Like fractions – properties, comparison and examples

Like fractions are groups of fractions having the same denominator. In this article, we are going to perform algebraic operations on these groups of fractions.

How to identify Like fractions

A group of fractions are like fractions if they have the following properties:

1. Denominators of all the fractions in the group are equal
2. The fractions may be proper or improper.

Examples:

The denominator 7 is common.

The denominator 5 is common.

Comparison of Like fractions

In a group of like fractions, the fraction having the greater numerator is the greater one and vice-versa.

Hence, we can compare these fractions by comparing the numerators only as the denominators are the same.

Examples:

\text { a) } \frac{1}{7}, \frac{6}{7}

Both have the same denominators.

Since 1 < 6, we can say that \frac{1}{7}<\frac{6}{7}.

 \text { b) } \frac{12}{5}, \frac{6}{5}

Both have the same denominators.

Since 12 > 6, we can say that \frac{12}{5}>\frac{6}{5}.

Addition of like fractions

While doing the addition of fractions, it becomes easier if they have the same denominator.

Since the denominator is already the same, we have to just add the numerators to obtain the results. The denominator remains unchanged.

\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}

Examples:

\text { a) } \frac{5}{6}+\frac{2}{6}=\frac{5+2}{6}=\frac{7}{6}

\text { b) } \frac{1}{9}+\frac{4}{9}=\frac{1+4}{9}=\frac{5}{9}

Subtraction of like fractions

While subtracting fractions, it becomes easier if they have the same denominator.

Since the denominator is already the same, we have to just subtract the numerators to obtain the results. The denominator remains unchanged.

\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}

Examples:

a) \frac{5}{6}-\frac{2}{6}=\frac{5-2}{6}=\frac{3}{6}

b) \frac{7}{9}-\frac{4}{9}=\frac{7-4}{9}=\frac{3}{9}

Solved example

1. Arrange \left(\frac{1}{7}, \frac{6}{7}, \frac{5}{7}, \frac{11}{7}, \frac{10}{7}, \frac{3}{7}\right) in ascending order.

All the fractions have 7 as the denominator. 

Comparing the numerators of these fractions:

1 < 3 < 5 < 6 < 10 < 11

\Rightarrow \quad \frac{1}{7}<\frac{3}{7}<\frac{5}{7}<\frac{6}{7}<\frac{10}{7}<\frac{11}{7}

Hence the fractions in ascending order are  \frac{1}{7}, \frac{3}{7}, \frac{5}{7}, \frac{6}{7}, \frac{10}{7}, \frac{11}{7}.

2. Add the following fractions \frac{2}{5}, \frac{3}{5}, \frac{5}{5}, \frac{12}{5}, \frac{6}{5}.

\frac{2}{5}+\frac{3}{5}+\frac{5}{5}+\frac{12}{5}+\frac{6}{5}=\frac{2+3+5+12+6}{5}=\frac{28}{5}

Hence, the sum of all the fractions given above is \frac{28}{5}.