Scholars & Parents
ExplainerMathGrades 3–5

Equivalent Fractions

What Is This?

Equivalent fractions are fractions that look different but represent exactly the same value. For example, 1/2, 2/4, 3/6, and 4/8 all mean the same thing — exactly half of a whole. Understanding equivalent fractions is the foundation for adding and subtracting fractions, comparing fractions, and simplifying answers.

Why Does It Matter?

Every time you add fractions with unlike denominators, you are creating equivalent fractions. When you simplify an answer like 6/12 to 1/2, you are using equivalent fractions. When you compare 3/4 and 5/6 to decide which is larger, you convert both to equivalent fractions with the same denominator. Equivalent fractions are the engine behind almost every fraction operation you will ever do.

How to Find Equivalent Fractions

Method 1 — Multiply the Numerator and Denominator by the Same Number

Whatever you multiply the denominator by, you must also multiply the numerator by. This keeps the value of the fraction unchanged while changing how it looks.

Example: Find three fractions equivalent to 2/3

  • 2/3 × 2/2 = 4/6
  • 2/3 × 3/3 = 6/9
  • 2/3 × 4/4 = 8/12

All four fractions — 2/3, 4/6, 6/9, 8/12 — are equivalent. They all equal the same point on the number line.

Method 2 — Divide the Numerator and Denominator by the Same Number (Simplifying)

This works in reverse — you can also find a simpler equivalent fraction by dividing both numerator and denominator by their greatest common factor (GCF).

Example: Simplify 12/18

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18
  • GCF = 6
  • 12/18 ÷ 6/6 = 2/3

So 12/18 and 2/3 are equivalent — 2/3 is the simplest form.

Worked Example 1: Are 3/4 and 9/12 equivalent?

Method — Cross multiply and compare:

  • 3 × 12 = 36
  • 4 × 9 = 36
  • Both products are equal — so yes, 3/4 and 9/12 are equivalent

Alternatively, simplify 9/12: GCF of 9 and 12 is 3. 9/12 ÷ 3/3 = 3/4 ✓

Worked Example 2: Fill in the missing numerator — 3/5 = ?/20

To go from denominator 5 to denominator 20, we multiply by 4. Whatever we do to the denominator, we must do to the numerator. 3 × 4 = 12

Answer: 3/5 = 12/20

Worked Example 3: Simplify 24/36 to its simplest form

  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • GCF = 12
  • 24/36 ÷ 12/12 = 2/3

The Cross-Multiplication Test

To check whether two fractions are equivalent without simplifying, cross-multiply:

  • Multiply the numerator of the first by the denominator of the second
  • Multiply the denominator of the first by the numerator of the second
  • If both products are equal, the fractions are equivalent

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

  • 4 × 9 = 36
  • 6 × 6 = 36
  • Equal — so yes, they are equivalent

Example: Are 2/3 and 3/5 equivalent?

  • 2 × 5 = 10
  • 3 × 3 = 9
  • Not equal — so no, they are not equivalent

Finding the Simplest Form

A fraction is in its simplest form (also called lowest terms) when the numerator and denominator share no common factor other than 1. To simplify in one step, divide by the GCF.

Example: Simplify 18/24

GCF of 18 and 24: factors of 18 are 1, 2, 3, 6, 9, 18; factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. GCF = 6.

18/24 ÷ 6/6 = 3/4

Common Mistakes

Mistake 1: Adding the same number instead of multiplying

To find an equivalent fraction for 1/3, some students write 2/4 (adding 1 to both). This is wrong — 2/4 = 1/2, not 1/3. You must MULTIPLY both numerator and denominator by the same number, not add.

Mistake 2: Multiplying only the numerator or only the denominator

If you multiply only the top number, the value changes. 1/3 with the numerator doubled gives 2/3 — a completely different fraction. Both numbers must be multiplied by the same factor.

Mistake 3: Not finding the GCF when simplifying

If you divide by a common factor that is not the greatest, your answer will be simplified but not fully simplified. For example, simplifying 12/18 by dividing by 2 gives 6/9 — correct but not fully simplified. Divide by the GCF (6) to get 2/3 in one step.

Mistake 4: Confusing equivalent with equal in size

Equivalent fractions are equal in value, but they are not the same fraction. 1/2 and 4/8 are equivalent because they represent the same amount, even though the numbers look different.

Key Takeaways

  • Equivalent fractions have the same value but different numerators and denominators
  • To create an equivalent fraction: multiply (or divide) both numerator and denominator by the same number
  • To simplify a fraction: divide both numerator and denominator by their GCF
  • A fraction is in simplest form when the GCF of numerator and denominator is 1
  • Cross-multiplication is a quick test to check whether two fractions are equivalent
  • Equivalent fractions are the foundation for adding, subtracting, and comparing fractions

Practice and Resources

Ready to practise? Try our Grade 3-5 Equivalent Fractions Worksheet with problems covering missing numerators, simplification, and comparison. Test yourself with the Grade 5 Math Practice Test.

Was this helpful?