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Fractions

Equivalent Fractions Calculator

Find equivalent fractions, simplify any fraction to its lowest terms, or check whether two fractions are equal — with every step shown so you can see why, not just what.

Equivalent fractions calculator

Enter any fraction — numerator on top, denominator on bottom.

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Step by step calculations

Equivalent Fractions Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where equivalent fractions show up

A recipe uses ¾ cup of milk. You're doubling it — so you need 1½ cups. That's ¾ × 2 = 6/4 = 1½: equivalent fractions in action. A weather report says "1 in 4 chance of rain" — that's also 25% and 2/8 and 3/12, all equivalent. Map scales like 1:50,000 work the same way.

Worked example

"Show that 3/4 = 9/12, and find two more equivalents."

Multiply top and bottom by 3: 3×3 = 9, 4×3 = 12 → 9/12 ✓

Multiply top and bottom by 5: 3×5 = 15, 4×5 = 20 → 15/20

Multiply top and bottom by 10: → 30/40

Always multiply (or divide) both top and bottom by the same number.

Common mistake to avoid

  • ✗ Adding instead of multiplying: doing 3/4 → 4/5 by adding 1 to top and bottom does NOT give an equivalent fraction. The fraction's value changes. You must multiply (or divide) both parts by the same number.
Good to know

Understanding equivalent fractions

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What makes fractions equivalent?
Two fractions are equivalent when they represent the same amount — the same portion of a whole. You can create equivalent fractions by multiplying (or dividing) both the numerator and denominator by the same non-zero number. The value doesn't change, only the way it's written.
1/2 = 2/4 = 3/6 = 4/8 = 5/10

Each one represents exactly half.
Multiply top and bottom by the same number.
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Simplifying to lowest terms
A fraction is in its simplest form (lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, divide both by their Greatest Common Divisor (GCD). You can do this in one step using the GCD, or in stages by dividing by common prime factors one at a time.
12/18
÷ 2 → 6/9
÷ 3 → 2/3 ✓ (lowest terms)

GCD(12,18) = 6 → 12÷6 / 18÷6 = 2/3
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Key method
Cross-multiplication to check equality
To check if two fractions a/b and c/d are equivalent, cross-multiply: if a × d = b × c, they are equal. This works because multiplying both sides of the equation a/b = c/d by b × d gives a × d = b × c. A quick, reliable test that avoids converting to decimals.
Are 3/4 and 9/12 equal?
3 × 12 = 36
4 × 9 = 36
36 = 36 ✓ Yes — they are equal!
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Finding the GCD
The Greatest Common Divisor (GCD) is the largest number that divides into both the numerator and denominator exactly. The fastest method is the Euclidean algorithm: divide the larger by the smaller, replace the larger with the remainder, and repeat until the remainder is zero — the last non-zero value is the GCD.
GCD(48, 36):
48 ÷ 36 = 1 r 12
36 ÷ 12 = 3 r 0
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GCD = 12
48/36 = 4/3