# Unlike Fraction

## 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.

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.

(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.

(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

(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

(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.

(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.