Fraction Calculator - Add, Subtract, Multiply, Divide Fractions

Fraction Operations Formulas

To add or subtract fractions, find a common denominator first:

Addition: a/b + c/d = (a×d + c×b) / (b×d)

Subtraction: a/b - c/d = (a×d - c×b) / (b×d)

Multiply numerators together and denominators together:

Multiplication: a/b × c/d = (a×c) / (b×d)

Multiply by the reciprocal of the divisor:

Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)

Example 1: Adding Fractions

Problem: 1/2 + 1/3

Step 1: Find common denominator (LCM of 2 and 3 = 6)

Step 2: Convert: 1/2 = 3/6, 1/3 = 2/6

Step 3: Add: 3/6 + 2/6 = 5/6

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

Example 2: Subtracting Fractions

Problem: 3/4 - 1/6

Step 1: Find common denominator (LCM of 4 and 6 = 12)

Step 2: Convert: 3/4 = 9/12, 1/6 = 2/12

Step 3: Subtract: 9/12 - 2/12 = 7/12

Result: 3/4 - 1/6 = 7/12

Example 3: Multiplying Fractions

Problem: 2/3 × 3/4

Step 1: Multiply numerators: 2 × 3 = 6

Step 2: Multiply denominators: 3 × 4 = 12

Step 3: Simplify: 6/12 = 1/2

Result: 2/3 × 3/4 = 1/2

Example 4: Dividing Fractions

Problem: 1/2 ÷ 1/4

Step 1: Find reciprocal of 1/4: 4/1

Step 2: Multiply: 1/2 × 4/1 = 4/2

Step 3: Simplify: 4/2 = 2

Result: 1/2 ÷ 1/4 = 2

Example 5: Complex Calculation

Problem: 5/6 - 1/4

Step 1: Find common denominator (LCM of 6 and 4 = 12)

Step 2: Convert: 5/6 = 10/12, 1/4 = 3/12

Step 3: Subtract: 10/12 - 3/12 = 7/12

Result: 5/6 - 1/4 = 7/12 (already in simplest form)