Fraction Calculator
3/4 + 1/6 = 11/12. 0.(3) = 1/3, and 1/3 = 0.(3).
How to use
- In Calculate, type two numbers (a fraction like 3/4, a mixed number like 1 3/4, or a decimal) and pick +, -, × or ÷.
- In Convert, type one number to reduce it, see it as a mixed number, or turn a decimal such as 0.(3) into a fraction.
- Read the answer in lowest terms with its mixed-number and decimal forms. Use Copy result to paste it.
How it works
Add and subtract: a/b ± c/d = (a·d ± c·b) / (b·d), then reduce. With a common denominator the numerators are added directly.
Multiply: a/b × c/d = (a·c) / (b·d). Divide: a/b ÷ c/d = (a·d) / (b·c), which is multiplying by the reciprocal. Dividing by zero is not defined.
Simplify: divide the numerator and denominator by their greatest common divisor, for example 12/18 ÷ 6 = 2/3.
Mixed number: divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator, so 7/4 = 1 3/4.
Decimal to fraction: 0.75 = 75/100 = 3/4. A repeating decimal a.b(c) equals (abc − ab) / (10^len(b) × (10^len(c) − 1)), so 0.(3) = 3/9 = 1/3. All arithmetic uses exact whole numbers, so there is no rounding.
Worked examples
Every result is reduced to lowest terms. A mixed number is shown only when the value is above 1 or below -1 and is not a whole number.
| Calculation | Result | Mixed number | Decimal |
|---|---|---|---|
| 3/4 + 1/6 | 11/12 | - | 0.91(6) |
| 5/6 − 1/4 | 7/12 | - | 0.58(3) |
| 2/3 × 9/10 | 3/5 | - | 0.6 |
| 3/5 ÷ 9/10 | 2/3 | - | 0.(6) |
| 1 3/4 + 2 1/2 | 17/4 | 4 1/4 | 4.25 |
| 0.(3) | 1/3 | - | 0.(3) |
| 12/18 | 2/3 | - | 0.(6) |
How to type a number
- Fraction: 3/4. A negative fraction: -3/4.
- Mixed number: 1 3/4 (a space between the whole part and the fraction). Negative: -1 3/4.
- Decimal: 0.75 or 0,75. A comma or a point both work.
- Repeating decimal: put the repeating digits in brackets, so 0.(3) is 0.333... and 1.2(34) is 1.2343434...
- Whole number: 5.
About the decimal form
Every fraction is either a terminating decimal such as 0.125 or a repeating one such as 0.(142857). The calculator finds the repeating block by long division. If the block is longer than 40 digits (1/97 repeats every 96 digits, for instance), it shows the first 40 digits and marks the value as rounded.
The conversion from 0.(9) to 1 is exact: 0.999... and 1 are the same number.
FAQ
How do I enter a mixed number?
Type the whole part, a space, then the fraction: 2 1/2. For a negative mixed number put the minus sign first: -2 1/2 means minus two and a half.
Can I type a repeating decimal?
Yes. Put the repeating digits in brackets: 0.(3) is one third, 0.1(6) is one sixth, and 0.(142857) is one seventh.
Why is 0.(9) equal to 1?
Because 0.(9) = 9/9 by the repeating-decimal rule, and 9/9 is 1. 0.999... and 1 are two ways of writing the same number.
What does the calculator do with a result that is a whole number?
It shows it as a whole number, such as 3 instead of 3/1. A fraction with a denominator of 1 is just an integer.
Are the results exact?
Yes. The calculator works with whole numbers of any size, not floating point, so 1/3 + 1/6 is exactly 1/2 and very large numerators and denominators stay correct.
Can I get a decimal that ends instead of repeating?
A fraction in lowest terms ends only when its denominator has no prime factors other than 2 and 5, as in 3/8 = 0.375. Otherwise the decimal repeats.