Fraction Calculator
Add, subtract, multiply, divide fractions
Fraction Calculator tool
Results
Fraction
—
Mixed Number
—
Decimal
—
Step-by-step:
- 1.Find common denominator: 2 × 4 = 8
- 2.Convert fractions: 1/2 = 4/8, 1/4 = 2/8
- 3.Add numerators: 4 + 2 = 6
- 4.Result: 6/8
- 5.Simplify: undefined/undefined
Fraction Calculator: key facts
- What it does
- Add, subtract, multiply, divide fractions
- Category
- Math Calculators
- Cost
- Free, with no account, sign-up, or install.
- Your data
- Runs entirely in your browser — the files and text you enter are never uploaded to a server.
- Last reviewed
- . Report an incorrect result.
About the Fraction Calculator
Fraction arithmetic trips up students and adults alike, because adding or dividing fractions means juggling common denominators and then simplifying. This calculator does all of it: pick an operation, enter two fractions, and it returns the answer fully simplified, as a mixed number, and as a decimal — with the steps shown.
It is a homework checker for students learning fractions and a quick utility for anyone scaling a recipe, splitting measurements, or working in trades where fractional inches are everyday. Because it shows the common-denominator step and the simplification, it teaches the method rather than just handing over a result.
How to use it
- Choose an operation: add, subtract, multiply, or divide.
- Enter the numerator and denominator of the first fraction.
- Enter the numerator and denominator of the second fraction.
- Read the simplified result, its mixed-number form, and its decimal equivalent.
- Follow the step-by-step breakdown to see the common denominator and simplification.
Common denominators, then simplification
Adding or subtracting fractions requires a common denominator, so the tool converts both operands before combining the numerators. Multiplication needs no such step — numerators and denominators multiply straight across — and division inverts the second fraction and multiplies.
Whatever the operation, the result is reduced to lowest terms by dividing both parts by their greatest common divisor, found with the Euclidean algorithm. That is why an answer comes back as 1/2 rather than 6/12: mathematically identical, conventionally preferred.
Where the numerator exceeds the denominator the tool also offers the mixed-number form, separating the whole part from the remainder. Improper fractions are easier to compute with; mixed numbers are easier to picture, which is why both have their place.
- 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6, already in lowest terms.
- 2/3 × 3/4 multiplies to 6/12, which reduces to 1/2.
- 7/4 expressed as a mixed number is 1 3/4.
Why use this version
- It returns three forms at once — a simplified fraction, a mixed number, and a decimal — so you have whichever you need.
- It reduces the answer to lowest terms automatically using the greatest common divisor, and shows that simplification step.
- The worked steps reveal the common-denominator process, making it a genuine learning aid rather than a black box.
- All arithmetic runs locally with no account required.
Why fractions beat decimals sometimes
A third written as a decimal never terminates, so any decimal representation of it is an approximation. Written as a fraction it is exact. That matters in any calculation where small errors accumulate, and it is why engineering drawings, musical time signatures, and cooking measurements have all kept fractional notation rather than converting to decimals.
A fraction terminates as a decimal only when its reduced denominator has no prime factors besides 2 and 5. That single rule explains why halves, quarters, fifths, eighths, and tenths convert cleanly while thirds, sevenths, and ninths recur forever.
Two practical notes. A zero denominator is undefined rather than infinite, since no number multiplied by zero yields a non-zero numerator. And when comparing fractions, cross-multiplying is quicker than converting both to decimals: a/b exceeds c/d exactly when ad exceeds cb, assuming positive denominators.
Frequently Asked Questions
How do you add fractions with different denominators?
You first rewrite both fractions over a common denominator, then add the numerators and keep that denominator, and finally simplify. This calculator finds the common denominator, performs the addition, and reduces the result, showing each step.
What is a mixed number?
A mixed number combines a whole number with a proper fraction, like 1¾ instead of the improper fraction 7/4. The calculator shows the mixed-number form alongside the simplified fraction so you can use whichever your work calls for.
How does the calculator simplify the result?
It divides both the numerator and denominator by their greatest common divisor, found with the Euclidean algorithm. That reduces the fraction to its lowest terms — for example, 6/8 becomes 3/4.
How do I divide one fraction by another?
You multiply the first fraction by the reciprocal (the flip) of the second: dividing by 2/3 is the same as multiplying by 3/2. Choose the divide operation and the calculator applies this rule and simplifies the result automatically.
