Subtraction of Fractions

We have already discussed how we can add fractions. A fraction is a rational number in the form of a/b where b cannot be zero. In a fraction a/b a is known as the numerator and b as the denominator.

For example: – 7/5 is a fraction, where 7 (the upper part) is the numerator and 5
(the lower part) is the denominator.

Complete Tutorials on Fraction

Part 1: Fractions From Basics
Part 2: Fractions From Basics.
Part 3: Multiplication of Fractions

How can we  Subtract the Fractions?

Subtraction of fractions is not very easy. There are some methods to perform subtraction. The methods or the cases are: –

1. Subtracting fractions having like or the same denominator
2. Subtracting fractions having unlike or different denominator
3. Subtracting mixed fractions with the same denominator
4. Subtracting mixed fractions with different denominators
5. Subtracting fractions from whole numbers

In this module, we will discuss subtraction of the fractions with all five methods.

1. Subtraction of Fractions with the same Denominator

We can subtract the fractions with the same denominator using 3 simple steps. They are: –

Step 1 = Firstly, check if the denominators are the same or not.
Step 2= If denominators are the same, simply subtract the numerators.
Step 3 = Now, write the answer with the denominator.

Let us understand these steps more briefly with the help of an example: –

Example 1: 11/5 – 8/5

Step 1 = Check the denominators.
11/5 = denominator is 5.
8/5 = denominator is 5.
So, the denominators are same.

Step 2 = Now, the denominators are same. Subtract the numerators.
= 11 – 8 = 3

Step 3 = Write the answer with the denominator.
= 3/5

Example 2:  15/7 – 3/7

Step 1 = Check the denominators.
15/7 = denominator is 7.
03/7 = denominator is 7.
So, the denominators are same.

Step 2 = Now, the denominators are same. Subtract the numerators.
= 15 – 3 = 12

Step 3 = Write the answer with the denominator.
= 12/7

Read More : Remember Multiplication Tables of Any Number Using Mental Mathematics

2. Subtraction of Fractions with Different Denominators

We can easily subtract the fractions with different denominators using a few simple steps. They are: –

Step 1 = First, Find the LCM ( least common multiple) of the denominators.
Step 2 = Now, convert the fractions into equivalent fractions such that their denominators will be the same.
Step 3 = Now, as the denominators are the same, simply subtract the numerators.
Step 4 = write the answer with the denominator.

Let us understand these steps more briefly with the help of an example:

Example 1: 12/7 – 1/3

Step 1 = Find the LCM of 7 and 3, which is 21.
Step 2 = Now, convert the fractions into equivalent fractions such that their denominators will be the 21.
= 12/7 * 3/3 = 36/21
= 1/3 * 7/7 = 7/21

Step 3 = The denominators are same now, simply subtract the numerators.
= 36 – 7 = 29

Step 4 = Write the answer with the denominator.
= 29/21

Example 2: 3/7 – 2/5

Step 1 = Find the LCM of 7 and 5, which is 35.
Step 2 = Now, convert the fractions into equivalent fractions such that their denominators will be the 35.
= 3/7 * 5/5 = 15/35
= 2/5 * 7/7 = 14/35

Step 3 = The denominators are same now, simply subtract the numerators.
= 15 – 14 = 01

Step 4 = Write the answer with the denominator.
= 1/35

Read More : How to find HCF in 10 seconds

3. Subtraction of Mixed Fractions with the same Denominator

We can subtract the mixed fractions with the same denominator using 3 simple steps. They are: –

Step 1 = Firstly, convert the mixed fractions into improper fractions.
Step 2 = Denominators are same now, simply subtract the numerators.
Step 3 = Now, write the answer with the denominator.

Let us understand these steps more briefly with the help of an example: –

Example 1: 5 ^{1 / 3} – 2 ^{1 / 3}

Step 1 = Convert the mixed fractions into improper fractions.
5 ⅓ = 16/3 when changed to improper fraction.
Similarly,
2 ⅓ = 7/3.

