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Fraction Calculator

Add, subtract, multiply, and divide fractions. Get simplified results with step-by-step explanations. Supports mixed numbers.

+
Result
5
6
≈ 0.83333333

Step-by-step solution

  1. Find common denominator: LCD = 6
  2. Convert: 3/6 + 2/6
  3. Simplify: GCD(5, 6) = 1 → 5/6

How to Use This Tool

  1. Select an operation: Add, Subtract, Multiply, or Divide.
  2. Enter the numerator and denominator for the first fraction.
  3. Enter the numerator and denominator for the second fraction.
  4. Enable "Use mixed numbers" if you want to enter or view values as a whole number plus a fraction.
  5. Review the result, which is automatically simplified to lowest terms using the GCD, along with its decimal equivalent and step-by-step solution.

Formula & How It Works

Addition / Subtraction

a/b ± c/d = (a×(LCD/b) ± c×(LCD/d)) / LCD

Convert both fractions to the least common denominator (LCD), then add or subtract the numerators.

Multiplication

a/b × c/d = (a × c) / (b × d)

Multiply the numerators together and the denominators together.

Division

a/b ÷ c/d = (a × d) / (b × c)

Multiply the first fraction by the reciprocal (flipped version) of the second fraction.

Simplification

Simplified fraction = (n ÷ GCD(n, d)) / (d ÷ GCD(n, d))

Divide both the numerator and denominator by their Greatest Common Divisor to reduce to lowest terms.

Practical Examples & Common Use Cases

Example: 1/2 + 1/3

The LCD of 2 and 3 is 6. Convert: 3/6 + 2/6 = 5/6, which is already in lowest terms.

Example: 2/3 × 3/4

Multiply numerators: 2 × 3 = 6. Multiply denominators: 3 × 4 = 12. Result = 6/12, simplified using GCD(6,12)=6 to 1/2.

Example: 1/2 ÷ 3/4

Flip the second fraction and multiply: 1/2 × 4/3 = 4/6, simplified using GCD(4,6)=2 to 2/3.

Frequently Asked Questions

Find the least common denominator (LCD), convert each fraction to an equivalent fraction with that denominator, then add the numerators and keep the denominator.

Divide both the numerator and denominator by their Greatest Common Divisor (GCD). For example, 6/8 → GCD(6,8)=2 → 3/4.

A mixed number combines a whole number and a proper fraction, like 2 1/3. Enable the "Use mixed numbers" toggle to input and receive results in mixed number form.

Multiply the first fraction by the reciprocal (flip) of the second fraction. For example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.

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