Equivalent Fractions Calculator
Find equivalent fractions or check if two fractions are equivalent
Calculate Equivalent Fractions
Original Fraction
Decimal: 0.500000
Simplified: 1/2
Equivalent Fractions
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
More Examples
Methods to Find Equivalent Fractions
Multiplication Method
Multiply both numerator and denominator by the same number
Example: 1/2 × 3/3 = 3/6
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
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