Fraction Multiplication & Division Calculator
Multiply or divide two, three or four fractions, mixed numbers or whole numbers, with every step shown — mixed to improper, keep-change-flip, cross-cancelling, multiplying across and simplifying — and the answer as a fraction, mixed number, decimal and percent.
How it works
a/b × c/d = (a × c)/(b × d) · a/b ÷ c/d = a/b × d/c · mixed number w n/m = (w × m + n)/m · whole number k = k/1 · simplify by dividing top and bottom by their greatest common factor
Multiplying fractions needs no common denominator: multiply the numerators together and the denominators together, then reduce. Division is multiplication by the reciprocal — keep the first fraction, change ÷ to × and flip the fraction that follows (“keep, change, flip”). The calculator handles up to four fractions in one problem, each joined by × or ÷, and works left to right. Type a mixed number by putting its whole part in the whole-number box; a whole number on its own goes in that box with the numerator set to 0. Every mixed number is first turned into an improper fraction. Before multiplying, the steps show the cross-cancelling shortcut: any numerator and any denominator that share a factor are divided by it, which keeps the numbers small. The final answer is reduced by the greatest common factor and shown as a fraction, a mixed number, a decimal (with any repeating block in brackets) and a percent, along with its reciprocal.
Worked example
For 2 1/2 ÷ 3/4 × 1 1/3, convert the mixed numbers: 2 1/2 = 5/2 and 1 1/3 = 4/3. Flip the divisor 3/4 to 4/3, giving 5/2 × 4/3 × 4/3. Cancel the 2 against the first 4: 5/1 × 2/3 × 4/3. Multiply across: 40/9, which is 4 4/9 ≈ 4.4444. With the default numbers, 2/3 × 3/4 = 6/12 = 1/2.
Frequently asked questions
Why do I flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of c/d is d/c, so a/b ÷ c/d becomes a/b × d/c. Dividing by 3/4 asks how many three-quarters fit, which is the same as multiplying by 4/3.
How do I multiply or divide mixed numbers?
Convert each mixed number to an improper fraction first: 2 3/5 = (2 × 5 + 3)/5 = 13/5. Then multiply (or flip and multiply) as usual. For 2 3/5 × 1 1/6 that is 13/5 × 7/6 = 91/30 = 3 1/30. Type the whole part in the whole-number box and the calculator does the conversion for you.
How do I multiply a fraction by a whole number?
Write the whole number over 1. 7/8 × 13 becomes 7/8 × 13/1 = 91/8 = 11 3/8. Here, type 13 in the whole-number box and set that numerator to 0.
Can I cross-cancel before multiplying?
Yes. Any numerator can be cancelled against any denominator in the product, not only the one diagonally across. In 4/9 × 3/8 the 4 and 8 share 4 and the 3 and 9 share 3, leaving 1/3 × 1/2 = 1/6. The steps show this shortcut whenever it applies; the answer is the same as multiplying first and simplifying.
What happens with more than two fractions?
Multiplication and division have equal priority, so they are worked from left to right. Every ÷ flips only the fraction right after it. For example 1/2 ÷ 3/4 × 2/5 = 1/2 × 4/3 × 2/5 = 8/30 = 4/15.
Why is the result negative?
The product is negative when an odd number of the fractions are negative. A minus sign in a denominator is moved up to the numerator, and a negative mixed number such as −2 3/4 counts as −11/4.
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This calculator is for educational purposes. Double-check important results before acting on them.