Equivalent Fractions Calculator
Find equivalent fractions for any fraction and check whether two fractions are equivalent.
Shows simplified form and a full list of equivalents.
Equivalent fractions are fractions that represent the same value, even though they look different. For example, 1/2, 2/4, 3/6, and 4/8 are all equivalent — they all equal 0.5.
How to find equivalent fractions: Multiply (or divide) both the numerator and denominator by the same non-zero number.
(a/b) = (a × n) / (b × n) for any non-zero integer n
Simplest form (lowest terms): Divide both numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both evenly.
Example: 6/8 → GCD(6, 8) = 2 → 6/2 = 3, 8/2 = 4 → simplest form is 3/4
Cross-multiplication test:
To check if two fractions a/b and c/d are equivalent:
a × d = b × c
If the products are equal, the fractions are equivalent. Example: Is 2/3 equivalent to 8/12? → 2 × 12 = 24, 3 × 8 = 24 → Yes, they are equivalent.
Real-world uses:
- Cooking and baking (halving or doubling recipes)
- Measurement conversion (inches to fractions of a foot)
- Comparing prices per unit
- Simplifying ratios in maps, blueprints, and models