Fraction Calculator
Enter two fractions and an operation. The answer is reduced to lowest terms and shown as a mixed number and a decimal, with each step of the working.
Result
- Mixed number
- 5/6
- Decimal
- 0.833333
Steps
- Find a common denominator: LCM(2, 3) = 6.
- Rewrite: 1/2 = 3/6 and 1/3 = 2/6.
- Add the numerators: 3 + 2 = 5, so the result is 5/6.
- The fraction is already in lowest terms.
How fraction arithmetic works
A fraction such as 3/4 means three parts out of four equal parts. The top number is the numerator and the bottom number is the denominator. Two fractions are equal if one can be turned into the other by multiplying or dividing both parts by the same number, which is why 2/4, 3/6 and 1/2 are the same value. The rules below follow from that single idea.
Formulas
Addition and subtraction: a/b ± c/d = (a·d ± c·b) / (b·d), then simplify. Using the least common multiple of b and d instead of b·d keeps the numbers smaller.
Multiplication: a/b × c/d = (a·c) / (b·d)
Division: a/b ÷ c/d = a/b × d/c = (a·d) / (b·c), i.e. multiply by the reciprocal.
Worked example: 1/2 + 1/3. The least common multiple of 2 and 3 is 6. Rewrite 1/2 as 3/6 and 1/3 as 2/6. Add the numerators: 3 + 2 = 5, so the sum is 5/6, which is about 0.8333. Because 5 and 6 share no common factor, the result is already in lowest terms.
How to use this calculator
- Type the numerator and denominator of the first fraction. Negative numerators are allowed.
- Choose add, subtract, multiply or divide.
- Type the second fraction. The reduced answer, mixed number, decimal and step-by-step working update immediately.
To work with a whole number, enter it over a denominator of 1. To work with a mixed number such as 2 1/4, enter it as the improper fraction 9/4.
Tips and common mistakes
- Never add denominators: 1/2 + 1/2 is 1, not 2/4.
- When dividing, flip only the second fraction before multiplying.
- Simplify at the end (or cancel common factors before multiplying) to keep numbers manageable.
- A denominator of 0 is undefined, so the calculator shows an error instead of a result.
Related tools: convert a fraction to a percentage with the percentage calculator, or compare quantities with the ratio calculator.
Frequently asked questions
Why do fractions need a common denominator to add or subtract?
Fractions are only comparable when they are cut into the same size pieces. 1/2 and 1/3 are halves and thirds; rewritten as 3/6 and 2/6 both are sixths, so the numerators can simply be added to give 5/6. Multiplication and division do not need this step.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor (GCD). For 6/8 the GCD is 2, giving 3/4. If the GCD is 1 the fraction is already in lowest terms.
How do I enter a mixed number like 1 1/2?
Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator. 1 1/2 becomes (1 × 2 + 1)/2 = 3/2, so enter 3 as the numerator and 2 as the denominator.
What does a negative result mean?
The sign is shown on the numerator, for example −1/6. For mixed numbers the sign is attached to the whole part, such as −3 1/4, meaning negative three and a quarter.