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Equivalent Fractions Calculator

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

  1. Choose a mode: list equivalents, check two fractions, or find a missing number.
  2. Enter the numerator and denominator of your fraction.
  3. For checks and missing numbers, fill in the second fraction; in missing-number mode leave the unknown box empty.
  4. 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× 10Decimal
1/22/43/64/85/1010/200.5
1/32/63/94/125/1510/300.333…
2/34/66/98/1210/1520/300.666…
1/42/83/124/165/2010/400.25
3/46/89/1212/1615/2030/400.75
1/52/103/154/205/2510/500.2
2/54/106/158/2010/2520/500.4
1/62/123/184/245/3010/600.166…
1/82/163/244/325/4010/800.125

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.

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