About the Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer in lowest terms, as a mixed number and as a decimal. You can type simple fractions (3/4), mixed numbers (2 1/4), whole numbers and decimals (0.75), and the calculator shows every step so you can follow or check your homework.
All arithmetic is exact: the calculator works with whole-number numerators and denominators, not rounded decimals, so 7/10 + 1/10 gives exactly 4/5 rather than 0.7999….
How it works
Each input is turned into a single fraction first. A mixed number such as 2 1/4 becomes 9/4, and a decimal such as 0.75 becomes 75/100, which simplifies to 3/4.
To add or subtract, the calculator rewrites both fractions over their least common denominator (LCD) and combines the numerators. To multiply, it multiplies the numerators and the denominators. To divide, it multiplies by the reciprocal of the second fraction. Every result is then simplified by dividing the top and bottom by their greatest common divisor (GCD).
a/b + c/d = (a·d + c·b) / (b·d) a/b − c/d = (a·d − c·b) / (b·d) a/b × c/d = (a·c) / (b·d) a/b ÷ c/d = (a·d) / (b·c) (c ≠ 0) Then divide numerator and denominator by GCD(numerator, denominator).
The decimal is found by long division. When the digits start repeating, the repeating block is shown in brackets: 5/6 = 0.8(3) means 0.8333… with the 3 repeating forever.
Assumptions and limits
- Accepted formats: 3/4, -3/4, 2 1/4, 0.75, 5, and the characters ½ ¼ ¾ ⅓ ⅔ and similar.
- Commas are not accepted, because 1,500 (one thousand five hundred) and 1,5 (one and a half in many countries) can't be told apart. Use a dot for decimals.
- In a mixed number the fraction part must be less than 1 (write 2 3/4, not 1 7/4).
- Numbers can have up to 60 digits. Decimal expansions longer than 40 digits are cut off and marked with …
Worked examples
Adding fractions with different denominators: 1/2 + 1/3
The least common denominator of 2 and 3 is 6, so 1/2 = 3/6 and 1/3 = 2/6. Adding the numerators gives 5/6, which is already in lowest terms. As a decimal that is 0.8(3).
1/2 + 1/3 = 3/6 + 2/6 = 5/6 = 0.8333…
Dividing a mixed number: 2 1/4 ÷ 3/8
Convert 2 1/4 to 9/4, then multiply by the reciprocal of 3/8, which is 8/3. The result 72/12 simplifies to 6.
2 1/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6
Subtracting to a negative answer: 1/2 − 2/3
The least common denominator is 6: 3/6 − 4/6 = −1/6. Negative results are shown with a minus sign in front of the whole fraction.
1/2 − 2/3 = 3/6 − 4/6 = −1/6 = −0.1(6)
Common fractions as decimals
A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5.
| Fraction | Decimal | Repeats? |
|---|---|---|
| 1/2 | 0.5 | No |
| 1/3 | 0.(3) = 0.333… | Yes |
| 2/3 | 0.(6) = 0.666… | Yes |
| 1/4 | 0.25 | No |
| 3/4 | 0.75 | No |
| 1/5 | 0.2 | No |
| 1/6 | 0.1(6) = 0.1666… | Yes |
| 1/8 | 0.125 | No |
| 1/9 | 0.(1) = 0.111… | Yes |
| 1/12 | 0.08(3) = 0.08333… | Yes |
How to use the Fraction Calculator
- Enter the first fraction. Type it as 3/4, a mixed number like 2 1/4, a whole number or a decimal.
- Pick the operation. Choose add, subtract, multiply or divide.
- Enter the second fraction and read the answer. The result appears straight away in lowest terms, as a mixed number and as a decimal, with the working underneath.
Frequently asked questions
How do I type a mixed number?
Leave a space between the whole number and the fraction, for example 3 1/2 for three and a half. A negative mixed number is written -3 1/2, and the minus sign applies to the whole value, so it means −3.5.
What do the brackets in the decimal mean?
They mark the digits that repeat forever. For example 1/7 = 0.(142857) means 0.142857142857… with the six digits in brackets repeating without end. Fractions whose denominators contain only the prime factors 2 and 5 have decimals that end, such as 1/8 = 0.125.
Is the answer exact or rounded?
The fraction answer is exact. The calculator stores every value as a whole-number numerator and denominator, so there is no rounding. Only very long repeating decimals are shortened for display, and that is marked with an ellipsis (…).
Can I use it to simplify a single fraction?
Yes. Type the fraction in the first box: the "Inputs as interpreted" line shows it in lowest terms straight away, for example 18/24 → 3/4. Multiplying by 1 in the second box gives the same simplified fraction as the answer.
Why can't I use a comma as the decimal separator?
In some countries 1,5 means one and a half, while in others 1,500 means one thousand five hundred. Because the calculator can't know which you mean, it asks you to use a dot for decimals and to leave out thousands separators.
This tool runs entirely in your browser. What you enter or upload stays on your device and is never sent to our servers.