Step 2 = Now, the denominators are the same. Subtract the numerators.
= 16 – 7 = 9

Step 3 = Write the answer with the denominator.
= 9/3 = 3

Example 2: 7 ^{2 / 3} – 4 ^{1 / 3}

Step 2 = Now, the denominators are the same. Subtract the numerators.
= 23 – 13 = 10

Step 3 = Write the answer with the denominator.
= 10/3

Read More : METHODS FOR SOLVING QUADRATIC EQUATION

4. Subtraction of Mixed Fractions with Different Denominators

We can add the mixed fractions with different denominators using a few simple steps. They are: –

Step 1 = Firstly, convert the mixed fractions into improper fractions.
Step 2 = Now, find the LCM ( least common multiple) of the denominators.
Step 3 = Convert the fractions into equivalent fractions such that their denominators will be the same.
Step 4 = Now, as the denominators are same, Subtract the numerators.
Step 5 = write the answer with the denominator.

Let us understand these steps more briefly with the help of an example: –

Example 1: 8 ^{1 / 3} – 3 ^{1 / 3}

Step 1 = Convert the mixed fractions into improper fractions.
8 ⅓ = 25/3 when changed to improper fraction.
Similarly,
3 ⅕ = 16/5.

Step 2 = Find the LCM of 3 and 5, which is 15.

Step 3 = Now, convert the fractions into equivalent fractions such that their denominators will be the 15.
= 25/3 * 5/5 = 125/15
= 16/5 * 3/3 = 48/15

Step 4 = The denominators are same now, simply add on the numerators.
= 125 – 48 = 77

Step 5 = Write the answer with the denominator.
= 77/15

Example 2: 5  ^{1 / 3} – 2 ^{1 / 5}

Step 1 = Convert the mixed fractions into improper fractions.
5 ⅓ = 16/3 when changed to improper fraction.
Similarly,
2 ⅕ = 11/5.

Step 2 = Find the LCM of 3 and 5, which is 15.

Step 3 = Now, convert the fractions into equivalent fractions such that their denominators will be the 15.
= 16/3 * 5/5 = 80/15
= 11/5 * 3/3 = 33/15

Step 4 = The denominators are same now, simply add on the numerators.
= 80 – 33 = 47

Step 5 = Write the answer with the denominator.
= 47/15

Read More : Find your LCM in 10 seconds

5. Subtraction of Fractions with Whole Numbers

We can subtract the fractions with the whole numbers using a few simple steps. They are: –

Step 1 = Firstly, convert the whole number in the form of a/b (fraction) . 3 can be written as 3/1 in fraction.
Step 2 = Now, find the LCM ( least common multiple) of the denominators.
Step 3 = Convert the fractions into equivalent fractions such that their denominators will be the same.
Step 4 = Now, as the denominators are same, subtract the numerators.
Step 5 = write the answer with the denominator.

Let us understand these steps more briefly with the help of an example: –

Example 1: 8 – 2/5

Step 1 = Convert the whole number into fraction.
8 = 8/1 when changed to a fraction..

Step 2 = Now, find the LCM of 1 and 5, which is 5 itself.

Step 3 = Now, convert the fractions into equivalent fractions such that their denominators will be the 5.
= 8/1 * 5/5 = 40/5
= 2/5 * 1/1 = 2/5

Step 4 = The denominators are same now, subtract the numerators.
= 40 – 2 = 38

Step 5 = Write the answer with the denominator.
= 38/5

Example 2: 9 – 3/7

Step 1 = Convert the whole number into fraction.
9 = 9/1 when changed to a fraction..

Step 2 = Now, find the LCM of 1 and 7, which is 7 itself.

Step 3 = Now, convert the fractions into equivalent fractions such that their denominators will be the 5.
= 9/1 * 7/7 = 63/7
= 3/7 * 1/1 = 3/7

Step 4 = The denominators are same now, subtract the numerators.
= 63 – 3 = 60

Step 5 = Write the answer with the denominator.
= 60/7

In the next module, we will learn how to multiply and divide the fractions.

Read More : Sum of cubes of n natural numbers

 Practice :

1. 98/5 – 13/5
2. 33/23 – 22/23
3. 72/7 – 14/9
4. 54/11 – 3/13
5. 32 ⅕ – 13 ⅕
6. 41 ¼ – 23 ¼
7. 13 ½ – 4 ⅕
8. 41 ⅔ – 12 ⅕
9. 7 – 2/9
10. 23 – 11/5