Equivalent Fractions Calculator

Find equivalent fractions or check if two fractions are equivalent

Calculate Equivalent Fractions

Original Fraction

1/2

Decimal: 0.500000

Simplified: 1/2

Equivalent Fractions

1/2
×1
0.5000
2/4
×2
0.5000
3/6
×3
0.5000
4/8
×4
0.5000
5/10
×5
0.5000
6/12
×6
0.5000
7/14
×7
0.5000
8/16
×8
0.5000
9/18
×9
0.5000
10/20
×10
0.5000

Pattern Explanation

All these fractions are equivalent to 1/2because they are created by multiplying both the numerator and denominator by the same number (k).

Formula: 1×k / 2×k where k = 1, 2, 3, 4, ...

Common Equivalent Fractions

Basic Fractions

1/2:2/4, 3/6, 4/8, 5/10
1/3:2/6, 3/9, 4/12, 5/15
1/4:2/8, 3/12, 4/16, 5/20
2/3:4/6, 6/9, 8/12, 10/15

More Examples

3/4:6/8, 9/12, 12/16, 15/20
1/5:2/10, 3/15, 4/20, 5/25
2/5:4/10, 6/15, 8/20, 10/25
5/6:10/12, 15/18, 20/24, 25/30

Methods to Find Equivalent Fractions

1

Multiplication Method

Multiply both numerator and denominator by the same number

Example: 1/2 × 3/3 = 3/6

2

Cross Multiplication

Check if a/b = c/d by verifying a×d = b×c

Example: 2/3 = 4/6 because 2×6 = 3×4 = 12

3

Simplification

Reduce to lowest terms using GCD

Example: 6/9 ÷ 3/3 = 2/3

Tips & Facts

Every fraction has infinitely many equivalent fractions

Equivalent fractions represent the same value or proportion

Always simplify to lowest terms for the simplest form

Cross multiplication is the fastest way to check equivalency

Equivalent fractions have the same decimal value

Understanding Equivalent Fractions

What Are Equivalent Fractions?

Equivalent fractions are different fractions that represent the same value or proportion. They look different but have equal mathematical value when simplified or converted to decimals.

Three Ways to Check Equivalence

  • Same simplified form: Both fractions reduce to the same lowest terms
  • Cross multiplication: a/b = c/d if a×d = b×c
  • Same decimal value: Both fractions give the same decimal result

How to Generate Equivalent Fractions

Step 1: Start with a fraction

Example: 2/3

Step 2: Multiply by k/k

Multiply both numerator and denominator by the same number k

2/3 × 2/2 = 4/6

2/3 × 3/3 = 6/9

2/3 × 4/4 = 8/12

Step 3: Continue the pattern

All resulting fractions are equivalent to the original

Formula: (2×k)/(3×k) where k = 1, 2, 3, 4, ...

Real-World Applications

Cooking & Recipes

Converting recipe measurements: 1/2 cup = 2/4 cup = 4/8 cup

Construction & Design

Scaling blueprints and maintaining proportions

Finance & Business

Converting between different percentage representations