Fraction Calculator

Fractions represent parts of a whole number. Operations with fractions require finding common denominators for addition/subtraction, and cross-multiplying for multiplication/division. Our calculator handles all four operations and automatically simplifies results.

Operations Explained

Addition/Subtraction: Find the least common denominator (LCD), convert both fractions, then add or subtract numerators. Example: 1/3 + 1/4 → LCD is 12 → 4/12 + 3/12 = 7/12.

Multiplication: Multiply numerators together and denominators together. Example: 2/3 × 3/4 = 6/12 = 1/2.

Division: Flip the second fraction and multiply. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Practical Examples

Example 1 — Cooking: A recipe calls for 2/3 cup flour but you're making 1.5× the recipe: 2/3 × 3/2 = 6/6 = 1 cup exactly.

Example 2 — Construction: A board is 3/4 inch thick. Stacking 5 boards: 5 × 3/4 = 15/4 = 3¾ inches total.

Example 3 — Time calculation: You worked 5/6 of an hour plus 3/4 of an hour: 5/6 + 3/4 = 20/24 + 18/24 = 38/24 = 1 14/24 = 1 7/12 hours (about 1h 35min).

Simplifying Fractions

To simplify, find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. For 12/18: GCD(12,18) = 6, so 12/18 = 2/3. Our calculator always returns the simplest form automatically.