Adding and Subtracting Fractions Calculator
Add and subtract fractions with step-by-step solutions and detailed explanations
Calculate Fraction Operations
Example Calculations
Same Denominators
Addition: 1/8 + 3/8 = 4/8 = 1/2
Subtraction: 5/12 − 2/12 = 3/12 = 1/4
Just add/subtract numerators!
Different Denominators
Addition: 1/3 + 1/4 = 4/12 + 3/12 = 7/12
Subtraction: 3/4 − 1/6 = 9/12 − 2/12 = 7/12
Find LCD first!
Mixed Numbers
Addition: 2 1/3 + 1 1/4 = 7/3 + 5/4 = 43/12
Result: 43/12 = 3 7/12
Convert to improper fractions first
Simplification
Before: 6/8 + 4/8 = 10/8
After: 10/8 = 5/4 = 1 1/4
Always simplify the result
Key Rules
Same Denominators
Add/subtract numerators, keep denominator
Different Denominators
Find LCD, then add/subtract
Mixed Numbers
Convert to improper fractions first
Simplify
Reduce to lowest terms
Quick Reference
LCD (Least Common Denominator)
The smallest number divisible by all denominators
GCD (Greatest Common Divisor)
Used to simplify fractions
Mixed → Improper
Multiply whole × denominator + numerator
Improper → Mixed
Divide numerator by denominator
Understanding Fraction Addition and Subtraction
Same Denominators
When fractions have the same denominator, adding or subtracting is straightforward. You simply add or subtract the numerators and keep the denominator the same.
Example:
2/7 + 3/7 = (2+3)/7 = 5/7
Different Denominators
When denominators differ, you must:
- • Find the Least Common Denominator (LCD)
- • Convert both fractions to equivalent fractions with the LCD
- • Add or subtract the new numerators
- • Simplify the result if possible
Mixed Numbers
To work with mixed numbers, first convert them to improper fractions:
Converting 2 3/4:
2 × 4 + 3 = 11, so 2 3/4 = 11/4
Simplification
Always check if your answer can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).
Example:
8/12 = (8÷4)/(12÷4) = 2/3