Equivalent Fractions Calculator
Equivalent fractions look different but have the same value, like 1/2, 2/4 and 50/100. You make one by multiplying (or dividing) the numerator and denominator by the same non-zero number. This calculator reduces a fraction to its simplest form and lists as many equivalents as you need, which helps with comparing and adding fractions.
How to use the equivalent fractions calculator
- Enter the numerator and denominator.
- Choose how many equivalent fractions to list.
- Read the simplest form first, then the list of equivalents made by multiplying top and bottom by 2, 3, 4 and so on.
Formula
a/b = (a × k)/(b × k) for any non-zero k. To simplify, divide by the GCF: a/b = (a ÷ g)/(b ÷ g) where g = GCF(a, b). Two fractions a/b and c/d are equivalent when a × d = b × c.
Worked examples
Simplifying
6/8: the GCF of 6 and 8 is 2, so 6/8 = 3/4.
Making equivalents
3/4 = 6/8 = 9/12 = 12/16 = 15/20. Each step multiplies top and bottom by the next whole number.
Why equivalent fractions matter
Whenever you need to compare, add or subtract fractions, you switch to equivalent ones with a common denominator. It is the single most reused skill in fraction arithmetic.
Worked example
Compare 3/4 and 5/8. Rewrite 3/4 as 6/8. Now 6/8 is larger than 5/8, so 3/4 is greater. Adding them: 6/8 + 5/8 = 11/8 = 1 3/8.
Equivalent fractions on a number line
All the fractions 1/2, 2/4, 3/6 and 4/8 sit at exactly the same point. Cutting the pieces smaller changes how many you have, not how much there is.
Equivalent to percent and decimal
| Fraction | Equivalent | Decimal | Percent |
|---|---|---|---|
| 1/2 | 50/100 | 0.5 | 50% |
| 1/4 | 25/100 | 0.25 | 25% |
| 3/5 | 60/100 | 0.6 | 60% |
Making the denominator 100 turns any such fraction into a percent, which is a handy trick for exams.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Simplify 12/18 and list equivalents.
Show answer
Simplest form: 2/3
- List fractions equivalent to 5/7.
Show answer
Simplest form: 5/7
Common mistakes to avoid
- Adding the same number to the top and bottom. 1/2 and 2/3 are not equivalent, even though 1 + 1 and 2 + 1 were added.
- Multiplying only the numerator or only the denominator, which changes the value.
- Stopping simplification too early. Keep dividing until the GCF is 1.
Frequently asked questions
What are equivalent fractions?
Different fractions that represent the same amount, such as 1/3 and 2/6.
How do I check if two fractions are equivalent?
Cross-multiply. If the two products are equal, they are equivalent: 3 × 8 = 4 × 6.
Why do I need equivalent fractions?
To add or subtract fractions with different denominators, you rewrite them with a common denominator.
How do I simplify a fraction?
Divide top and bottom by their greatest common factor. See how to simplify fractions.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.