fractions with same denominator:
Nr1Dr−Nr2Dr=Nr1−Nr2DrNr1Dr−Nr2Dr=Nr1−Nr2Dr
Steps to subtracting fractions with different denominators:a) Convert the given fractions to like fractions by taking the LCM of the denominator.
b) Find the equivalent fractions of the given fractions whose denominator is the LCM.
c) Subtract the numerators and retain the same denominator.
For unlike fractions, never subtract the numerators and denominators directly.
(3/5 – 2/3) ≠ (1/2)
When subtracting unlike fractions, it is not necessary to find the LCM of the denominators. Any common multiple will do. So, simply multiplying the two denominators gives us a common multiple. This may lead to larger looking numbers, but it can be reduced to its lowest form.