Fraction calculator
Fractions can only be added or subtracted once their denominators match: you convert them to a common denominator, do the operation on the numerators, and reduce the result. Multiplication and division need no common denominator — you multiply numerators and denominators straight across.
- As a mixed number
- 5/6
- As a decimal
- 0.833333
- Common denominator
- 6
Rates and thresholds
- Addition
- a/b + c/d = (ad + cb) / bd
- Multiplication
- a/b × c/d = ac / bd
- Division
- a/b ÷ c/d = a/b × d/c
- Reducing
- Divide numerator and denominator by their greatest common divisor
How do you find a common denominator?
The simplest common denominator is the product of the denominators: for 1/2 and 1/3 that is 2 × 3 = 6. The lowest common denominator is the least common multiple of the denominators, which keeps the numbers smaller — for 1/4 and 1/6 the product is 24 but the least common multiple is 12. Either gives the right answer; the lower one leaves less reducing to do.
What is the difference between a proper fraction, an improper fraction and a mixed number?
A proper fraction has a numerator smaller than its denominator, such as 3/4, and its value lies between zero and one. An improper fraction has a numerator greater than or equal to the denominator, such as 7/4. The same number can be written as the mixed number 1 3/4, with the whole part pulled out. Improper fractions are easier to calculate with, while mixed numbers usually read better in an answer, so both are shown here.
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