List as many fractions equal to yours as you need, check whether two fractions are equivalent with cross products, or fill in the missing numerator or denominator in problems like 3/4 = ?/20. Shaded bars show that the amounts match.
Last updated:
What do you want to do?
In missing-number mode, leave one of the four boxes empty.
e.g. 100 to see the fraction as hundredths, if possible.
Enter your values to see the result.
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How to use the Equivalent Fractions Calculator
Choose a mode: list equivalents, check two fractions, or find a missing number.
Enter the numerator and denominator of your fraction.
For checks and missing numbers, fill in the second fraction; in missing-number mode leave the unknown box empty.
Press Find equivalents to see the answer, steps and fraction bars.
The rule behind equivalent fractions
For any nonzero number k, a/b = (a × k)/(b × k). Multiplying top and bottom by k is multiplying by k/k = 1, so the value never changes; only the size and number of pieces do. Two fractions a/b and c/d are equivalent exactly when a × d = b × c.
Equivalent fractions chart
Fraction
× 2
× 3
× 4
× 5
× 10
Decimal
1/2
2/4
3/6
4/8
5/10
10/20
0.5
1/3
2/6
3/9
4/12
5/15
10/30
0.333…
2/3
4/6
6/9
8/12
10/15
20/30
0.666…
1/4
2/8
3/12
4/16
5/20
10/40
0.25
3/4
6/8
9/12
12/16
15/20
30/40
0.75
1/5
2/10
3/15
4/20
5/25
10/50
0.2
2/5
4/10
6/15
8/20
10/25
20/50
0.4
1/6
2/12
3/18
4/24
5/30
10/60
0.166…
1/8
2/16
3/24
4/32
5/40
10/80
0.125
Where equivalent fractions are used
Adding and subtracting: rewrite fractions with a common denominator, e.g. 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
Comparing: with the same denominator, the larger numerator is the larger fraction.
Percents: a fraction over 100 is a percent, so 3/4 = 75/100 = 75%.
Recipes and scaling: 2/3 cup is the same as 4/6 cup, handy when a measuring cup is marked in sixths.
Frequently asked questions
What are equivalent fractions?
Equivalent fractions name the same amount using different numbers, like 1/2, 2/4 and 50/100. You get them by multiplying or dividing the numerator and denominator by the same nonzero number, which is the same as multiplying by 1.
How do I find equivalent fractions?
Multiply the top and bottom by the same whole number. For 3/4: × 2 gives 6/8, × 3 gives 9/12, × 5 gives 15/20. You can also divide both by a common factor to go the other way, for example 9/12 ÷ 3/3 = 3/4.
How can I tell if two fractions are equivalent?
Cross-multiply. For a/b and c/d, compare a × d with c × b. If the products are equal the fractions are equivalent. For 6/8 and 9/12: 6 × 12 = 72 and 9 × 8 = 72, so they are equal. Simplifying both to lowest terms (3/4) gives the same result.
How do I find a missing number in equivalent fractions?
Find what the known denominator (or numerator) was multiplied by and do the same to the other part. For 3/4 = ?/20, 4 × 5 = 20, so the numerator is 3 × 5 = 15. In general, use cross products: ? = 3 × 20 ÷ 4 = 15.
Can I write any fraction with a denominator of 100?
Only if 100 is a multiple of the denominator in simplest form. 2/5 = 40/100 works because 5 × 20 = 100, but 1/3 has no whole-number numerator over 100 (it is about 33.33/100). The calculator tells you when a chosen denominator is not possible.
Is 2/3 equivalent to 4/6?
Yes. 2 × 6 = 12 and 4 × 3 = 12, so the cross products match, and 4/6 simplifies to 2/3 by dividing both numbers by 2.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.