Fractions Calculator

Result

The calculated result will appear here with full step-by-step process.

How to Use the Fractions Calculator

This Fractions Calculator helps you add, subtract, multiply, or divide fractions with clear step-by-step explanations. Results include simplified fractions, mixed numbers, and decimals.

Step-by-Step Guide

  1. Enter the first fraction (e.g., 5/6 or mixed number 1 2/3).
  2. Select the operation: +, -, *, or /.
  3. Enter the second fraction (e.g., 7/8 or 2 1/2).
  4. Click Calculate to see a full solution including:
    • Conversion to improper fractions
    • Applied formula for the operation
    • Simplified fraction
    • Mixed number result
    • Decimal equivalent
  5. Use Copy Result to save results or Reset to restore example values.

Fraction Formulas

Operation Formula Example
Addition a/b + c/d = (a×d + b×c)/(b×d) 5/6 + 7/8 = 86/48 → 1 19/24 → 1.7917
Subtraction a/b - c/d = (a×d - b×c)/(b×d) 5/6 - 7/8 = -1/24 → -0.0417
Multiplication a/b × c/d = (a×c)/(b×d) 5/6 × 7/8 = 35/48 → 0.7292
Division a/b ÷ c/d = (a×d)/(b×c) 5/6 ÷ 7/8 = 20/21 → 0.9524

How Fractions Are Simplified

Divide numerator and denominator by their greatest common divisor (GCD).

  • Example: 86/48 → GCD 2 → Simplified: 43/24
  • Example: 40/42 → GCD 2 → Simplified: 20/21

Mixed Number Conversion

If the numerator is larger than the denominator:

  • 43/24 → 1 19/24
  • 35/48 → stays proper fraction

Decimal Conversion

  • 43/24 = 1.7917
  • 20/21 ≈ 0.9524

Example Calculations

Addition Example

Inputs: 5/6 + 7/8

  1. Convert to improper fractions: 5/6, 7/8
  2. Apply formula: (5×8 + 6×7)/(6×8) = 86/48
  3. Simplify: 43/24
  4. Mixed number: 1 19/24
  5. Decimal: 1.7917

Subtraction Example

5/6 - 7/8 = -1/24 → Decimal ≈ -0.0417

Multiplication Example

5/6 × 7/8 = 35/48 → Decimal ≈ 0.7292

Division Example

5/6 ÷ 7/8 = 20/21 → Decimal ≈ 0.9524

Student Tips

  • Enter fractions correctly (numerator/denominator)
  • Use a space for mixed numbers: e.g., 1 2/3
  • Calculator automatically simplifies
  • Copy or print results for homework
  • Practice proper, improper, mixed, and negative fractions

Frequently Asked Questions

Q1: Can I enter whole numbers?
Yes, 3 → 3/1
Q2: Can I use mixed numbers?
Yes, like 1 2/3
Q3: Difference between simplified and mixed numbers?
Simplified keeps numerator/denominator, mixed shows whole + fraction
Q4: How is decimal calculated?
Divide numerator by denominator
Q5: What if numerator < denominator?
Fraction remains proper

Benefits for Students

  • Step-by-step understanding of fraction operations
  • See formulas and simplification process
  • Multiple result formats: simplified, mixed, decimal
  • Homework checking and practice
  • Copy or print results easily
  • Practice proper, improper, mixed, and negative fractions