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Multiplying Negative and Positive Fractions Calculator

Reviewed by Calculator Editorial Team

Multiplying fractions is a fundamental math skill that extends to negative numbers. This guide explains the rules for multiplying positive and negative fractions, provides a calculator for quick results, and includes practical examples.

How to Multiply Fractions

Multiplying fractions follows a simple rule: multiply the numerators together and the denominators together. The formula is:

Fraction Multiplication Formula

(a/b) × (c/d) = (a × c) / (b × d)

Where:

  • a and c are the numerators
  • b and d are the denominators

After multiplying, simplify the fraction if possible by dividing both numerator and denominator by their greatest common divisor (GCD).

Multiplying Negative Fractions

When multiplying negative fractions, follow these rules:

  1. Multiply the absolute values of the numerators and denominators as with positive fractions
  2. Count the number of negative signs:
    • If there's an even number of negatives (0 or 2), the result is positive
    • If there's an odd number of negatives (1 or 3), the result is negative

Negative Sign Rules

Negative × Negative = Positive
Negative × Positive = Negative
Positive × Negative = Negative
Positive × Positive = Positive

For example, (-2/3) × (-4/5) = (2×4)/(3×5) = 8/15 (positive because there are two negatives)

Worked Examples

Example 1: Positive Fractions

Calculate (3/4) × (2/5):

  1. Multiply numerators: 3 × 2 = 6
  2. Multiply denominators: 4 × 5 = 20
  3. Result: 6/20
  4. Simplify by dividing numerator and denominator by 2: 3/10

Example 2: Negative Fractions

Calculate (-5/6) × (3/4):

  1. Multiply absolute values: 5 × 3 = 15 and 6 × 4 = 24
  2. Count negatives: 1 (odd number)
  3. Result: -15/24
  4. Simplify by dividing numerator and denominator by 3: -5/8

Example 3: Two Negative Fractions

Calculate (-2/3) × (-4/5):

  1. Multiply absolute values: 2 × 4 = 8 and 3 × 5 = 15
  2. Count negatives: 2 (even number)
  3. Result: 8/15 (positive)

FAQ

Can I multiply fractions with different denominators?

Yes, you can multiply fractions with different denominators directly using the formula (a/b) × (c/d) = (a×c)/(b×d). No need to find a common denominator first.

What if one fraction is a whole number?

Treat the whole number as a fraction with denominator 1. For example, 2 × (3/4) = (2/1) × (3/4) = 6/4 = 3/2.

How do I multiply mixed numbers?

Convert mixed numbers to improper fractions first, then multiply as usual. For example, 1 1/2 × 2 1/3 = (3/2) × (7/3) = 21/6 = 7/2.

What's the difference between multiplying and dividing fractions?

When dividing fractions, you invert the second fraction and then multiply. The formula is (a/b) ÷ (c/d) = (a×d)/(b×c).