Fraction Multiplication Calculator

Multiply any two fractions with step-by-step solutions. See cross-cancellation, numerator and denominator multiplication, and automatic simplification.

📐 Fraction Multiplication Calculator
Result
Visual Diagram
Definition

What is Fraction Multiplication Calculator?

A Fraction Multiplication Calculator multiplies two fractions by multiplying the numerators together and the denominators together. Unlike addition and subtraction, multiplying fractions does NOT require a common denominator.

Fraction multiplication is one of the simpler fraction operations — multiply straight across. The result is then simplified to lowest terms. An optional optimization called cross-cancellation simplifies before multiplying to keep numbers smaller.

Fraction multiplication is used in scaling recipes, calculating areas (1/2 × 3/4 of a yard), probability (independent events), discounts, and proportional reasoning.

Interactive Visualization
Formula

Fraction Multiplication Calculator Formula

a/b × c/d = (a × c) / (b × d)

Steps:

  1. Multiply the numerators: a × c
  2. Multiply the denominators: b × d
  3. Simplify the result

Cross-cancellation shortcut: Before multiplying, check if any numerator and any denominator share a common factor. Cancel first, then multiply.

Example: 2/3 × 3/4 → Cross-cancel: 3 in numerator and denominator → 2/1 × 1/4 = 2/4 = 1/2

Examples

Worked Examples

2/3 × 4/5

Multiply: (2×4)/(3×5) = 8/15. Result: 8/15.

3/4 × 2/3

Cross-cancel 3: (1×2)/(4×1) = 2/4 = 1/2. Result: 1/2.

5/6 × 3/10

Cross-cancel: GCF(5,10)=5, GCF(3,6)=3 → 1/2 × 1/2 = 1/4. Result: 1/4.

7/8 × 4/7

Cross-cancel 7: (1×4)/(8×1) = 4/8 = 1/2. Result: 1/2.

Related Tools

Related Fraction Calculators

Fraction Division Calculator Fraction Simplifier Calculator Cross Multiplication Calculator Mixed Number Calculator
FAQ

Frequently Asked Questions

Common questions about the fraction multiplication calculator.

Multiply numerator × numerator and denominator × denominator. Example: 2/5 × 3/4 = (2×3)/(5×4) = 6/20 = 3/10 (simplified).

No. Unlike addition/subtraction, multiplication does not require a common denominator. Multiply straight across.

Cross-cancellation is a shortcut where you simplify before multiplying. If a numerator and a denominator (from different fractions) share a common factor, divide both by that factor first. This keeps numbers smaller.

Convert each mixed number to an improper fraction first, then multiply. Example: 1 1/2 × 2 1/3 → 3/2 × 7/3 = 21/6 = 3 1/2.

The result is always 1. Example: 3/5 × 5/3 = 15/15 = 1. This is because a fraction times its reciprocal equals 1.