Fraction Calculator
Enter two fractions, pick an operation, and get the exact answer reduced to lowest terms — with the steps.
Whole numbers only. Leave the whole box empty for a simple fraction; use it for mixed numbers like 2 1/4. Negative signs are allowed.
Enter any fraction to reduce it to lowest terms. Whole numbers only.
Working with fractions: the rules behind the calculator
Fractions turn up anywhere a whole is split into equal parts: a recipe calling for 2 1/4 cups of flour, a carpenter marking a board at 5 3/8 inches, a grade sheet reporting 17/20 correct, or a spreadsheet formula that needs an exact ratio instead of a rounded decimal. Unlike a calculator that only handles decimals, working in fractions keeps the answer exact — 1/3 stays 1/3 instead of turning into a rounded 0.333. That matters whenever a measurement, a recipe, or a shared bill has to divide evenly, and it's why this tool keeps every result as a fraction first, with the decimal shown only as a secondary reference.
How to enter a fraction
- In the Calculate tab, fill in Fraction A: leave the "whole" box empty for a plain fraction like 3/4, or fill it in for a mixed number like 2 1/4 (whole = 2, numerator = 1, denominator = 4).
- Pick an operation — add, subtract, multiply, or divide — then fill in Fraction B the same way.
- The result panel shows the answer as a reduced fraction, as a mixed number if it's greater than one, and as a decimal, with a step-by-step breakdown available underneath.
- Switch to the Simplify tab to reduce a single numerator/denominator pair to lowest terms without doing an operation.
- Negative signs are accepted on the numerator or whole part (e.g. -3/4 or -1 1/2); denominators should stay positive.
The arithmetic behind each operation
Add or subtract — the denominators must match first. Convert both fractions to a common denominator (the calculator uses the least common multiple of the two denominators so the numbers stay as small as possible), then add or subtract only the numerators:
a/b + c/d = (a·d + c·b) / (b·d), then reduced by dividing through by the greatest common divisor (GCD).
Multiply — no common denominator needed. Multiply numerator by numerator and denominator by denominator: a/b × c/d = (a·c)/(b·d).
Divide — flip (take the reciprocal of) the second fraction and multiply: a/b ÷ c/d = a/b × d/c = (a·d)/(b·c). A mixed number is first converted to an improper fraction (whole × denominator + numerator, over the same denominator) before any of these operations run.
Worked examples
1. Adding mixed numbers. 1 3/4 + 2 1/3 → convert to improper fractions: 7/4 and 7/3. LCD of 4 and 3 is 12: 7/4 = 21/12, 7/3 = 28/12. Sum: 49/12. As a mixed number that's 4 1/12, and as a decimal ≈ 4.0833.
2. Subtracting with borrowing. 3 1/6 − 1 1/2 → improper form: 19/6 − 3/2. LCD of 6 and 2 is 6: 3/2 = 9/6. 19/6 − 9/6 = 10/6, which reduces (GCD 2) to 5/3, i.e. 1 2/3 or ≈ 1.6667.
3. Multiplying then simplifying. 8/9 × 3/4 = 24/36. The GCD of 24 and 36 is 12, so 24/36 reduces to 2/3 ≈ 0.6667. Multiplying first and reducing afterward always gives the same reduced answer as canceling common factors before multiplying.
4. Dividing fractions. 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12, which reduces (GCD 3) to 5/4, or the mixed number 1 1/4 (1.25).
Quick reference: common fractions as decimals
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/2 | 0.5 | 1/8 | 0.125 |
| 1/3 | 0.333… | 3/8 | 0.375 |
| 2/3 | 0.666… | 5/8 | 0.625 |
| 1/4 | 0.25 | 7/8 | 0.875 |
| 3/4 | 0.75 | 1/6 | 0.1666… |
| 1/5 | 0.2 | 5/6 | 0.8333… |
Common mistakes to avoid
- Adding numerators and denominators straight across. 1/2 + 1/3 is not 2/5 — you must find a common denominator first (it's 5/6).
- Forgetting to convert a mixed number before dividing. 2 1/2 ÷ 1/4 needs 2 1/2 turned into 5/2 first; dividing the whole and fraction parts separately gives the wrong answer.
- Stopping before the fraction is fully reduced. 6/8 and 3/4 are the same value, but only 3/4 is in lowest terms — always divide by the full GCD, not just any common factor.
- Reading a repeating decimal as exact. 1/3 truncated to 0.33 loses precision; when exactness matters (splitting a bill, cutting a board), keep the fraction form rather than a rounded decimal.
What this tool doesn't do
This calculator handles two fractions and one operation at a time (or one fraction to simplify) using exact integer arithmetic — it does not evaluate multi-step expressions with parentheses, nor does it work with fractions that have variables (algebraic fractions) or irrational denominators. For very large numerators or denominators the display switches to a compact layout so the exact value still fits on screen without rounding. If a calculation needs unit conversion (say, feet to inches before dividing), convert to the same unit first — the tool only performs the fraction arithmetic itself.
Sources & further reading
- Khan Academy Arithmetic — lessons on adding, subtracting, multiplying and dividing fractions
- GOV.UK National Curriculum — the mathematics programmes of study that define fraction and decimal expectations
- NIST Special Publication 811 — guidance on significant digits and rounding when converting exact values to decimals
Frequently asked questions
How do you add and subtract fractions?
Give both fractions the same (common) denominator, then add or subtract the numerators and keep the denominator. Example: 1/2 + 1/3 → 3/6 + 2/6 = 5/6. This fraction calculator does it for you and reduces the answer to lowest terms.
How do you multiply and divide fractions?
To multiply, multiply straight across: 2/3 × 4/5 = 8/15. To divide, flip the second fraction and multiply — dividing is the same as multiplying by the reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What's the difference between a mixed number and an improper fraction?
An improper fraction has a numerator larger than its denominator, like 7/3. A mixed number writes the same value as a whole part plus a proper fraction: 7/3 = 2 1/3. This calculator shows both, so you can convert either way.
How do you simplify a fraction to lowest terms?
Divide the numerator and denominator by their greatest common divisor (GCD). For 8/12 the GCD is 4, so 8/12 = 2/3. The Simplify tab does this for any fraction and shows the GCD it used — handy for reducing fractions to lowest terms.
Is my calculation sent to a server?
No. Every calculation runs entirely in your browser using exact integer math, and your inputs are saved only in your browser's local storage. Nothing is uploaded, there's no sign-up, and there are no ads.