# Comparing Fractions - An Overview

Fraction is defined as a part of a whole or any number of equal parts.  Sometimes it is required to compare two fractions, in order to find out which is larger or smaller.

The following methods are used to compare fractions.

1. Using decimals
2. Conversion to like fractions

## Comparing fractions – Decimal method

In the decimal method, each fraction is converted into a decimal by directly dividing the numerator by denominator. After division, the decimal value is compared.

For example:

Which is smaller:$\frac{2}{4}$ or $\frac{5}{12}$?

Step 1: Convert each fraction into decimal.

$\frac{2}{4}$ = $0.5$

$\frac{5}{12}$ = $0.416$

Step 2: Compare decimal.

As 0.5 is greater than 0.416 therefore, $\frac{5}{12} ~\lt~ \frac{2}{4}$

Comparing fractions: Like fractions method

As we know every fraction is composed of two terms: Numerator and Denominator. The term on top is numerator and the term at the bottom is the denominator.

Example: In a fraction $\frac{3}{4}$ , 3 is the numerator and 4 is the denominator.

Like fractions can be compared easily as their denominator is same but to compare unlike fraction, it should be converted to like-fraction. Let us now see the method of comparison of both these types.

### Comparing like fractions :

Comparing fractions is very easy when two fractions have the same denominator.

Let us compare two fractions $\frac{3}{4}$ and $\frac{1}{4}$.

$\frac{3}{4}$ represents three parts out of four. The shaded region as shown below represents the required fraction.

Similarly, $\frac{1}{4}$ can be shown as below:

As the denominator is same, by comparing the numerator only, the larger fraction can be identified.

Here,$\frac{3}{4}~\gt~\frac{1}{4}$ as the numerator i.e. 3 in $\frac{3}{4}$ is greater than the numerator 1 in $\frac{1}{4}$.

#### Comparing unlike fractions

As the denominators in unlike fractions are different, therefore for comparing unlike fractions, we need to make the denominators same.

Let us take an example to understand the method of comparison of unlike fraction.

Consider the fractions, $\frac{3}{8}$ and $\frac{5}{12}$.The given fractions are unlike as the numerators and denominators are different. To compare them following steps are followed:

Step 1: Take LCM of denominators of given fractions i.e. 8 and 12 respectively.

(LCM is the smallest number which is a common multiple of given numbers)

24 is the least common multiple of  8 and 12.

Step 2: To convert the given fractions into like fractions, multiply numerator and denominator by ratio of LCM and denominator of the fraction

In $\frac{3}{8}$, multiply numerator and denominator by 3 = $\frac{3}{8}~\times~\frac{3}{8}$ = $\frac{9}{24}$

In $\frac{5}{12}$, multiply numerator and denominator by 2 = $\frac{5}{12}~\times~\frac{2}{2}$ = $\frac{10}{24}$

Step 3: Now, the denominators of both fractions are the same.

$\frac{9}{24}$, $\frac{10}{24}$

Now, the same method is followed for comparison i.e. method of comparison of like fractions. As numerator in $\frac{10}{24}$ is greater than the numerator in $\frac{9}{24}$.

Therefore $\frac{10}{24}~\gt~\frac{9}{24}$

$\Rightarrow~\frac{5}{12}~\gt~\frac{3}{8}$

Let us now see another example for a better insight

For example Madhu has 2 ½ pizza slices in her plate and Malini has 2¾ pizza slices in her plate. Out of the two, who has more pizza slices?

Solution:

Pizza in Madhu’s plate = $\frac{5}{2}$ = $\frac{10}{4}$

Pizza in Malini’s plate= $\frac{11}{4}$

Since, the numerator in fraction $\frac{11}{4}$ is greater than that in $\frac{10}{4}$, therefore $\frac{10}{4}~\gt~\frac{10}{4}$..

Thus, Malini has more pizza slices compared to Madhu.