How to solve it
- Pick a number other than 0 (the factor).
- Multiply the numerator and the denominator by that factor.
- Or divide both by a common divisor.
- Check that the value did not change: both fractions sit at the same point on the number line.
3/5 = (3 × 4)/(5 × 4) = 12/20
Result: 12/20
Common mistake:Wrong: 2/3 = 4/5.Right: 2/3 = 4/6.Adding the same number to the top and bottom changes the value. Only multiply or divide both by the same number.
Two fractions are equivalent when they name the same number with different terms. The calculator generates equivalent forms of a fraction and checks whether another fraction has the same value. If what you need is to rewrite a fraction with a denominator of your choice, one multiplication does it, as in this example.
Worked example: 3/4 with denominator 20
A recipe calls for 3/4 of a liter, but your pitcher is marked only in twentieths of a liter. How many twentieths is that?
- Divide the denominators. 20 ÷ 4 = 5, so the factor is 5.
- Multiply both terms by that factor. 3 × 5 = 15 and 4 × 5 = 20.
- Write the result. 3/4 = 15/20.
Result: 15/20 of a liter.
Check: with cross products, 3 × 20 = 60 and 4 × 15 = 60. Reducing 15/20 by 5 brings you back to 3/4.
The same fraction in the calculator, with four results, gives 6/8, 9/12, 12/16 and 15/20: the fourth is the one you were after.
Which denominators allow an equivalent fraction
The factor comes from dividing the denominator you want by the one you have. If the division is exact, there is an equivalent with a whole-number numerator; if not, the numerator would have decimals and the fraction is no longer a useful way to write the same value. The table covers three situations.
| You want | What you do | Result |
|---|---|---|
| 2/9 with denominator 45 | 45 ÷ 9 = 5, multiply by 5 | 10/45 |
| 5/6 with denominator 8 | 8 ÷ 6 = 1.333…, not a whole number | No whole-number equivalent |
| 18/30 with denominator 5 | Divide by 30 ÷ 5 = 6 | 3/5 |
The third row goes the other way: when the denominator you want is smaller, you divide both terms by the same number, and that only works if the number divides both of them. If instead one term of the equation is missing, as in x/20 = 3/4, the missing fraction value calculator solves it.
Scaling up and simplifying
They are two sides of the same rule: multiply or divide the numerator and denominator by the same nonzero number. Scaling up means multiplying, and the fraction ends up with smaller parts: 7/10 × 4/4 = 28/40. Simplifying means dividing by a common factor, and the fraction ends up with larger parts: 28/40 ÷ 4/4 = 7/10. Neither changes the value.
A fraction is fully simplified, or in lowest terms, when the greatest common factor (GCF, also called the GCD or HCF) of its terms is 1. To get to that form, use simplify fractions.
What the results list shows
The list starts from the reduced form of what you enter and multiplies it by 2, 3, 4 and so on. That is why, with 2/4 and two results, you see 2/4 and 3/6: they are the factors 2 and 3 applied to 1/2. It does not mean your fraction was written wrong, only that the list always starts from lowest terms. Each row shows the factor used, and the maximum is 50 results.
Checking whether two fractions are equivalent
To find out whether a/b and c/d have the same value, cross-multiply and compare a × d with b × c. With 6/9 and 4/6 you get 6 × 6 = 36 and 9 × 4 = 36, so they are equivalent: both reduce to 2/3. In the calculator, open “Check another fraction” and fill in the numerator and denominator; if you leave one empty, it does not calculate.
Two similar fractions may not be equivalent. With 3/5 and 4/7, the products are 3 × 7 = 21 and 5 × 4 = 20. The difference is small, but exact equality is decided with whole numbers, never with rounded decimals. When the products differ, the larger one tells you which fraction is greater; to order several at once, use compare fractions, which applies cross multiplication and shows the result on a number line.
What they are used for in practice
Most often they are used to give several fractions the same denominator. Before adding 1/6 and 1/4, for example, you rewrite them as 2/12 and 3/12. The add fractions calculator makes that choice for you, and if you want to see which common denominator is the smallest, there is the least common denominator calculator. They are also used to scale a ratio and to confirm that the answer to an exercise has the same value as yours even when it is written differently.
For practice, the equivalent fractions worksheets include exercises with answers, and the fraction wall lets you see equivalences as pieces of the same length. OpenStax explains equivalent fractions with visual models. The calculator accepts up to 100 digits per number and rejects denominators equal to zero.
Frequently asked questions
How many equivalent fractions does a fraction have?
Infinitely many, because you can always try a larger factor. The calculator shows 1 to 50 per calculation, using the factors from 2 up. For 1/3 with 50 results, the list ends at 51/153. If you need a specific factor, multiply both terms yourself and check the pair in the optional section.
Is equivalent the same as equal?
They represent the same number, but they are written differently. 1/2 and 3/6 are equivalent and both equal 0.5. Of all the ways to write one value, only one is in lowest terms, the one whose numerator and denominator share no common factor greater than 1. For 3/6 that is 1/2, which you can get with the simplify fractions calculator.
Can I scale up a fraction that has decimals in it?
No. The calculator works with whole-number numerators and denominators. If you have a decimal, convert it first: 0.35 is 35/100, which reduces to 7/20, and from there you can generate equivalents. Decimal to fraction does that step, and fraction to decimal does the reverse.
Why can't you multiply by zero?
Because both terms would become 0 and you would get 0/0, which is not a fraction: the denominator cannot be zero. Multiplying by k/k equals multiplying by 1 only when k is not zero. That is why the list starts at factor 2 and never uses 0.