Last modified on June 28th, 2024

chapter outline

 

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

Adding and Subtracting

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

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

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

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

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

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

Like Fractions vs. Unlike Fractions

BasisLike FractionsUnlike Fractions
DenominatorsSame.Different.
ComparisonNumerators are compared directly.Converted to like fractions for comparing.
Addition / SubtractionThe numerators are added by keeping the denominators the same.Converted to the like fractions, and the numerators are then added.
Examples${\dfrac{2}{9}}$, ${\dfrac{5}{9}}$, ${\dfrac{4}{9}}$, and ${\dfrac{7}{9}}$${\dfrac{7}{9}}$, ${\dfrac{3}{5}}$, ${\dfrac{2}{7}}$, and ${\dfrac{6}{11}}$

Solved Examples

Add the fractions:
${\dfrac{2}{13}+\dfrac{7}{13}+\dfrac{5}{13}}$

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 ${\dfrac{4}{13}}$ 
${\dfrac{4}{11}}$ 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, ${\dfrac{12}{5}-\dfrac{9}{5}+\dfrac{1}{5}}$
= ${\dfrac{12-9+1}{5}}$
= ${\dfrac{4}{5}}$

Last modified on June 28th, 2024