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Common Fraction Operations Reference
- Addition/Subtraction: find LCD, convert, then add/subtract numerators
- Multiplication: multiply numerators × numerators, denominators × denominators
- Division: multiply by the reciprocal (flip the second fraction)
- Simplification: divide both numerator and denominator by their GCD
- Mixed to improper: (whole × denominator + numerator) / denominator
The Fraction Calculator on TechConverter.me handles all fraction types — proper, improper, and mixed numbers — with full step-by-step solutions that make it useful for both checking answers and understanding the process.
Examples
Example 1: Adding Fractions with Different Denominators
Problem: 3/4 + 2/3
Step 1: Find the Least Common Denominator (LCD)
Denominators: 4 and 3
LCD = 12
Step 2: Convert to equivalent fractions
3/4 = 9/12 (multiply numerator and denominator by 3)
2/3 = 8/12 (multiply numerator and denominator by 4)
Step 3: Add the numerators
9/12 + 8/12 = 17/12
Step 4: Simplify (check if reducible)
GCD(17, 12) = 1 — already in lowest terms
Result: 17/12 = 1 5/12 (as mixed number)
Decimal: 1.4167
Example 2: Subtracting Mixed Numbers
Problem: 3 1/2 - 1 3/4
Step 1: Convert to improper fractions
3 1/2 = 7/2
1 3/4 = 7/4
Step 2: Find LCD
LCD of 2 and 4 = 4
Step 3: Convert to equivalent fractions
7/2 = 14/4
7/4 = 7/4
Step 4: Subtract
14/4 - 7/4 = 7/4
Step 5: Convert back to mixed number
7/4 = 1 3/4
Result: 1 3/4
Decimal: 1.75
Example 3: Multiplying Fractions
Problem: 2/3 × 5/8
Step 1: Multiply numerators
2 × 5 = 10
Step 2: Multiply denominators
3 × 8 = 24
Step 3: Simplify
10/24 — GCD(10, 24) = 2
10/24 ÷ 2/2 = 5/12
Result: 5/12
Decimal: 0.4167
Tip: Cross-cancel before multiplying for simpler numbers:
2/3 × 5/8 → (2÷2)/(8÷2) × 5/3 = 1/4 × 5/3 = 5/12