Equivalent fractions name the same amount in different ways: 2/3 = 4/6 = 6/9. They are needed to add fractions, compare them and simplify answers.
How to use the Equivalent Fractions Calculator
- I want to…
- Numerator
- Denominator
- Number of equivalent fractions
- Second numerator
- Second denominator
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Multiplying the numerator and denominator by the same number gives an equivalent fraction. Two fractions are equivalent exactly when their cross products are equal.
Formula
a/b = (k·a)/(k·b) for any k ≠ 0; a/b = c/d ⇔ a·d = b·c
Worked example
Inputs — I want to…: Find equivalent fractions; Numerator: 2; Denominator: 3; Number of equivalent fractions: 10.
Results — Result = 2/3 in lowest terms; Equivalent fractions / cross products = 2/3, 4/6, 6/9, 8/12, 10/15, 12/18, 14/21, 16/24, 18/27, 20/30; Simplest form = 2/3.
Key terms
- Equivalent fractions
- Different fractions with the same value.
Frequently asked questions
Are 2/3 and 10/15 equivalent?
Yes: 2 × 15 = 30 = 3 × 10.
How do I find an equivalent fraction with denominator 12 for 3/4?
Multiply top and bottom by 3: 9/12.
Is there a "simplest" equivalent fraction?
Yes – the one in lowest terms.
Do equivalent fractions have the same decimal?
Yes.