Comparing Fractions: Easy Methods, Rules and Examples

Comparing Fractions is determining if a fraction is greater than, less than or equal to another fraction. It is an important math skill for solving problems involving measurements, ratios and everyday calculations. This guide will teach you the different methods to compare fractions like fractions, unlike fractions, fractions with different denominators with clear examples and practice questions.

Table of Contents

• What is Comparing Fractions?
• How to Compare Fractions?
• Comparing Fractions with Like Denominator
• Comparing Fractions with Unlike Denominator
• Comparing Fractions Using the Decimal Method
• Comparing Fractions Using Cross Multiplication
• Practice Questions on Comparing Fractions
• Frequently Asked Questions of Comparing Fractions

What is Comparing Fractions?

Comparing fractions simply means checking which of two or more fractions is bigger, smaller, or if they are equal, using the same greater than, less than and equal to signs we already use for whole numbers.

For example: 3/5 > 3/8

How to Compare Fractions?

There is no single formula for comparing every kind of fraction. Instead, you pick a method depending on what the fractions look like.

Comparing Fractions with Like Denominator

When two fractions already have the same denominator, both fractions are being cut out of a whole that is divided into the same number of parts, the one with more parts shaded is simply the larger fraction.

1. Check that both denominators are equal.

2. Compare only the numerators.

3. The fraction with the bigger numerator is the bigger fraction. If the numerators match too, the fractions are equal.

Example: Riya scored 7/12 marks out of the total weightage in her unit test, and Farhan scored 9/12 marks out of the same weightage. Whose share was higher?

Solution: 

Both fractions have 12 as the denominator, so we simply compare the numerators. 

Since 9 > 7, Farhan's share, 9/12, is greater than Riya's share, 7/12.

$\frac{9}{12} > \frac{7}{12}$

Comparing Fractions with Unlike Denominator

When two fractions have different denominators, we compare the fractions using LCM method.

1. Find the LCM of the two denominators.

2. Work out what each denominator needs to be multiplied by to reach the LCM.

3. Multiply the numerator and denominator of each fraction by that same number.

4. Now that the denominators match, compare the new numerators.

Example: Anaya's family used 3/4 kg of rice on Monday and 5/6 kg of rice on Tuesday. On which day did they use more rice?

Solution: 

Step 1: Find the least common multiple (LCM) of 4 and 6.

LCM(4, 6) = 12.

Step 2: Convert both fractions to equivalent fractions with a denominator of 12.

3/4 = 9/12 (multiply the numerator and denominator by 3)

5/6 = 10/12 (multiply the numerator and denominator by 2)

Step 3: Compare the equivalent fractions.

$\frac{10}{12} > \frac{9}{12}$

Since 5/6 kg > 3/4 kg, Anaya's family used more rice on Tuesday.

Comparing Fractions Using the Decimal Method

With the decimal method we just change each fraction to a decimal by dividing the numerator by a denominator and then compare the decimal values.

1. Divide the numerator of each fraction by its own denominator.

2. Write both answers as decimals, up to two or three places.

3. Compare the decimal numbers directly.

Example: Vihaan spent 7/10 of his ₹200 pocket money on a notebook, while Zara spent 9/15 of her ₹200 pocket money on stationery. Who spent a larger fraction of their money?

Solution: Convert both fractions to decimals.

7/10 = 0.7

9/15 = 0.6

Compare the decimals: 0.7 > 0.6

Since 0.7 > 0.6, Vihaan spent a larger fraction of his pocket money.

Comparing Fractions Using Cross Multiplication

In cross multiplication method you multiply diagonally across the two fractions and compare the two products you get.

1. Multiply the numerator of the first fraction with the denominator of the second fraction. Write this product beside the first fraction.

2. Multiply the numerator of the second fraction with the denominator of the first fraction. Write this product beside the second fraction.

3. Compare the two products. The side with the bigger product belongs to the bigger fraction.

Example: Compare 5/9 and 7/11, the fractions representing the matches won by two cricket teams in a season.

Solution: 

Use the cross-multiplication method.

Multiply the numerator of each fraction by the denominator of the other fraction:

5 × 11 = 55

7 × 9 = 63

Now compare the results: 63 > 55

$\frac{7}{11} > \frac{5}{9}$

Therefore, the team with a win rate of 7/11 had the better performance.

Practice Questions on Comparing Fractions

Q1. Which fraction is greater, 4/7 or 4/9?

a) 4/7

b) 4/9

c) They are equal

Q2. Using the LCM method, which is greater, 2/3 or 5/8?

Q3. Fill in the blank: The decimal value of 3/4 is ______.

Q4. True or False: When two fractions have the same numerator, the one with the larger denominator is the larger fraction.

Q5. Using cross multiplication, compare 3/5 and 4/7.

Answers: 

Q1. 4/7

Q2. 2/3

Q3. 0.75

Q4. False

Q5. 3/5 > 4/7