Comparing Fractions

A 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. In Mathematics, there are two methods used for comparing fractions. They are

1. Decimal Method
2. Same Denominator Method

Let us discuss the two methods of comparing fractions using like fraction and unlike fraction with examples in detail.

Comparing Fractions Using Decimal Method

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

Example for Comparing Fractions using Decimal Method

Which of the following fraction is smaller: 2/4 or 5/12?

Step 1: Convert each fraction into a decimal value.

2/4 = 0.5

5/12 = 0.416

Step 2: Compare the decimal value.

As 0.5 is greater than 0.416 therefore, 5/12 is smaller than 2/4.

Comparing Fractions Using the Same Denominator Method

As we know every fraction is composed of two terms: Numerator and Denominator. The term on top is the numerator and the term at the bottom is the denominator. For example, consider a fraction of 3/4. Here, 3 is the numerator and 4 is the denominator.

Example for Comparing Fractions Using the Same Denominator Method:

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

Comparing Fractions with the Same Denominator

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

Let us compare two fractions: 3/4 and 1/4

3/4 represents three parts out of four. The shaded region as shown below represents the required fraction.

Similarly, 1/4 can be shown as below:

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

Here, 3/4 is greater than 1/4 as the numerator i.e. the numerator 3 in the fraction 3/4 is greater than the numerator 1 in the fraction 1/4.

This is a way to compare the fractions when it contains the same denominator.

Comparing Fractions With Different Denominators

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

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

Consider the fractions, 3/8 and 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 the numerator and denominator by the ratio of LCM and denominator of the fraction

In 3/8, multiply the numerator and denominator by 3 = (3 ×3)/(8 ×3) = 9/24

In 5/12, multiply the numerator and denominator by 2 = (5 ×2)/ (12  × 2) = 10/24

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

i.e., 9/24 and 10/24

Now, the same method is followed for comparison i.e. method of comparison of like fractions.

As the numerator 10 in the fraction 10/24  is greater than the numerator 9 in the fraction 9/24.

Therefore, 10/24 is greater than 9/24

⇒ 5/12 is greater than 3/8.

These are the different methods of comparing fractions.

Video Lesson on Comparing Fractions

Comparing Fractions Example

Let us see another example for a better insight

Question:

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

Solution:

First, convert the mixed fractions into the simple fraction

Pizza in Madhu’s plate =5/2

Pizza in Malini’s plate=  11/4

Since the obtained fractions are unlike fractions, convert them into the like fractions.

10/4 and 11/14

Since the numerator in fraction 11/4 is greater than that in 10/4.

Hence, Malini has more pizza slices compared to Madhu.

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