Fractions having the same denominators but different numerators are known as like fractions. $\frac{5}{12}$ , $\frac{7}{12}$ , $\frac{8}{12}$ , $\frac{11}{12}$ ........... are called as like fractions.

There are a number of basic operations that can be performed on like fractions. Some of them are as follows:

  • Adding like Fractions
  • Subtracting Like Fractions
  • Multiplying Like Fractions
  • Comparing Like Fractions

Fractions such as $\frac{1}{5}$ and $\frac{3}{5}$ are like fractions because they have a common denominator. In the above example, the common denominator is 5.

In other words, fractions with like denominators are categorized as like fractions. Performing any mathematical operations on like fractions is comparatively easier as we can make use of the common denominator for fraction operations like addition, subtraction, multiplication and division.

For adding two like fractions, the numerators are added and the denominators remain the same.

Adding fractions with like denominators (like fractions) can be done by following the steps given below:
Step 1: Add the numerators
Step 2: Retain the common denominator.
Step 3: Sum of the fractions = $\frac{(Sum\ of\ Numerators)}{(Common\ Denominator)}$

Therefore, $\frac{a}{b}$ + $\frac{c}{b}$ = $\frac{(a+c)}{b}$

Examples for adding like fractions

Given below are some examples on adding like fractions

Example 1:

Add $\frac{2}{7}$ and $\frac{3}{7}$

Solution:

We know $\frac{a}{b}$ + $\frac{c}{b}$ = $\frac{(a+c)}{b}$

Therefore, $\frac{2}{7}$ + $\frac{3}{7}$ = $\frac{(2+3)}{7}$

= $\frac{5}{7}$

Example 2:

Add $\frac{4}{11}$ , $\frac{5}{11}$ and $\frac{7}{11}$

Solution:

We know $\frac{a}{b}$ + $\frac{c}{b}$ = $\frac{(a+c)}{b}$

Therefore, $\frac{4}{11}$ + $\frac{5}{11}$ + $\frac{7}{11}$ =

$\frac{(4+5+7)}{11}$

= $\frac{16}{11}$

Subtracting fractions with like denominators can be explained as follws:

Consider the following figure. The rectangle is divided into four equal parts and three of them are shaded, two in red and one in yellow. We can say that a $\frac{3}{4}$ of the rectangle is shaded.

Subtraction of Like Fractions
Like Fractions Subtraction

Now, let us unshade one of the shaded areas. That is, $\frac{1}{4}$ of the rectangle is unshaded.

Subtracting Like Fractions
We are left with $\frac{2}{4}$ of the rectangle shaded. In other words, we can write this as,

$\frac{3}{4}$ - $\frac{1}{4}$ = $\frac{2}{4}$

This is the basic principle of subtraction of like fractions. We have to subtract the numerators and retain the same denominator.

$\frac{a}{b}$ - $\frac{c}{b}$ = $\frac{(a-c)}{b}$

Examples for subtracting like fractions

Given below are some examples on subtracting like fractions

Example 1:

Simplify $\frac{4}{7}$ - $\frac{3}{7}$

Solution:

We know $\frac{a}{b}$ - $\frac{c}{b}$ = $\frac{(a-c)}{b}$

Therefore,

$\frac{4}{7}$ - $\frac{3}{7}$ = $\frac{(4-3)}{7}$

= $\frac{1}{7}$

Example 2:

Simplify $\frac{7}{3}$ - $\frac{2}{3}$

Solution:

We know $\frac{a}{b}$ - $\frac{c}{b}$ = $\frac{(a-c)}{b}$

Therefore,

$\frac{7}{3}$ - $\frac{2}{3}$ = $\frac{(7-2)}{3}$

= $\frac{5}{3}$

The procedure for multiplying like fractions is as follows:

1. Multiply the numerators of both the fractions
2. Multiply the denominators of both the fractions
3. Write the product fraction by placing the product of numerators over the product of the denominators
4. Simplify the fraction by canceling the common factors in the numerator and the denominator.
5. Write the fraction in the lowest terms.

