Equivalent Fractions Calculator
List equivalent fractions for any fraction by multiplying the top and bottom by the same number, find its simplest form, or check whether two fractions are equivalent by cross-multiplying.
How it works
a/b = (a × k)/(b × k) for any whole number k ≠ 0 · a/b and c/d are equivalent ⇔ a × d = b × c (cross products are equal)
Equivalent fractions name the same amount with different numbers. Multiplying (or dividing) the numerator and the denominator by the same non-zero number does not change the value, because you are multiplying by k/k = 1. Every fraction therefore has infinitely many equivalents, and exactly one simplest form, found by dividing by the greatest common factor. Two fractions are equivalent exactly when their cross products are equal.
Worked example
2/3: multiplying the top and bottom by 2, 3, 4 … 9 gives 4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, 18/27 — all equal to 0.666667 (66.6667%). To check 2/3 and 8/12: 2 × 12 = 24 and 3 × 8 = 24, so they are equivalent.
Sources: Common Core State Standards — 4.NF.1 (equivalent fractions) · Khan Academy — Equivalent fractions
Frequently asked questions
How do you find equivalent fractions?
Multiply the numerator and the denominator by the same number. 3/4 × 2/2 = 6/8 and 3/4 × 5/5 = 15/20 are both equivalent to 3/4.
How do I know if two fractions are equivalent?
Cross-multiply: a/b = c/d exactly when a × d = b × c. You can also simplify both fractions and compare, or compare their decimals.
What is the simplest form of a fraction?
The equivalent fraction whose numerator and denominator have no common factor except 1, such as 2/3 for 8/12. Divide both by their greatest common factor.
Why do we need equivalent fractions?
To add, subtract or compare fractions you rewrite them with a common denominator, e.g. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
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