Interactive calculator
Fraction calculator
Add, subtract, multiply, divide two fractions.
Result-
Decimal-
Mixed-
About this tool
The Fraction Calculator performs addition, subtraction, multiplication, and division of fractions. Results are automatically simplified to lowest terms and shown as both improper fractions and mixed numbers.
What this fraction calculator does
A fraction is a way of writing a part of a whole as one number over another: the numerator on top counts the parts you have, and the denominator on the bottom says how many equal parts make a whole. This tool takes two fractions and an operation (add, subtract, multiply, or divide) and returns the answer fully simplified, plus its decimal and mixed-number forms. It all runs in your browser.
Fractions show up everywhere exact parts matter: halving a recipe, splitting a bill, reading a tape measure in sixteenths of an inch, or combining ratios. Doing the arithmetic by hand means juggling common denominators and simplifying at the end, which is exactly the fiddly part this calculator removes.
How it works: the four operations
Each operation follows a fixed rule. Addition and subtraction need a common denominator first; multiplication and division do not.
Add a/b + c/d = (a*d + c*b) / (b*d) Subtract a/b - c/d = (a*d - c*b) / (b*d) Multiply a/b * c/d = (a*c) / (b*d) Divide a/b / c/d = (a*d) / (b*c) (flip and multiply) Simplify divide top and bottom by gcd(top, bottom)
After applying the rule the calculator simplifies by dividing the numerator and denominator by their greatest common divisor (GCD), found with the Euclidean algorithm. It also normalises the sign so any negative lives in the numerator, giving a clean result like -2/3 rather than 2/-3.
Worked example: 1/2 + 2/3
Add one-half and two-thirds, the default inputs.
- Common denominator: multiply the denominators, 2 x 3 = 6.
- Convert each fraction: 1/2 = 3/6 and 2/3 = 4/6.
- Add the numerators: 3 + 4 = 7, over 6, giving 7/6.
- Simplify: gcd(7, 6) = 1, so 7/6 is already in lowest terms.
- Other forms: 7 / 6 = 1.166667 as a decimal, and 1 and 1/6 as a mixed number.
Result: 7/6, which is 1 and 1/6, or about 1.1667. Because the result is improper (top larger than bottom), the mixed-number form is often the most readable.
When fractions beat decimals
Decimals are convenient on a calculator, but fractions stay exact where decimals only approximate. One-third is exactly 1/3, while 0.3333 is rounded and quietly loses accuracy every time you reuse it. For recurring values and for ratios that must add back to a whole, fractions are the safer choice.
They are also the native language of several trades. Imperial measurements run in halves, quarters, eighths, and sixteenths of an inch, so a tape measure is read in fractions, not decimals. Recipes scale cleanly in fractions (half of 3/4 cup is 3/8 cup), and musical timing, gear ratios, and odds are all expressed as whole-number fractions because the parts are meant to be counted, not measured.
Common fractions and their decimals
Recognising these by sight speeds up mental estimates and sanity-checks the calculator.
| Fraction | Decimal | Percent | Common use |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half of anything |
| 1/3 | 0.3333... | 33.33% | Thirds, recurring decimal |
| 1/4 | 0.25 | 25% | Quarters, money |
| 3/4 | 0.75 | 75% | Three quarters |
| 1/5 | 0.2 | 20% | Fifths |
| 1/8 | 0.125 | 12.5% | Inches, cooking |
| 2/3 | 0.6667... | 66.67% | Two thirds, recurring |
Common pitfalls
- Adding numerators and denominators straight across. 1/2 + 1/3 is not 2/5. You must find a common denominator first; only multiplication works across the top and bottom directly.
- Forgetting to simplify. 6/12 and 1/2 are the same value. This tool always reduces to lowest terms so answers are comparable.
- Entering zero as a denominator. A denominator of zero is undefined, and the calculator flags it rather than returning a number.
- Dividing without flipping. To divide by a fraction you multiply by its reciprocal. Skipping the flip gives the wrong answer.
- Mishandling negatives. -1/2 and 1/-2 are equal, but mixing signs in your own working causes errors. Keep the sign on the numerator as the tool does.
- Confusing improper fractions with mistakes. 7/6 is a valid improper fraction, not an error; it simply equals the mixed number 1 and 1/6.
Frequently asked questions
How do you add or subtract fractions?
Give both fractions a common denominator, convert the numerators to match, then add or subtract the numerators and keep the denominator. For example 1/3 + 1/4 = 4/12 + 3/12 = 7/12. This calculator does it in one step and simplifies the answer for you.
How do you multiply and divide fractions?
To multiply, multiply the numerators together and the denominators together: 2/3 x 3/4 = 6/12 = 1/2. To divide, flip the second fraction and multiply: 1/2 divided by 3/4 = 1/2 x 4/3 = 4/6 = 2/3. No common denominator is needed for either.
How does the calculator simplify the result?
It finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both by it. So 6/12 has a GCD of 6 and reduces to 1/2. It also moves any negative sign to the numerator so the result is in standard form.
What is a mixed number and how is it shown?
A mixed number is a whole number plus a proper fraction, like 1 and 3/4 for the improper fraction 7/4. The calculator shows the result three ways: as a simplified fraction, as a decimal, and as a mixed number, so you can use whichever form your task needs.
Why does it say the result is undefined?
Because a denominator worked out to zero, which has no value. This happens if you enter zero as a denominator, or if you divide by a fraction whose numerator is zero (dividing by 0/5 means dividing by zero). Fix the input so no denominator is zero.