Let us look at few examples on multiplying fractions with like denominators.

Examples for multiplying like fractions

Given below are some examples on multiplying like fractions

Example 1:

Find the product of $\frac{2}{4}$ and $\frac{3}{4}$

Solution:

In the fractions $\frac{2}{4}$ and $\frac{3}{4}$

The product of the numerator is 2 x 3 = 6
The product of the denominator is 4 x 4 = 16

Now, place the product of numerator over the product of the denominator

$\frac{2}{4}$ X $\frac{3}{4}$ = $\frac{6}{16}$
Reducing the product fraction into the simplest form, we get

$\frac{6}{16}$ = $\frac{(2\times3)}{(2\times8)}$ = $\frac{3}{8}$

Therefore, the product of $\frac{2}{4}$ and $\frac{3}{4}$ is $\frac{3}{8}$

Example 2:

Find the product of $\frac{5}{6}$ and $\frac{4}{6}$

Solution:

In the fractions $\frac{5}{6}$ and $\frac{4}{6}$

The product of the numerator is 5 x 4 = 20
The product of the denominator is 6 x 6 = 36

Now, place the product of the numerator over the product of the denominator

$\frac{5}{6}$ X $\frac{4}{6}$ = $\frac{20}{36}$

Reducing the product fraction into the simplest form, we get

$\frac{20}{36}$ = $\frac{2\times10}{2\times18}$ = $\frac{10}{18}$

Therefore, the product of $\frac{5}{6}$ and $\frac{4}{6}$ is $\frac{10}{18}$

While comparing two like fractions, the one with the greatest numerator is greater than the one with the smaller denominator. Let us look at few examples on comparing fractions with like denominators.

Examples for comparing like fractions:

Given below are some examples for comparing like fractions

Example 1:

Compare the two fractions $\frac{2}{4}$ and $\frac{3}{4}$

Solution:

In the fractions $\frac{2}{4}$ and $\frac{3}{4}$, the numerator of $\frac{3}{4}$ is greater than the numerator of $\frac{2}{4}$.

Therefore, $\frac{3}{4}$ is greater than $\frac{2}{4}$. That is, $\frac{3}{4}$ > $\frac{2}{4}$

Example 2:

Compare the two fractions $\frac{4}{10}$ and $\frac{5}{10}$

Solution:

In the fractions $\frac{4}{10}$ and $\frac{5}{10}$, the numerator of $\frac{5}{10}$ is greater than the numerator of $\frac{4}{10}$

Therefore, $\frac{5}{10}$ is greater than $\frac{4}{10}$. That is, $\frac{5}{10}$ > $\frac{4}{10}$

or

$\frac{1}{2}$ > $\frac{2}{5}$

Given below are some examples on like fractions.

Example 1:

Add $\frac{8}{9}$ and $\frac{3}{9}$

Solution:

Given $\frac{8}{9}$ and $\frac{3}{9}$

We know $\frac{a}{b}$ + $\frac{c}{b}$ = $\frac{(a+c)}{b}$

Therefore, $\frac{8}{9}$ + $\frac{3}{9}$ = $\frac{(8+3)}{9}$
= $\frac{11}{9}$

Example 2:

Subtract $\frac{13}{8}$ and $\frac{10}{8}$

Solution:

Given $\frac{13}{8}$ and $\frac{10}{8}$

We know $\frac{a}{b}$ - $\frac{c}{b}$ = $\frac{(a-c)}{b}$

Therefore, $\frac{13}{8}$ - $\frac{10}{8}$ = $\frac{13-10}{8}$ = $\frac{3}{8}$

Example 3:

Find the product of $\frac{11}{7}$ and $\frac{2}{7}$

Solution:

Given $\frac{11}{10}$ and $\frac{2}{10}$

In the fractions $\frac{11}{10}$ and $\frac{2}{10}$

The product of the numerators is 11 $\times$ 2 = 22