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Calculator for Fractions with Negatives

Reviewed by Calculator Editorial Team

This calculator helps you perform arithmetic operations with fractions that include negative numbers. Whether you're adding, subtracting, multiplying, or dividing negative fractions, this tool provides accurate results and explains the process step by step.

How to Use This Calculator

Using this calculator is straightforward. Follow these steps:

  1. Select the operation you want to perform (addition, subtraction, multiplication, or division).
  2. Enter the numerator and denominator for the first fraction.
  3. Enter the numerator and denominator for the second fraction.
  4. Click the "Calculate" button to see the result.
  5. Review the detailed solution and explanation.

The calculator will display the result in its simplest form and provide a step-by-step breakdown of how the calculation was performed.

Formulas Used

The calculator uses standard fraction arithmetic formulas:

Addition of Fractions

To add two fractions, find a common denominator and add the numerators:

a/b + c/d = (a×d + b×c)/(b×d)

Subtraction of Fractions

To subtract two fractions, find a common denominator and subtract the numerators:

a/b - c/d = (a×d - b×c)/(b×d)

Multiplication of Fractions

To multiply two fractions, multiply the numerators together and the denominators together:

a/b × c/d = (a×c)/(b×d)

Division of Fractions

To divide two fractions, multiply the first fraction by the reciprocal of the second:

a/b ÷ c/d = (a×d)/(b×c)

After performing the operation, the calculator simplifies the result by dividing both the numerator and denominator by their greatest common divisor (GCD).

Worked Examples

Let's look at some examples to see how the calculator works with negative fractions.

Example 1: Adding Negative Fractions

Calculate -3/4 + -2/5:

  1. Find a common denominator: 4 × 5 = 20
  2. Convert fractions: -3/4 = -15/20, -2/5 = -8/20
  3. Add numerators: -15 + (-8) = -23
  4. Result: -23/20 (already in simplest form)

Example 2: Subtracting Negative Fractions

Calculate -5/6 - -3/4:

  1. Find a common denominator: 6 × 4 = 24
  2. Convert fractions: -5/6 = -20/24, -3/4 = -18/24
  3. Subtract numerators: -20 - (-18) = -2
  4. Result: -2/24 = -1/12 (simplified)

Example 3: Multiplying Negative Fractions

Calculate -2/3 × -4/5:

  1. Multiply numerators: -2 × -4 = 8
  2. Multiply denominators: 3 × 5 = 15
  3. Result: 8/15 (already in simplest form)

Example 4: Dividing Negative Fractions

Calculate -3/4 ÷ -5/8:

  1. Find reciprocal of second fraction: -8/5
  2. Multiply: -3/4 × -8/5 = 24/20
  3. Simplify: 24/20 = 6/5
  4. Result: 6/5

Frequently Asked Questions

Can this calculator handle mixed numbers?
No, this calculator works with improper fractions only. You'll need to convert mixed numbers to improper fractions before using this calculator.
What happens if I enter a zero in the denominator?
The calculator will display an error message because division by zero is undefined in mathematics.
How does the calculator simplify fractions?
The calculator uses the greatest common divisor (GCD) to simplify fractions. It divides both the numerator and denominator by their GCD to get the simplest form.
Can I use this calculator for decimal numbers?
No, this calculator is specifically designed for fractions. For decimal calculations, you should use a different calculator.
Is there a way to save my calculations?
Currently, this calculator does not have a save feature. You can manually record your results or use your browser's print function to save a copy.