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 viceversa. 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 = \(1\frac {3}{4}\)
Subtraction of Fractions Related Topics
Check out these interesting articles to know more about the subtraction of fractions.
 Fractions
 Numerator
 Types of Fractions
 Multiplication of Fractions
 Division of Fractions
 Adding and Subtracting Fraction Worksheets for 4th Grade
 5th Grade Adding and Subtracting Fractions Worksheets
 Like Fractions Calculator
 Adding Fractions Calculator
 Fraction Calculator
Tips to Remember

Recall the steps to subtracting fractions with same denominator:
\(\begin{align} \frac {\text{Nr\(_1\)}}{ \text{Dr} }  \frac { \text{Nr\(_2\)} }{ \text{Dr}} = \frac{ \text{Nr\(_1\)}  \text{Nr\(_2\)} }{ \text{Dr} } \end{align}\) 
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.
Solved Examples

Example 1: Find the difference of 5/7 & 3/7.
Solution: The given fractions are like fractions. We subtract the numerators and retain the same denominator.
5/7  3/7 = (5  3)/7 = 2/7
Therefore, the difference is 2/7. 
Example 2: Subtract 2/5 from 2/3.
Solution: The given fractions are unlike fractions. We have to find the LCM of the denominators and convert 2/5 and 2/3 to equivalent fractions of same denominator and then subtract.
LCM of (3 , 5 = 15)
2/3  2/5 = (2/3 × 5/5)  (2/5 × 3/3)
= 10/15  6/15 = 4/15
Therefore, the difference is 4/15. 
Example 3: Subtract 1/3 from 3.
Solution:
3  1/3 = 3/1  1/3
(3/1 × 3/3)  (1/3) = 9/3  1/3 = 8/3
= \(2\frac{2}{3}\)
Therefore, the difference is \(2\frac{2}{3}\).
FAQs on Subtraction of Fractions
How to Subtract Fractions?
We can subtract like fractions and unlike fractions using the steps given below:
 For like fractions, subtract the numerators and retain the same denominator.
 For subtracting unlike fractions, take the LCM of the denominators and convert the fractions to like fractions and subtract them.
 Reduce to its lowest term if needed.
How to Subtract Fractions from Whole Numbers?
We can use the steps given below to subtract fractions from whole numbers.
 We convert the whole number into a fraction.
 Once it is done, we obtain two unlike fractions.
 Now, both we subtract the unlike fractions and the answer is obtained.
 The obtained answer is then converted into mixed fraction.
Let us see an example:
1  1/5 = 2/1  1/5
(2/1 × 5/5)  (1/5) = 10/5  1/5 = 9/5
= \(1\frac{4}{5}\)
How Do You Subtract Fractions with Different Denominators?
The fractions with different denominators can be subtracted using the steps below:
 First we take the LCM of denominators
 Now, the fractions are converted to their equivalents and both of them are like fractions.
 Hence, the fractions are subtracted as like fractions.
Why Do You Need Common Denominators to Subtract Fractions?
We always subtract like quantities and making denominators common makes the fractions like quantities. Hence, the common denominators are needed to subtract fractions.
How Do You Simplify Subtracting Fractions?
We can simplify subtracting fractions in the below ways:
 In case of like fractions, the fractions can be subtracted and the output can be simplified easily.
 For unlike fractions, the denominators are first made common and only then the fractions are subtracted. Once subtracted, the output can be simplified easily.
Let us see an example of it.
2/4  2/5 = (2/4 × 5/5)  (2/5 × 4/4)
= 10/20  8/20 = 2/20 = 1/10
How Do You Subtract Improper Fractions?
The improper fractions are subtracted similarly as in case of proper fractions:
 For like fractions, subtract the numerators and retain the same denominator.
 For subtracting unlike fractions, take the LCM of the denominators and convert the fractions to equivalent fractions and subtract them as like fractions.
Once the subtraction is done, we convert the fraction to a mixed number to write it in simplest form.