The equivalent fractions calculator lists equivalent fractions of any fraction, checks whether two fractions are equivalent and finds a missing numerator or denominator. Enter whole numbers, press Calculate and read the steps. It is free and runs in your browser.
Leave exactly one box empty. The calculator fills it in.
Whole numbers only. Equivalent fractions come from multiplying or dividing the top and bottom by the same non-zero number.
How to Use the Equivalent Fractions Calculator
- List equivalent fractions: type a numerator and denominator. You get the simplest form and the equivalent fractions you get by multiplying by 2 to 10.
- Are they equivalent? type two fractions. The calculator cross-multiplies and says whether they are equal.
- Find the missing number: type three of the four numbers and leave one box empty. The calculator works out what is missing.
How the Calculator Works
Two fractions a/b and c/d are equivalent when a × d = b × c. To list equivalent fractions, the calculator divides the numerator and denominator by their greatest common factor to find the simplest form, then multiplies both by 2, 3, 4 and so on. To find a missing number it uses the same cross-product rule: for 3/5 = ?/20, the missing numerator is 3 × 20 ÷ 5 = 12.
In short: Equivalent fractions come from multiplying or dividing the top and bottom by the same non-zero number.
Worked Examples
Example: List equivalent fractions of 3/4: 6/8, 9/12, 12/16, 15/20. 3/4 is already in simplest form.
Example: Are 4/6 and 10/15 equivalent? 4 × 15 = 60 and 6 × 10 = 60. The products match, so yes. Both simplify to 2/3.
Example: Find the missing number in 5/8 = ?/24. 24 ÷ 8 = 3, so 5 × 3 = 15.
For a full explanation with diagrams and practice problems, read the guide to equivalent fractions, or browse all equivalent fraction guides.
Equivalent Fractions Calculator: FAQ
How do I find equivalent fractions?
Multiply or divide the numerator and denominator by the same non-zero number. For example, 2/3 × 2/2 = 4/6.
How do I know if two fractions are equivalent?
Cross-multiply. If the numerator of the first times the denominator of the second equals the denominator of the first times the numerator of the second, the fractions are equivalent.
Can the calculator simplify fractions?
Yes. The list tool shows the simplest form of the fraction you enter, found by dividing by the greatest common factor.
Why does the calculator say there is no whole-number answer?
The missing number in an equivalent fraction must be a whole number. If the numbers you entered do not allow that, the fraction cannot be written with that numerator or denominator.
Is the equivalent fractions calculator free?
Yes. It is free, needs no sign-up and runs entirely in your browser.
Sources and Further Reading
- Math is Fun, Equivalent Fractions.
- Math is Fun, Simplifying Fractions.
- OpenStax, Prealgebra 2e, Section 4.2: Multiply and Divide Fractions (the Equivalent Fractions Property and simplifying), Rice University.
Also see the percentage calculator and the CalcSolver calculator.
More equivalent fractions guides
Equivalent Fractions of 1/3: List and How to Find Them
Equivalent fractions of 1/3: 2/6, 3/9, 4/12, 5/15. Learn how to find and check them, with a diagram, worked examples, practice and a free calculator.
Equivalent Fractions of 2/3: List and How to Find Them
Equivalent fractions of 2/3: 4/6, 6/9, 8/12, 10/15. Learn how to find and check them, with a diagram, worked examples, practice and a free calculator.
Equivalent Fractions of 3/4: List and How to Find Them
Equivalent fractions of 3/4: 6/8, 9/12, 12/16, 15/20. Learn how to find and check them, with a diagram, worked examples, practice and a free calculator.