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Multiply Fractions Calculator

Enter the numerators and denominators of both fractions to multiply them.

How it is calculated

For the fractions a/b and c/d the tool multiplies straight across: numerator = a × c, denominator = b × d. It then divides both by their greatest common divisor to reach lowest terms, so no common denominator is needed. If the denominator is negative, the minus sign is moved to the numerator. The reduced fraction is shown together with its decimal value (4 decimals) and a mixed number when the fraction is improper. All four entries are rounded to whole numbers before the calculation, so 1.5 becomes 2; to use a decimal, convert it to a fraction first. A denominator of 0 gives no result. The result shows as a whole number when the denominator reduces to 1.

Worked example

Multiply 5/6 by 9/4. Numerator = 5 × 9 = 45 and denominator = 6 × 4 = 24, giving 45/24. The greatest common divisor of 45 and 24 is 3, so dividing both gives 15/8. As a decimal, 15 / 8 = 1.8750. Because 15 is larger than 8, the mixed number is 1 7/8 (15 = 1 × 8 + 7). A shortcut is to cancel the 3 first: 5/6 × 9/4 becomes 5/2 × 3/4, which is 15/8 as well.

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Common mistakes

  • Looking for a common denominator first, as you would when adding. For multiplication you multiply across directly, and the common factors are removed at the end.
  • Typing decimals such as 0.5 in a numerator or denominator. Entries are rounded to whole numbers, so 0.5 becomes 1 (or 0), which silently changes your fraction.
  • Entering a mixed number, like 1 1/2, in a single box. Convert it to an improper fraction (3/2) first.
  • Expecting the product to be smaller every time. Multiplying by a fraction greater than 1, such as 9/4, makes the result bigger.
  • Putting a minus sign on both numerator and denominator and expecting a negative result. Two negatives cancel, so the product is positive.

About this calculator

Multiplying fractions is one of the more mechanical operations in arithmetic: multiply the numerators together, multiply the denominators together, then reduce the result using the greatest common divisor of the two products to reach lowest terms. Unlike addition, fraction multiplication doesn't need a common denominator, which is what makes it a common early stumbling point for students used to the addition rule.

This calculator carries out that process on any two fractions a/b and c/d, and also converts the reduced answer into decimal and mixed-number form so the result is usable however it's needed. It's a staple of middle-school and early high-school math, and the same operation shows up any time a real-world quantity is scaled by a fractional rate — halving a recipe, applying a discount expressed as a fraction, or working through unit-rate and ratio problems.

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Comments (1)

  • Editorial team

    Scaling a recipe is a handy use: half of three quarters of a cup is entered as 1/2 times 3/4 and returns 3/8. Negative fractions keep their sign on the numerator, so minus 2/3 times 9/4 shows -3/2 and the mixed form -1 1/2. A mixed number such as 1 1/2 has to be entered as the improper fraction 3/2 first. What everyday fraction problems come up for you most?

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