Fraction
Calculator
Add, subtract, multiply, or divide fractions and mixed numbers in a click, with the simplified result, decimal equivalent, and every working step shown alongside.
Add Two Fractions
Fraction 1
Fraction 2
Result
5/6
Step-by-Step Solution
- 1Fraction 1 as an improper fraction: 1/2
- 2Fraction 2 as an improper fraction: 1/3
- 3Common denominator: 2 × 3 = 6
- 4Combine numerators: (1 × 3) + (1 × 2) = 3 + 2 = 5
- 5Already in lowest terms: 5/6
How to Work with Fractions
A fraction represents a part of a whole: the numerator (top number) counts how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is split into. Adding or subtracting fractions only works when the pieces being counted are the same size, so both fractions first need a common denominator — usually found by multiplying the two denominators together. Multiplying and dividing skip that step entirely, since those operations combine the numerators and denominators as pairs regardless of what size the original pieces were.
Fraction Operation Formulas
Addition/Subtraction: a/b ± c/d = (a×d ± c×b) / (b×d), then simplify by dividing by GCD(numerator, denominator)Multiplication: a/b × c/d = (a×c) / (b×d)Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)Simplify: a/b → divide both a and b by GCD(a, b)➕
Addition
Rewrite both fractions over a common denominator, then add the numerators. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
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Subtraction
Same rule as addition, but subtract the second numerator from the first once both share a denominator.
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Multiplication
Multiply the numerators together and the denominators together — no common denominator needed. 1/2 × 2/3 = 2/6 = 1/3.
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Division
Flip the second fraction and multiply. 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4.
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