Equivalent Fractions Calculator

Equivalent fractions are different fractions with the same value: 3/4, 6/8, 9/12 and 15/20 are all 0.75. You make one by multiplying (or dividing) the numerator and the denominator by the same nonzero number, which is the same as multiplying by 1.

Listing equivalent fractions. Multiply top and bottom by 2, 3, 4 and so on. From 3/4: 6/8, 9/12, 12/16, 15/20, 18/24. The list never ends, and every fraction on it simplifies back to 3/4.

Rewriting over a given denominator. This is the version homework and recipes ask for: 3/4 = ?/20. Divide the new denominator by the old one, 20 / 4 = 5, then multiply the numerator by the same 5: 3 x 5 = 15, so 3/4 = 15/20. Enter the denominator you want as the second denominator.

When it cannot be done. The new denominator must be a multiple of the reduced denominator. 3/4 cannot be written over 10 with a whole-number numerator, because 10 / 4 is not a whole number; the nearest denominators that work are 8 and 12. The calculator says so and gives those.

Checking two fractions. Two fractions are equivalent exactly when their cross products are equal. 3/4 and 15/20: 3 x 20 = 60 and 15 x 4 = 60, so they match. 3/4 and 14/20 give 60 and 56, so they do not. To compare fractions that are not equivalent, use the comparing fractions calculator, which also says which is larger.

Where this is used. Adding and subtracting fractions both depend on it: 3/4 + 1/5 needs both over 20, which is 15/20 + 4/20 = 19/20. Simplifying is the same idea run backward, dividing top and bottom until nothing more divides.