Adding fractions needs a common denominator: halves and thirds cannot be added until both are written as sixths. Using the least common denominator keeps the numbers small and the final simplification easy.
How to use the Adding Fractions Calculator
- How many fractions?
- Fraction form
- Fraction 1: whole
- Fraction 1: numerator
- Fraction 1: denominator
- Fraction 2: whole
- Fraction 2: numerator
- Fraction 2: denominator
- Fraction 3: whole
- Fraction 3: numerator
- Fraction 3: denominator
- Fraction 4: whole
- Fraction 4: numerator
- Fraction 4: denominator
- Fraction 5: whole
- Fraction 5: numerator
- Fraction 5: denominator
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The least common multiple of the denominators is found, each fraction is rewritten over it, the numerators are added and the result is simplified by the greatest common factor.
Formula
a/b + c/d + … = (sum of numerators over the LCD) ÷ LCD, then simplify
Worked example
Inputs — How many fractions?: 3; Fraction form: Simple fraction; Fraction 1: numerator: 1; Fraction 1: denominator: 2; Fraction 2: numerator: 1; Fraction 2: denominator: 3; Fraction 3: numerator: 1; Fraction 3: denominator: 6.
Results — Result = 1; Mixed number = 1; Decimal = 1; Steps = 1. LCD of 2, 3, 6 = 6
2. Rewrite over 6: 3/6 + 2/6 + 1/6
3. Add the numerators: 6/6
4. Simplify: 1.
Key terms
- Least common denominator (LCD)
- The least common multiple of the denominators.
Frequently asked questions
How do I add 1/2 and 1/3?
Rewrite as 3/6 + 2/6 = 5/6.
Do I add the denominators?
No – only the numerators are added once the denominators match.
How do I add fractions with the same denominator?
Add the numerators and keep the denominator: 2/7 + 3/7 = 5/7.
What if the sum is an improper fraction?
It can be written as a mixed number, e.g. 7/4 = 1 3/4.