Fractions can only be added or subtracted when they share a denominator. The least common denominator keeps the numbers small, so the final simplification is easy. Mixed numbers are first turned into improper fractions.
How to use the Adding and Subtracting Fractions Calculator
- Operation
- My fractions are in
- Fraction 1: whole
- Fraction 1: numerator
- Fraction 1: denominator
- Fraction 2: whole
- Fraction 2: numerator
- Fraction 2: denominator
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator finds the least common multiple of the denominators, rewrites each fraction over it, adds or subtracts the numerators and simplifies with the greatest common factor.
Formula
a/b ± c/d = (a·(L/b) ± c·(L/d)) / L, L = LCM(b, d)
Worked example
Inputs — Operation: Addition; My fractions are in: Simple fraction; Fraction 1: numerator: 3; Fraction 1: denominator: 4; Fraction 2: numerator: 2; Fraction 2: denominator: 5.
Results — Result = 23/20; Mixed number = 1 3/20; Decimal = 1.15; Steps = 1. Least common denominator: LCD(4, 5) = 20
2. Rewrite: 3/4 = 15/20, 2/5 = 8/20
3. Add the numerators: 15 + (8) = 23, giving 23/20
4. Simplify: 23/20 = 1 3/20.
Key terms
- Least common denominator
- The smallest number that all denominators divide.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite them over the least common denominator, add the numerators and simplify.
How do I subtract mixed numbers?
Convert them to improper fractions, subtract, then convert back.
Do I need the least common denominator?
Any common denominator works, but the least one keeps the numbers small.
What is 1/2 + 1/3?
3/6 + 2/6 = 5/6.