Multiplying Fractions Calculator

Multiply two fractions and get simplified results with step-by-step GCD solutions.

Enter Fractions

×

Result

Product
5/8
= 0.625
Unsimplified15/24
GCD3
Simplified5/8
Decimal0.625
Mixed Number5/8

Step-by-Step Solution

(3/4) x (5/6) = 15/24 = 5/8

How to Multiply Fractions

Multiplying fractions is one of the most straightforward operations in fraction arithmetic. Unlike addition and subtraction, you do not need a common denominator. Simply multiply the numerators together and the denominators together, then simplify the result using the greatest common divisor (GCD).

The Fraction Multiplication Formula

Basic Formula

Multiply numerators and denominators straight across.

(a/b) x (c/d) = (a x c) / (b x d)

Simplification

Divide both numerator and denominator by their GCD.

Result / GCD(num, den)

Cross-Cancellation

Simplify diagonally before multiplying for easier arithmetic.

(a/b) x (c/d) - cancel common factors

Step-by-Step Process

  1. Multiply the numerators: Multiply the top numbers of both fractions to get the new numerator.
  2. Multiply the denominators: Multiply the bottom numbers of both fractions to get the new denominator.
  3. Find the GCD: Determine the greatest common divisor of the resulting numerator and denominator.
  4. Simplify: Divide both the numerator and denominator by the GCD to get the fraction in lowest terms.

Example

Multiply 3/4 by 5/6:

  • Numerators: 3 x 5 = 15
  • Denominators: 4 x 6 = 24
  • Unsimplified: 15/24
  • GCD(15, 24) = 3
  • Simplified: 5/8

Common Mistakes to Avoid

  • Do not add the denominators - multiply them.
  • Always simplify your final answer.
  • When multiplying by a whole number, write it as n/1 first.
  • Remember that a negative times a positive gives a negative result.

Multiplying Mixed Numbers

To multiply mixed numbers, first convert them to improper fractions. Multiply a whole number part by the denominator and add the numerator to get the new numerator. Then proceed with the standard fraction multiplication steps.

Applications

Fraction multiplication is used in cooking (scaling recipes), construction (calculating partial measurements), probability (finding combined probabilities), and many areas of science and engineering where proportional relationships matter.