Dividing Fractions Calculator

Fraction division looks harder than it is: there is a single rule, it never changes, and it works the same for proper fractions, improper fractions, mixed numbers and whole numbers. This calculator applies that rule and prints every intermediate line, so the answer can be checked rather than trusted.

The formula and where it comes from

Dividing by a number means multiplying by its reciprocal — the number you multiply it by to get 1. The reciprocal of c/d is d/c, because (c/d) × (d/c) = cd/dc = 1. Replacing the division with a multiplication by the reciprocal therefore does not change the value; it only turns the problem into one that is easy to compute, since multiplying fractions is just multiplying straight across.

Step-by-step guide

1. Write both numbers as fractions. A whole number goes over 1 (4 = 4/1); a mixed number becomes an improper fraction (2 3/4 = (2 × 4 + 3)/4 = 11/4).
2. Keep the first fraction exactly as it is.
3. Flip the second fraction — swap its numerator and denominator — and change ÷ into ×.
4. Multiply the numerators together, then the denominators together.
5. Reduce the result by the greatest common factor of the two parts, and write it as a mixed number if the numerator is larger than the denominator.

Common fraction divisions

Where fraction division is used

• Cooking: splitting a recipe that calls for 3/4 cup between two servings, or working out how many 1/3-cup scoops fit into 2 cups.
• Woodworking and sewing: cutting a board of 5 1/2 feet into pieces of 3/4 foot, where the answer has to be exact rather than rounded.
• School homework: the "keep, change, flip" rule is taught in grades 5–7 and is the single most-tested operation on fractions.
• Unit rates: if 2/3 of a job takes 1/4 of an hour, dividing gives the time for the whole job.
• Scaling drawings and models: converting a 1/8 scale into how many times smaller a part is than another at 1/2 scale.

Limits and things to watch

• The divisor can never be zero. There is no number that multiplied by zero gives the dividend, so the calculator rejects a zero divisor instead of printing an answer.
• Order matters. 3/4 ÷ 2/3 and 2/3 ÷ 3/4 are different questions with different answers — division is not commutative.
• The decimal form is often not exact. 5/6 is 0.8333… forever; whenever the reduced denominator has a prime factor other than 2 or 5, the decimal repeats and the page marks it with ≈. The fraction is the exact answer.
• An unreduced input is not a different problem. 2/4 and 1/2 divide to the same value: the page multiplies first and reduces the product at the end, so reducing beforehand only changes the numbers along the way, never the answer.