# Like Fractions

When two or more fractions have the same denominator, they are called like fractions.

${\dfrac{2}{3}}$, ${\dfrac{5}{3}}$, and ${\dfrac{7}{3}}$ are a few examples of like fractions.

Thus, we can easily compare and perform arithmetic operations such as addition and subtraction involving like fractions.

## Comparing

We look at the numerators to compare the like fractions, which share the same denominators. The fraction with the larger numerator is greater.

Let us compare the like fractions ${\dfrac{2}{7}}$ and ${\dfrac{5}{7}}$

Since 5 > 2

Thus, ${\dfrac{5}{7}}$ > ${\dfrac{2}{7}}$

We can also compare ${\dfrac{2}{7}}$ < ${\dfrac{5}{7}}$ by representing them in blocks.

This shows the shaded region for ${\dfrac{2}{7}}$ is less than the shaded region for ${\dfrac{5}{7}}$

Thus, ${\dfrac{2}{7}}$ < ${\dfrac{5}{7}}$

To add two or more like fractions, we directly add the numerators by keeping the denominators the same.

Let us add ${\dfrac{2}{7}+\dfrac{5}{7}}$

${\dfrac{2}{7}+\dfrac{5}{7}}$

= ${\dfrac{2+5}{7}}$

= ${\dfrac{9}{7}}$

Similar to addition, when subtracting two like fractions, we directly subtract the numerators by keeping the denominators the same.

Let us subtract ${\dfrac{11}{3}-\dfrac{4}{3}}$

${\dfrac{11}{3}-\dfrac{4}{3}}$

= ${\dfrac{11-4}{3}}$

= ${\dfrac{7}{3}}$

## Multiplying and Dividing

When multiplying two or more like fractions, we multiply the numerators and the denominators separately and then reduce it into its simplest form if needed.

On multiplying ${\dfrac{4}{3}\times \dfrac{2}{3}}$, we get

${\dfrac{4}{3}\times \dfrac{2}{3}}$

= ${\dfrac{4\times 2}{3\times 3}}$

= ${\dfrac{8}{9}}$

To divide a like fraction by another like fraction, we multiply the first fraction by the reciprocal of the second.

On dividing ${\dfrac{7}{2}\div \dfrac{9}{2}}$, we get

${\dfrac{7}{2}\div \dfrac{9}{2}}$

= ${\dfrac{7}{2}\times \dfrac{2}{9}}$

= ${\dfrac{7\times 2}{2\times 9}}$

= ${\dfrac{14}{18}}$

= ${\dfrac{7}{9}}$

## Solved Examples

${\dfrac{2}{13}+\dfrac{7}{13}+\dfrac{5}{13}}$

Solution:

Here, ${\dfrac{2}{13}+\dfrac{7}{13}+\dfrac{5}{13}}$
= ${\dfrac{2+7+5}{13}}$
= ${\dfrac{14}{13}}$

Which of the following pairs are like fractions:
${\dfrac{4}{11}}$, ${\dfrac{7}{13}}$, ${\dfrac{4}{13}}$, ${\dfrac{8}{11}}$, ${\dfrac{1}{7}}$, and ${\dfrac{4}{7}}$

Solution:

Here, the like fractions are:
${\dfrac{7}{13}}$ and ${\dfrac{4}{13}}$Â
${\dfrac{4}{11}}$ and ${\dfrac{8}{11}}$
${\dfrac{1}{7}}$ and ${\dfrac{4}{7}}$

Find the value of ${\dfrac{12}{5}-\dfrac{9}{5}+\dfrac{1}{5}}$

Solution:

Here, ${\dfrac{12}{5}-\dfrac{9}{5}+\dfrac{1}{5}}$
= ${\dfrac{12-9+1}{5}}$
= ${\dfrac{4}{5}}$