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Multiply Negative Fractions Calculator

Reviewed by Calculator Editorial Team

Multiplying negative fractions can be tricky, but this calculator makes it simple. Learn the rules, see worked examples, and understand how negative signs affect the result.

How to Multiply Negative Fractions

When multiplying fractions with negative signs, follow these steps:

  1. Identify the signs of each fraction (positive or negative).
  2. Multiply the absolute values of the numerators together.
  3. Multiply the absolute values of the denominators together.
  4. 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), the result is negative.
  5. Simplify the resulting fraction if possible.

Key Rule

A negative times a negative is a positive. This is because the negatives cancel each other out.

Formula

Multiplying Negative Fractions

Given two fractions: a/b and c/d, the product is calculated as:

(a × c) / (b × d)

The sign of the result depends on the number of negative signs in the original fractions.

Examples

Example 1: Both Fractions Negative

Multiply -3/4 by -5/6:

  1. Multiply numerators: 3 × 5 = 15
  2. Multiply denominators: 4 × 6 = 24
  3. Count negatives: 2 (even) → result is positive
  4. Final result: 15/24, which simplifies to 5/8

Example 2: One Fraction Negative

Multiply -2/3 by 4/5:

  1. Multiply numerators: 2 × 4 = 8
  2. Multiply denominators: 3 × 5 = 15
  3. Count negatives: 1 (odd) → result is negative
  4. Final result: -8/15

Common Mistakes

  • Forgetting to count the negative signs properly, leading to incorrect results.
  • Not simplifying the final fraction, which can make the answer appear more complex than it needs to be.
  • Assuming that multiplying by a negative always makes the result negative, ignoring the second negative sign.

FAQ

Can I multiply more than two negative fractions at once?
Yes, you can multiply any number of fractions. Count all the negative signs and apply the same rules.
What if one of the fractions 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 negative fractions with variables?
Follow the same steps, but keep the variables separate. For example, -a/2 × -3b/5 = (a × 3b)/(2 × 5) = 3ab/10.