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

Equivalent fractions are an important concept in Class 6 Maths that help students understand how different fractions can represent the same value. Two or more fractions are called equivalent fractions when they have different numerators and denominators but are equal in value. They are formed by multiplying or dividing both the numerator and denominator by the same non-zero number. In this guide, you'll learn the meaning of equivalent fractions for Class 6, the rules and methods to find them, along with solved examples and practice questions to strengthen your understanding.

Table of Contents

• What are Equivalent Fractions for Class 6?
• Rules for Equivalent Fractions
• Methods to Find Equivalent Fractions
• How to Check Whether Two Fractions Are Equivalent
• Understanding Equivalent Fractions Using Fraction Strips
• Equivalent Fractions Quick Reference Table
• Solved Examples on Equivalent Fractions for Class 6
• Practice Questions on Equivalent Fractions for Class 6
• Frequently Asked Questions of Equivalent Fractions

What are Equivalent Fractions for Class 6?

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.

Rules for Equivalent Fractions

Equivalent fractions may look different, but they always represent the same part of a whole. By following these simple rules, you can quickly determine whether two fractions are equivalent and solve fraction problems easily.

Rule	Explanation	Example
Multiply the numerator and denominator by the same number	Multiplying both parts of a fraction by the same non-zero whole number creates an equivalent fraction.	$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$
Divide the numerator and denominator by the same common factor	Dividing both the numerator and denominator by their common factor gives another equivalent fraction, often in its simplest form.	$\frac{12}{18} \div \frac{6}{6} = \frac{2}{3}$
Never multiply or divide only one part of the fraction	Changing only the numerator or only the denominator changes the value of the fraction, so the fractions are no longer equivalent.	$\frac{2}{5} \neq \frac{4}{5}$
Equivalent fractions always represent the same value	Although the numerator and denominator may be different, the fraction represents the same quantity.	$\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$

Methods 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.

Understanding Equivalent Fractions Using Fraction Strips

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,  $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10}$are all equivalent fractions.

Here, $\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$are equivalent fractions.

Equivalent Fractions Quick Reference Table

The table below shows how equivalent fractions are formed by multiplying both the numerator and denominator by the same whole number. Although the numbers change, the value of the fraction remains the same.

Solved Examples on Equivalent Fractions for Class 6

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 for Class 6

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.

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