Math
Equivalent Fractions Calculator
Three tools in one: list equivalent fractions for any fraction, rewrite a fraction with a specific denominator, or check whether two fractions are equivalent using cross products.
Every mode shows the simplest form, decimal, and percent.
Type a fraction (3/4), a mixed number (2 1/3), a whole number, or a decimal (1.75). Repeating decimals work too: 0.(3).
Lists fractions made by multiplying top and bottom by 2, 3, 4, and so on.
Try an example
Result
Result
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- Simplest form
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- Decimal
- —
- Percent
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What equivalent fractions are
Equivalent fractions name the same amount with different numbers: 2/3, 4/6, 6/9, and 8/12 all equal 0.(6). You make one by multiplying or dividing both the The top number of a fraction; it counts how many parts you have. and the The bottom number of a fraction; it says how many equal parts make one whole. by the same nonzero number, which is the same as multiplying the fraction by 1.
Checking equivalence with cross products
Two fractions a/b and c/d are equivalent exactly when a × d = b × c. For 2/3 and 8/12: 2 × 12 = 24 and 3 × 8 = 24, so they are equivalent. Cross products avoid decimals and work even when neither fraction is simplified.
Rewriting with a target denominator
To write 2/3 with denominator 12, divide 12 by 3 to get the multiplier 4, then multiply the numerator by 4 too: 8/12. This only works when the target denominator is a multiple of the simplified denominator; 2/3 cannot be written exactly as some number over 10.
| Fraction | × 2 | × 3 | × 4 | × 5 |
|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 |
| 5/8 | 10/16 | 15/24 | 20/32 | 25/40 |
How to use it
- Pick a mode: list equivalents, rewrite with a target denominator, or check two fractions.
- Type the fraction (or both fractions) as fractions, A whole number written next to a fraction, like 2 1/3., whole numbers, or decimals.
- Read the result: the list, the rewritten fraction, or the yes/no verdict with cross products.
- Use the simplest-form and decimal fields to double-check any answer by hand.
How to read the answer
Equivalent fractions have identical decimals and identical simplest forms. In check mode, equal cross products mean 'yes'. In target mode, an error means the denominator you asked for is not a multiple of the simplified denominator, so no exact equivalent exists.
Common mistakes and edge cases
- Adding the same number to the numerator and denominator does not make an equivalent fraction: 2/3 and 3/4 are different.
- Both parts must be multiplied by the same number. 2/3 × 2 on top only gives 4/3, a different value.
- Comparing decimals rounded to two places can hide a difference; cross products are exact.
- The equivalents list starts from the simplified fraction, so it may include fractions with smaller numbers than the one you typed.
- A target denominator that is not a multiple of the simplified denominator has no exact equivalent.
Worked examples
List equivalents
Fractions equal to 2/3
Result
4/6, 6/9, 8/12, 10/15, 12/18, 14/21
Equivalent check (yes)
Are 2/3 and 8/12 equal?
Result
Yes, 2/3 = 8/12
Equivalent check (no)
Are 3/5 and 5/8 equal?
Result
No, 3/5 ≠ 5/8
Target denominator
Write 3/4 over 20
Result
15/20
Impossible target
2/3 over 10 has no exact match
Result
No exact match
Negative fraction
Equivalents of -1/2
Result
-2/4, -3/6, -4/8
Decimal input
Is 0.75 equivalent to 6/8?
Result
Yes, 3/4 = 6/8
Zero
Equivalents of 0/5
Result
0/1, 0/2, 0/3, 0/4, 0/5
Frequently asked questions
How do you find equivalent fractions?+
Multiply or divide the numerator and denominator by the same nonzero number. 3/4 × 2/2 = 6/8, and 6/8 ÷ 2/2 = 3/4.
How can I tell if two fractions are equivalent?+
Cross-multiply. If a × d equals b × c for a/b and c/d, the fractions are equivalent. You can also simplify both and see whether the results match.
Are 1/2 and 0.5 equivalent?+
Yes. 0.5 is 5/10, which simplifies to 1/2. The calculator accepts decimals and converts them exactly.
Why does 2/3 have no equivalent with denominator 10?+
An equivalent fraction's denominator must be a multiple of the simplified denominator. 10 is not a multiple of 3, so 2/3 cannot be written exactly as tenths (it is 6.(6)/10).
Do equivalent fractions have the same decimal?+
Always. Equivalent fractions are the same number, so their decimals and percents match exactly.
Is every fraction equivalent to infinitely many others?+
Yes. There is no limit to the multipliers you can use, so the list of equivalents never ends.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026