Fraction
calculator.
Add, subtract, multiply and divide fractions, mixed numbers and decimals with exact arithmetic, or simplify and convert a single number. Every answer comes as a simplified fraction, a mixed number and an exact decimal.
Exact answers,
no rounding.
- a/b + c/d = (a × d′ + c × b′) / LCD, where LCD is the least common denominator and d′, b′ scale each fraction to it.
- a/b × c/d = (a × c) / (b × d).
- a/b ÷ c/d = a/b × d/c (multiply by the reciprocal); dividing by zero is undefined.
- Results are reduced by the greatest common divisor; decimals show repeating digits in brackets, e.g. 1/3 = 0.(3).
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, add the numerators, then simplify. For ¾ + ⅚, the least common denominator is 12: 9/12 + 10/12 = 19/12 = 1 7/12. Mixed numbers work the same way once written as improper fractions: 1 ½ = 3/2.
Multiplying and dividing fractions
Multiply straight across: ⅔ × 9/4 = 18/12 = 3/2. To divide, multiply by the reciprocal of the second fraction: 2 ½ ÷ ¾ = 5/2 × 4/3 = 20/6 = 10/3 = 3 ⅓.
Exact, not approximate
The calculator keeps every number as an exact fraction of whole numbers, so 0.1 + 0.2 is exactly 3/10. Ordinary binary floating-point arithmetic gives 0.30000000000000004 for the same sum.
Converting decimals and repeating decimals
A terminating decimal becomes a fraction over a power of ten, then simplifies: 0.375 = 375/1000 = 3/8. Fractions whose denominators have prime factors other than 2 and 5 repeat forever: 1/7 = 0.142857142857…, shown as 0.(142857).
Worked examples.
Add mixed numbers
1 ½ cups plus ⅔ cup.
2 1/6 (13/6), using the common denominator 6.
Load this exampleSubtract fractions
¾ − ⅚.
-1/12 (common denominator 12).
Load this exampleDivide by a fraction
2 ½ ÷ ¾.
3 1/3 (10/3 = 3.(3)): multiply by the reciprocal 4/3.
Load this exampleDecimal to fraction
0.375 as a fraction.
3/8.
Load this exampleA repeating decimal
1/7 as a decimal.
0.(142857): the six digits 142857 repeat forever.
Load this exampleWhat this calculator
does not do.
- Inputs are limited to 30 digits in the numerator and denominator.
- Very long repeating decimals are cut off after 60 digits and marked with an ellipsis.
- It does not solve equations with unknowns.
Common questions.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. 18/24 has a GCD of 6, so it simplifies to 3/4.
How do I turn a mixed number into an improper fraction?
Multiply the whole number by the denominator and add the numerator: 2 ⅓ = (2 × 3 + 1)/3 = 7/3.
Can I type decimals?
Yes. 0.25, 1,5 and 1e-3 are converted to exact fractions (1/4, 3/2 and 1/1000).
- Math is Fun, Adding Fractions — common denominators
Exact BigInt rational arithmetic. Tests include hand-worked vectors, repeating-decimal detection, input parsing (mixed, vulgar, decimal-comma and scientific forms), division by zero, and 400 randomized pairs checked against floating point and the exact identity (a + b) − b = a.