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Fraction Calculator with Negatives Numbers

Reviewed by Calculator Editorial Team

This fraction calculator handles negative numbers for all basic operations: addition, subtraction, multiplication, and division. Learn how to perform these operations with negative fractions and understand the rules for working with negative signs.

How to Use This Calculator

Enter two fractions with negative numbers in the format -a/b or a/-b. Select the operation you want to perform, then click "Calculate". The calculator will show the result in its simplest form and explain the steps.

Note: When entering negative fractions, you can either put the negative sign before the numerator (-a/b) or before the denominator (a/-b). Both formats are accepted.

Fraction Operations with Negatives

Addition and Subtraction

To add or subtract fractions with negatives, follow these steps:

  1. Find a common denominator for both fractions.
  2. Convert each fraction to have this common denominator.
  3. Add or subtract the numerators while keeping the denominator the same.
  4. Simplify the result if possible.

Addition Formula

(a/b) + (c/d) = [(a × d) + (c × b)] / (b × d)

Subtraction Formula

(a/b) - (c/d) = [(a × d) - (c × b)] / (b × d)

Multiplication

Multiplying fractions with negatives is straightforward:

  1. Multiply the numerators together.
  2. Multiply the denominators together.
  3. Simplify the result if possible.

Multiplication Formula

(a/b) × (c/d) = (a × c) / (b × d)

Division

Dividing fractions with negatives requires finding the reciprocal of the second fraction:

  1. Multiply the first fraction by the reciprocal of the second fraction.
  2. Simplify the result if possible.

Division Formula

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

Worked Examples

Example 1: Adding Negative Fractions

Calculate (-3/4) + (1/2)

  1. Find common denominator: 4
  2. Convert fractions: (-3/4) + (2/4) = (-3 + 2)/4 = -1/4
  3. Result: -1/4

Example 2: Multiplying Negative Fractions

Calculate (-2/3) × (4/-5)

  1. Multiply numerators: (-2) × 4 = -8
  2. Multiply denominators: 3 × (-5) = -15
  3. Result: -8/-15 = 8/15
Comparison of Fraction Operations with Negatives
Operation Example Result
Addition (-1/2) + (3/4) 5/4 or 1 1/4
Subtraction (-2/3) - (-1/6) -1/2
Multiplication (-3/4) × (2/-5) 3/10
Division (-4/5) ÷ (2/-3) 6/5 or 1 1/5

FAQ

Can I enter mixed numbers in this calculator?
No, this calculator only accepts improper fractions or fractions with negative signs. You can convert mixed numbers to improper fractions before entering them.
What happens if I divide by zero?
The calculator will display an error message since division by zero is undefined in mathematics.
How do I simplify the result?
The calculator automatically simplifies the result to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).
Can I perform multiple operations at once?
No, this calculator performs one operation at a time. You'll need to perform operations sequentially if you need to combine multiple steps.