What this tool does
This calculator adds, subtracts, multiplies, and divides two fractions — and instead of just handing you the answer, it walks you through how the answer was found: the least common multiple (LCM) of the denominators, the equivalent fractions, the simplification with the greatest common divisor (GCD) using Euclid’s algorithm, and the mixed-number form whenever the result is an improper fraction. It also shows the decimal value, with the repeating block in parentheses when the decimal never ends, e.g. 5/6 = 0.8(3).
It accepts plain fractions like 3/4, mixed numbers like 1 1/2, whole numbers like 5, and negatives like -2/3. Everything runs with exact integer arithmetic in your browser: no intermediate rounding, and nothing gets sent anywhere.
How to use it
- Type the first fraction. For a mixed number, leave a space between the whole part and the fraction:
1 1/2. - Pick the operation with the +, −, ×, or ÷ buttons.
- Type the second fraction. The result and the full step-by-step appear instantly.
- Hit Copy result to grab the whole equation, e.g.
1/2 + 1/3 = 5/6.
If a denominator is 0, or you try to divide by a fraction that equals 0, the tool warns you instead of producing a bogus answer.
The method, operation by operation
| Operation | Rule | Example |
|---|---|---|
| Addition | LCM of the denominators, then add numerators | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Subtraction | same as addition, subtracting numerators | 3/4 − 1/6 = 9/12 − 2/12 = 7/12 |
| Multiplication | numerator × numerator, denominator × denominator | 2/3 × 3/4 = 6/12 = 1/2 |
| Division | multiply by the reciprocal of the second fraction | 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2 |
After the operation there is always one last step: simplifying. The GCD of the numerator and denominator is found with Euclid’s algorithm (divide, keep the remainder, repeat until it hits zero), and both parts are divided by it. That is how 6/12 becomes 1/2, since GCD(6, 12) = 6.
Worked example
Let’s compute 1/2 + 1/3 by hand, exactly the way the tool does:
- The denominators are 2 and 3. Their LCM is 6 — the smallest number that shows up in both the 2 and 3 times tables.
- Rewrite each fraction over 6: 1/2 = 3/6 (multiply top and bottom by 3) and 1/3 = 2/6 (multiply by 2).
- Add the numerators: 3 + 2 = 5. The provisional result is 5/6.
- Simplify: GCD(5, 6) = 1, so 5/6 is already in lowest terms.
Answer: 1/2 + 1/3 = 5/6, which as a decimal is 0.8(3), i.e. 0.8333… with the 3 repeating forever.
A second example with a mixed number: 1 1/2 ÷ 3/4. First convert the mixed number: 1 1/2 = (1×2 + 1)/2 = 3/2. Dividing means multiplying by the reciprocal: 3/2 × 4/3 = 12/6. Simplify with GCD(12, 6) = 6 and you get 2/1 = 2. That checks out intuitively: one and a half units hold exactly two three-quarter portions.
Frequently asked questions
How do I type a mixed number or a negative fraction?
Mixed number: whole part, a space, then the fraction — e.g. 2 3/4. Negative: a minus sign in front of the whole thing, e.g. -1/2 or -1 1/2 (which equals -3/2). A minus in front of a mixed number applies to the entire value, not just the whole part.
Why do I need the LCM to add fractions but not to multiply them?
Adding fractions means combining pieces, and you can only combine pieces of the same size — that is why the denominators are first matched using the LCM. Multiplying is different: it means taking a fraction of another fraction, so the rule is direct, numerator times numerator over denominator times denominator.
Does the result always come out simplified?
Yes. The tool computes the GCD with Euclid’s algorithm and divides numerator and denominator by it, listing every division of the algorithm in the step-by-step panel. If the GCD is 1, it tells you the fraction was already in lowest terms.
What does the decimal with parentheses mean, like 0.8(3)?
The parentheses mark the repeating block — the digits that go on forever: 0.8(3) means 0.83333… It is the exact way to write a repeating decimal. When the decimal terminates, like 1/2 = 0.5, it is shown without parentheses.
Does it work with large numbers?
Yes. All arithmetic uses arbitrary-precision integers (BigInt), so you can operate on fractions with very large numerators and denominators without any rounding error — the result is always exact.