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Fraction Calculator for Negative and Positive Numbers

Reviewed by Calculator Editorial Team

This fraction calculator handles both positive and negative fractions with precision. Whether you need to add, subtract, multiply, or divide fractions, this tool simplifies the process while maintaining mathematical accuracy.

How to Use This Calculator

Using our fraction calculator is straightforward. Follow these steps:

  1. Enter the first fraction in the format "a/b" where a is the numerator and b is the denominator.
  2. Select the operation you want to perform (+, -, ×, ÷).
  3. Enter the second fraction in the same format.
  4. Click "Calculate" to see the result.
  5. Review the simplified result and the step-by-step solution.

Note: The calculator automatically simplifies results to their lowest terms. Mixed numbers are converted to improper fractions for calculation.

Fraction Operations

This calculator performs four basic operations with fractions:

  • Addition: To add fractions, find a common denominator and add the numerators.
  • Subtraction: Similar to addition, but subtract the numerators.
  • Multiplication: Multiply the numerators together and the denominators together.
  • Division: Multiply the first fraction by the reciprocal of the second fraction.

Formula Used

For addition and subtraction with common denominator d:

(a/d) + (c/d) = (a + c)/d

For multiplication:

(a/b) × (c/d) = (a × c)/(b × d)

For division:

(a/b) ÷ (c/d) = (a × d)/(b × c)

Worked Examples

Example 1: Adding Fractions

Calculate 1/4 + 3/4:

  1. Find a common denominator: 4
  2. Convert fractions: 1/4 + 3/4 = 4/4 + 3/4
  3. Add numerators: (4 + 3)/4 = 7/4
  4. Simplify: 7/4 is already in simplest form

Result: 7/4 or 1 3/4

Example 2: Dividing Negative Fractions

Calculate -2/3 ÷ 4/5:

  1. Find reciprocal of second fraction: 5/4
  2. Multiply: (-2/3) × (5/4) = (-2 × 5)/(3 × 4) = -10/12
  3. Simplify: -10/12 = -5/6

Result: -5/6

FAQ

Can I use mixed numbers in this calculator?

Yes, you can enter mixed numbers in the format "a b/c" where a is the whole number, b is the numerator, and c is the denominator. The calculator will convert them to improper fractions for calculation.

What happens if I enter a fraction with a zero denominator?

The calculator will display an error message since division by zero is undefined in mathematics. Please enter valid fractions with non-zero denominators.

How does the calculator handle negative fractions?

Negative fractions are handled the same way as positive fractions. The sign is preserved through all operations, and the result will be negative when appropriate based on the operation performed.