Fraction Calculator
Add, subtract, multiply, or divide fractions, automatically simplified.
What this calculator does
Adds, subtracts, multiplies, or divides two fractions and returns the answer in simplest form. Enter the numerator and denominator for each fraction, choose the operation, and it handles finding a common denominator, the arithmetic itself, and reducing the result — all the steps that make fraction math error-prone when done by hand.
Who this is for
Students checking homework or studying for a math test, parents helping with schoolwork, anyone working with recipes or measurements given in fractional form (cups, inches on a tape measure), and anyone who wants to double-check a manual fraction calculation before relying on it.
Methodology
Addition/Subtraction: convert both fractions to a common denominator (the product or least common multiple of the two denominators), then add or subtract the numerators. Multiplication: multiply numerators together and denominators together directly. Division: multiply the first fraction by the reciprocal (flipped version) of the second. Every result is automatically simplified by dividing both parts by their greatest common divisor (GCD).
Worked examples
Addition: 1/2 + 1/3. Common denominator is 6, so this becomes 3/6 + 2/6 = 5/6.
Multiplication: 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2.
Division: 1/2 ÷ 1/4 means multiplying by the reciprocal: 1/2 × 4/1 = 4/2 = 2.
Common mistakes
- Adding numerators and denominators directly. 1/2 + 1/3 is not 2/5 — you must find a common denominator first, giving 3/6 + 2/6 = 5/6.
- Forgetting to flip the second fraction when dividing. Dividing by 1/3 means multiplying by 3/1, not dividing straight across.
- Leaving the answer unsimplified. 4/8 and 1/2 are the same value, but 1/2 is the expected simplified form in most contexts.
- Multiplying denominators when adding. The common denominator for addition/subtraction should be the least common multiple where possible, not always the raw product — using the raw product still gives a correct (if unsimplified) answer, but LCM keeps the numbers smaller and easier to work with.
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Frequently Asked Questions
Why do fractions need a common denominator to add or subtract?
A fraction's denominator defines the size of each piece. You can only directly add or subtract pieces that are the same size, which is why the denominators must match first.
Why does dividing fractions mean multiplying by the reciprocal?
Dividing by a number is the same as multiplying by its reciprocal — this holds true for fractions just as it does for whole numbers.
What does it mean to simplify a fraction?
Simplifying means dividing both the numerator and denominator by their greatest common divisor (GCD), reducing the fraction to its smallest equivalent form.
How do you multiply fractions?
Multiply the two numerators together to get the new numerator, and multiply the two denominators together to get the new denominator — no common denominator is needed for multiplication, unlike addition and subtraction.
Can this calculator handle mixed numbers?
Convert a mixed number to an improper fraction first (multiply the whole number by the denominator and add the numerator) before entering it, since the calculator works with standard numerator/denominator fraction inputs.