**What are Unlike Fractions?**

The** fraction with different denominators** are called **unlike fraction**.

The fraction is made of two parts, namely numerator and denominator.

The upper part is called **numerator** and lower part is called **denominator**.

Hence, the unlike fractions have different number in lower part.

For Example;

In the above image, all the fractions have different denominator. Hence, they are examples of unlike fractions.

**Adding Unlike Fraction**

Understand that unlike fractions have different denominators.

In order to add the fractions, **we have to first make the common denominator** and then do the addition.

For adding unlike fractions, **follow the below steps**;

(a) Take the LCM of denominators

(b) Multiply the fractions to make denominator equal to LCM value.

(c) Add the numerators and keep the denominator as it is.

**Example 01**

Add the fractions \mathtt{\frac{2}{3} \ \&\ \frac{4}{5}}

**Solution**

Both the fractions have different denominator so they are unlike fraction.

Follow the below steps;**(a) Take LCM of denominators**

LCM (3, 5) = 15

**(b) Multiply the fractions to make denominator 15**.**Fraction 2/3**

Multiply numerator and denominator by 5

\mathtt{\Longrightarrow \ \frac{2\times 5}{3\times 5} \ =\ \frac{10}{15}}

**Fraction 4/5**

Multiply numerator and denominator by 3.

\mathtt{\Longrightarrow \ \frac{4\times 3}{5\times 3} \ =\ \frac{12}{15}}

Hence, we got the fraction 10/15 and 12/15.

Both the fractions have same denominator.

**(c) Add the numerator and keep the same denominator**

Hence, 22/15 is the solution.

**Example 02**

Add the unlike fractions; \mathtt{\frac{5}{7} \ \&\ \frac{8}{3}}

**Solution**

Follow the below steps;

**(a) Find LCM of denominator**

LCM ( 7, 3 ) = 21

**(b) Multiply fractions to make denominator 21****Fraction 5/7**

Multiply numerator and denominator by 3

\mathtt{\Longrightarrow \ \frac{5\times 3}{7\times 3} \ =\ \frac{15}{21}}

**Fraction 8/3**

Multiply numerator and denominator by 7

\mathtt{\Longrightarrow \ \frac{8\times 7}{3\times 7} \ =\ \frac{56}{21}}

We got the fractions 15/21 and 56/21.

Both the fractions have same denominator, hence they have become like fractions.

**(c) Add the numerator and leave the denominator as it is.**

Hence, 73/21 is the solution.

**Subtracting Unlike Fraction**

Subtraction of unlike fraction is done by first converting the numbers into like fractions and then subtracting the numerators to get the final solution.

To subtract the unlike fractions, **follow the below steps;**

(a) Find the LCM of denominators

(b) Multiply the fractions to make denominator same as LCM.

(c) Now subtract the numerator and keep the denominator same.

**Example 01**

Subtract the fractions \mathtt{\frac{3}{5} \ \&\ \frac{2}{11}}

**Solution**

Follow the below steps;

**(a) Find LCM of denominators**.

LCM ( 5, 11 ) = 55**(b) Multiply the fractions to make denominator 55**

**Fraction 3/5**

Multiply numerator and denominator by 11.

\mathtt{\Longrightarrow \ \frac{3\times 11}{5\times 11} \ =\ \frac{33}{55}}

**Fraction 2/11**

Multiply numerator and denominator by 5

\mathtt{\Longrightarrow \ \frac{2\times 5}{11\times 5} \ =\ \frac{10}{55}}

Now we got the like fractions 33/55 and 10/55

**(c) Subtract the numerators and keep the denominator as it is.**

Hence, 23/55 is the solution.

**Example 02**

Subtract the fractions, \mathtt{\frac{9}{2} \ \&\ \frac{7}{9}}

**Solution**

The given fractions 9/2 & 7/9 have different denominators.

First convert the numbers into like fraction and then do the subtraction.

Follow the below steps;

**(a) Find LCM of denominators**

LCM ( 2, 9 ) = 18

(b) Multiply the fractions to make denominator 18

**Fraction 9/2**

Multiply numerator and denominator by 9

\mathtt{\Longrightarrow \ \frac{9\times 9}{2\times 9} \ =\ \frac{81}{18}}

**Fraction 7/9**

Multiply numerator and denominator by 2

\mathtt{\Longrightarrow \ \frac{7\times 2}{9\times 2} \ =\ \frac{14}{18}}

Now we got the like fractions, 81/18 & 14/18.

**(c) Subtract the numerators**

Hence, 67/18 is the solution.