Equivalent Fractions for Class 6: Definition, Methods and Solved Examples

Equivalent fractions are fractions that represent the same value, even though their numerators and denominators are different. They are formed by multiplying or dividing both the numerator and denominator by the same non-zero number. This concept helps students understand that fractions can look different but still be equal in value. In this guide, you will learn about the definition, methods, and examples of equivalent fractions.

Table of Contents

• What are Equivalent Fractions?
• How to Find Equivalent Fractions
• How to Check Whether Two Fractions Are Equivalent
• Fraction Strips: Visualising Equivalent Fractions
• Equivalent Fractions Quick Reference Table
• Solved Examples on Equivalent Fractions
• Practice Questions on Equivalent Fractions

What are Equivalent Fractions?

Equivalent fractions are fractions that represent the same part of a whole, even though their numerators and denominators are different. In other words, they have the same value when reduced or compared.

The word ‘equivalent’ comes from the Latin 'aequivalens', meaning ‘of equal worth’. So, equivalent fractions are literally fractions of equal worth. Imagine you cut a pizza into 2 equal slices and take 1. Now imagine another pizza (the same size) cut into 4 slices, and you take 2. You've eaten the same amount of pizza both times, exactly half.

So 1/2 = 2/4 = 3/6.

How to Find Equivalent Fractions

When you multiply or divide both the numerator and denominator by the same non-zero number, the value of the fraction does not change. Therefore, equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number.

Finding Equivalent Fractions by Multiplying

The most common way to find equivalent fractions is to multiply the numerator and denominator by the same number.

Step-by-Step

• Start with your fraction, say 3/5.

• Choose any non-zero whole number to multiply by; let's try 2, 3, and 4.

• Multiply both the numerator and denominator by that number.

• Each result is an equivalent fraction.

So the equivalent fractions of 3/5 include 6/10, 9/15, 12/20, and so on. There are infinitely many equivalent fractions for any given fraction.

Finding Equivalent Fractions by Dividing

Just like you multiply to go up, you can divide to come down. Dividing both numerator and denominator by a common factor gives you an equivalent fraction.

Start with 18/24. Both 18 and 24 are divisible by 6:

So 18/24, 9/12, and 3/4 are all equivalent fractions. The simplest form here is 3/4.

How to Check Whether Two Fractions Are Equivalent

There are two reliable methods to verify whether two fractions are equivalent.

Method 1: Cross-multiplication

Cross-multiply the two fractions. If the products are equal, the fractions are equivalent.

Cross-multiplication Rule:

a/b = c/d   if   a × d = b × c

Multiply the numerator of the first by the denominator of the second, and vice versa. Equal products = equivalent fractions.

Example: Check if 3/4 and 9/12 are equivalent.

3 × 12 = 36

4 × 9 = 36

Both products are equal ⇒ 3/4 and 9/12 are equivalent.

Method 2: Simplify Both to Lowest Terms

Reduce both fractions to their simplest form. If they simplify to the same fraction, they're equivalent.

Example: Are 8/12 and 6/9 equivalent?

8/12 ÷ (4/4) = 2/3

6/9 ÷ (3/3) = 2/3

Both simplify to 2/3 ⇒ 8/12 and 6/9 are equivalent.

Fraction Strips: Visualising Equivalent Fractions

Fraction strips (also called fraction bars) are one of the most powerful visual tools for understanding equivalent fractions. Each strip represents the same whole, just divided into a different number of equal parts.

Here,  12=24=36=48=510are all equivalent fractions.

Here, 23=46=69are equivalent fractions.

Equivalent Fractions Quick Reference Table

Solved Examples on Equivalent Fractions

Example 1: Find four equivalent fractions of 2/3.

Solution: Multiply numerator and denominator by 2, 3, 4, and 5 separately.

× 2 ⇒ (2×2)/(3×2) = 4/6

× 3 ⇒ (2×3)/(3×3) = 6/9

× 4 ⇒ (2×4)/(3×4) = 8/12

× 5 ⇒ (2×5)/(3×5) = 10/15

Equivalent fractions of 2/3 are 4/6, 6/9, 8/12, 10/15

Example 2: Find the missing number: 3/7 = ?/35

Solution: The denominator changed from 7 to 35. 

7 × x = 35  ⇒ x = 35 ÷ 7 = 5

Multiply the numerator by the same number: 3 × 5 = 15

Therefore, 3/7 = 15/35

Example 3: Are 4/6 and 10/15 equivalent fractions?

Solution: By the method of cross-multiplication.

4 × 15 = 60

6 × 10 = 60

60 = 60 

Therefore, 4/6 and 10/15 are equivalent fractions.

Example 4: Are 16/24 and 6/9 equivalent?

Solution: The GCF of 16 and 24 is 8.

⇒ 16÷8 / 24÷8 = 2/3

The GCF of 6 and 9 is 3.

⇒  6÷3 / 9÷3 = 2/3

Both  16/24 and 6/9 reduce to 2/3

Therefore, 16/24 and 6/9 are equivalent fractions.

Example 5: Riya ate 3 slices of a pizza cut into 6 equal pieces. Arjun ate 4 slices of an identical pizza cut into 8 equal pieces. Did they eat the same amount?

Solution: Riya ate 3 slices of a pizza cut into 6 equal pieces = 3/6

Dividing the numerator and denominator by 3, 3/6 = 1/2.

Arjun ate 4 slices of an identical pizza cut into 8 equal pieces = 4/8 

Dividing numerator and denominator by 4, 4/8 = 1/2

Compare

1/2 = 1/2

Riya and Arjun both ate exactly half their pizza. 3/6 and 4/8 are equivalent fractions.

Practice Questions on Equivalent Fractions

1. Write three equivalent fractions for 4/7.

2. Find the missing number: 5/9 = ?/45.

3. Fill in the blank: 7/? = 21/36.

4. Are 5/8 and 15/24 equivalent? 

5. Reduce 45/60 to its simplest form.

6. Mohan read 2/6 of a book on Monday, and Priya read 1/3 of the same book. Did they read the same amount?

7. List all fractions equivalent to 1/5 with denominators up to 30.

8. Fill in the blank: 5/8 = 25/?

9. Write three equivalent fractions of 5/8.

10. If x/12 = 3/4. Find the value of x.