What this calculator does
An equivalent fractions calculator finds fractions that represent the same value as the one you enter, just written with different numbers. Multiplying (or dividing) both the numerator and denominator by the same whole number never changes the value of the fraction, so 1/2, 2/4 and 3/6 are all the same amount, just scaled differently.
This is a different job from simplifying a fraction down to its lowest terms. Simplifying goes one direction only, toward the smallest whole numbers. Finding equivalent fractions goes the other way too, generating larger versions of the same fraction, which is the skill needed for adding fractions with different denominators or matching a fraction to a specific denominator a worksheet or recipe calls for.
The formula
The fraction is first reduced to its simplest form by dividing both numbers by their greatest common divisor. From there, multiplying the simplified numerator and denominator by 2, 3, 4 and so on produces a family of equivalent fractions. If you supply a target denominator, the calculator checks whether it is a whole-number multiple of the simplified denominator, and if so scales the numerator to match.
| Term | Meaning |
|---|---|
| Equivalent fraction | A fraction with a different numerator and denominator that represents the same value. |
| Simplest form | The equivalent fraction with the smallest possible whole-number numerator and denominator. |
| Target denominator | A specific denominator you want the equivalent fraction expressed in, such as matching another fraction before adding them. |
The inputs explained
| Field | What to enter |
|---|---|
| Numerator | The numerator (top number) of the fraction. |
| Denominator | The denominator (bottom number) of the fraction. Cannot be zero. |
| Target denominator (0 to skip) | Leave at 0 to just see a list of equivalents. Enter a denominator to find the matching numerator at that specific denominator, if one exists. |
When to use it
Adding or comparing fractions
Fractions with different denominators cannot be added or compared directly. Converting each to an equivalent fraction with a shared denominator is the standard first step, and this calculator finds that match once you know the denominator you are aiming for.
Checking homework or teaching the concept
Seeing a fraction alongside a short list of its equivalents makes the underlying idea concrete: the value never changes, only the numbers describing it get larger.
Matching a recipe or measurement to available units
A recipe or plan written as one fraction sometimes needs restating at a denominator that matches the tool or measurement you have on hand, such as converting 3/4 into eighths.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What are the equivalent fractions for a few common starting fractions?
A sample of starting fractions, each scaled up by whole-number multipliers from 2 to 6.
Questions
How is this different from simplifying a fraction?
Simplifying reduces a fraction to the smallest possible whole numbers. This calculator does that too, but also works in the other direction, generating larger equivalent fractions or matching a fraction to a denominator you specify. For simplifying only, see the simplify fraction calculator.
Why is my target denominator sometimes "not possible"?
An equivalent fraction only exists at denominators that are whole-number multiples of the simplified denominator. If the simplified fraction is 2/3, equivalents exist at 6, 9, 12 and so on, but not at 8, since 8 is not evenly divisible by 3.
Do equivalent fractions always reduce back to the same simplest form?
Yes. Any fraction equivalent to another will reduce to exactly the same simplest form, since scaling the numerator and denominator by the same number does not change their ratio.
Can a fraction have infinitely many equivalent fractions?
Yes. Multiplying by any whole number 2, 3, 4 and onward produces a new, valid equivalent fraction, so the list never runs out; this calculator just shows the first few.
To reduce a fraction to its lowest terms rather than find equivalents, use the simplify fraction calculator. For a general ratio in the same lowest-terms form, see the ratio simplifier.