Fraction Calculator

Fraction Calculator with Step-by-Step Solutions

🔢 Perform all operations with fractions: addition, subtraction, multiplication, and division. Get simplified results, decimal equivalents, mixed numbers, and detailed step-by-step solutions.

How to Use

1. Enter the numerator and denominator for both fractions
2. Select the operation you want to perform (+, −, ×, ÷)
3. See the result automatically with simplified form
4. Review the step-by-step solution

Fraction Operations Explained

Addition & Subtraction

To add or subtract fractions, you need a common denominator:

• Find the Least Common Multiple (LCM) of denominators
• Convert both fractions to equivalent fractions with the common denominator
• Add or subtract the numerators
• Simplify the result

Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Multiplication

Multiplying fractions is straightforward:

• Multiply the numerators together
• Multiply the denominators together
• Simplify the result

Example: 1/2 × 2/3 = 2/6 = 1/3

Division

To divide fractions, use the "flip and multiply" rule:

• Keep the first fraction as is
• Flip the second fraction (reciprocal)
• Multiply the fractions
• Simplify the result

Example: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1½

Simplifying Fractions

A fraction is simplified when the numerator and denominator have no common factors other than 1. To simplify, divide both by their Greatest Common Divisor (GCD).

Example: 8/12 = 2/3 (divide both by 4)

Mixed Numbers vs Improper Fractions

• Proper Fraction: Numerator < Denominator (e.g., 3/4)
• Improper Fraction: Numerator ≥ Denominator (e.g., 7/4)
• Mixed Number: Whole number + fraction (e.g., 1¾)

Common Applications

• Cooking and recipes (scaling ingredients)
• Carpentry and construction (measurements)
• Mathematics homework and education
• Financial calculations (portions, shares)
• Time calculations (hours and minutes)

💡 Pro Tip: Always simplify your final answer to make it easier to understand. Our calculator automatically shows both the exact fraction and decimal equivalent for convenience.