Fraction calculator
Add, subtract, multiply and divide fractions and mixed numbers, simplified with steps.
Step by step
- Write both as improper fractions
1/2 + 1/3 - Find the least common denominator
LCD(2, 3) = 6 - Rewrite over that denominator
3/6 + 2/6 - Combine the numerators
5/6 - Divide top and bottom by their GCD
GCD(5, 6) = 1 → 5/6
How it works
Fractions only add and subtract when they are cut into the same size pieces — that is what a common denominator is for. Multiplication and division need no such setup, which is why they are, counter-intuitively, the easier operations.
a/b + c/d = (ad + cb) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = a/b × d/c Why dividing flips the second fraction
Dividing by a number is the same as multiplying by its reciprocal. “How many halves are in 3?” is 3 ÷ ½, and the answer is 6 — because you are asking how many times the smaller piece fits, which multiplication by 2 answers directly.
Lowest terms
A fraction is simplified when the numerator and denominator share no factor but 1. Dividing both by their greatest common divisor does it in one step, which is what the last step above shows.