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Dividing Negative and Positive Fractions Calculator

Reviewed by Calculator Editorial Team

Dividing fractions is a fundamental math operation that appears in many real-world problems. This guide explains how to divide both negative and positive fractions, including the rules for handling signs and the step-by-step process.

How to Divide Fractions

The basic rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping its numerator and denominator.

Division Formula

a/b ÷ c/d = a/b × d/c = (a × d)/(b × c)

To divide fractions:

  1. Find the reciprocal of the second fraction (flip it).
  2. Multiply the first fraction by this reciprocal.
  3. Multiply the numerators together and the denominators together.
  4. Simplify the resulting fraction if possible.

Note: When dividing mixed numbers, first convert them to improper fractions before applying the division rule.

Dividing Negative Fractions

When dividing negative fractions, follow the same basic steps as with positive fractions, but pay special attention to the signs:

  1. Determine if the result will be positive or negative by applying the rules of signs:
    • Negative ÷ Negative = Positive
    • Negative ÷ Positive = Negative
    • Positive ÷ Negative = Negative
    • Positive ÷ Positive = Positive
  2. Find the reciprocal of the second fraction.
  3. Multiply the numerators and denominators as usual.
  4. Apply the sign determined in step 1 to the final result.

Negative Division Example

-3/4 ÷ -2/5 = (-3/4) × (5/2) = -15/8 = 1 7/8

Dividing Positive Fractions

Dividing positive fractions follows the same process as negative fractions, but with positive results:

  1. Find the reciprocal of the second fraction.
  2. Multiply the numerators and denominators.
  3. Simplify the result if possible.

Positive Division Example

2/3 ÷ 5/6 = (2/3) × (6/5) = 12/15 = 4/5

Worked Examples

Example 1: Dividing Negative Fractions

Calculate -5/6 ÷ -3/4

  1. Determine the sign: Negative ÷ Negative = Positive
  2. Find reciprocal of -3/4: 4/3
  3. Multiply: (-5/6) × (4/3) = -20/18 = -10/9
  4. Apply positive sign: 10/9

Example 2: Dividing Mixed Sign Fractions

Calculate -7/8 ÷ 3/4

  1. Determine the sign: Negative ÷ Positive = Negative
  2. Find reciprocal of 3/4: 4/3
  3. Multiply: (-7/8) × (4/3) = -28/24 = -7/6
  4. Apply negative sign: -7/6

FAQ

What is the rule for dividing fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
How do you handle negative signs when dividing fractions?
Apply the standard rules of signs: two negatives make a positive, and a positive and negative make a negative.
Can you divide mixed numbers directly?
No, convert mixed numbers to improper fractions before dividing.
What happens if the denominator becomes zero?
Division by zero is undefined. Ensure your fractions have non-zero denominators.
How do you simplify the result of a fraction division?
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.