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: –

- Subtracting fractions having like or the same denominator
- Subtracting fractions having unlike or different denominator
- Subtracting mixed fractions with the same denominator
- Subtracting mixed fractions with different denominators
- 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 }

^{1 / 3}– 2

**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}

^{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}

^{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}

^{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 :

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