Equivalent fractions calculator
Handy for fraction homework and for finding a common denominator before adding or comparing. Add a second fraction to test whether it equals the first.
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How to use it
- Enter numerator, denominator, how many equivalent fractions, second numerator (optional) and second denominator (optional).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Simplify by dividing the top and bottom by their greatest common divisor, then multiply both by 2, 3, 4 and so on: 3/4 = 6/8 = 9/12. Two fractions a/b and c/d are equivalent when a × d = b × c.
Example
Inputs: Numerator = 6, Denominator = 8, How many equivalent fractions = 8. Result: Simplest form: 3/4; Decimal value: 0.75.
Limits and caveats
- The list starts at the simplest form and multiplies it by 1, 2, 3 and so on, so your original fraction only appears if the list is long enough to reach it.
- Whole numbers only: for a fraction like 1.5/3, multiply the top and bottom by 10 first.
Questions about this tool
What are equivalent fractions?
Fractions written with different numbers that have the same value, such as 1/2, 2/4 and 50/100, which all equal 0.5.
How do I tell if two fractions are equivalent?
Multiply the first numerator by the second denominator, and the first denominator by the second numerator. If the results match, the fractions are equivalent: 3/4 and 9/12 give 3 × 12 = 4 × 9 = 36.
Why do I need equivalent fractions?
To give fractions a common denominator before adding, subtracting or comparing them. To add 1/2 and 1/3, write them as 3/6 and 2/6, then add the numerators.