Fraction Calculator
Add, subtract, multiply, divide, or simplify fractions with exact whole-number math — no rounding, no floating-point error, every result in lowest terms.
Calculator
Exact Result
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Mixed Number
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Decimal
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GCD Used
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Result
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How Fraction Calculator Works
What Is a Fraction?
A fraction represents part of a whole, written as one number over another: numerator/denominator. The numerator (top number) counts how many parts you have; the denominator (bottom number) says how many equal parts the whole is divided into. In 3/4, you have 3 parts out of a whole divided into 4.
Proper vs. Improper Fractions
| Type | Meaning | Example |
|---|---|---|
| Proper fraction | Numerator smaller than denominator — less than one whole | 3/4 |
| Improper fraction | Numerator equal to or greater than denominator — one whole or more | 7/3 |
Mixed Numbers
A mixed number writes an improper fraction as a whole number plus a proper fraction — 7/3 is the same value as the mixed number 2 1/3 (two whole parts, plus 1/3 left over). This calculator shows the mixed-number form for any result that has a whole-number part, alongside the exact improper-fraction form.
Equivalent Fractions & Simplifying
Equivalent fractions represent the same value with different numerators and denominators — 2/4, 3/6, and 4/8 are all equivalent to 1/2. Simplifying (or reducing) a fraction means dividing both numerator and denominator by their greatest common divisor (GCD) until no further whole-number division is possible. 8/12 simplifies to 2/3 because their GCD is 4 (8 ÷ 4 = 2, 12 ÷ 4 = 3).
Adding and Subtracting Fractions
Fractions need a common denominator before you can add or subtract their numerators directly. This calculator handles that automatically:
a/b + c/d = (a×d + c×b) / (b×d), then reduced to lowest terms.
Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
Example: 3/4 − 1/2 = (3×2 − 1×4) / (4×2) = 2/8 = 1/4
Multiplying and Dividing Fractions
Multiplying is the most direct fraction operation — multiply the numerators together and the denominators together:
a/b × c/d = (a×c) / (b×d)
Example: 2/3 × 3/5 = 6/15 = 2/5
Dividing by a fraction is the same as multiplying by its reciprocal (flip the second fraction upside down):
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Common Mistakes
- Adding numerators and denominators directly. 1/2 + 1/3 is NOT 2/5 — you must find a common denominator first, not just add across.
- Forgetting to simplify the result. 2/8 is a correct but not fully reduced answer to 3/4 − 1/2; the simplest form is 1/4.
- Flipping the wrong fraction when dividing. a/b ÷ c/d flips the SECOND fraction (c/d becomes d/c), not the first.
- Rounding too early. Converting fractions to decimals before adding or subtracting can introduce rounding error that exact fraction arithmetic avoids entirely.
Fractions vs. Decimals
Every fraction has a decimal equivalent (1/4 = 0.25), but not every decimal has a short exact fraction — 1/3 = 0.3333... repeats forever. This calculator always computes the EXACT fraction result first, using whole-number arithmetic with no rounding, and only converts to a decimal afterward purely for display — the decimal is never used to calculate the fraction answer, so results stay exact even when the decimal equivalent would repeat or need rounding.
Worked Example
Simplify 8/12:
GCD of 8 and 12 = 4
8 ÷ 4 = 2, 12 ÷ 4 = 3
Simplified: 2/3
Related Tools
Once you have a fraction, convert it or use it elsewhere with the Percentage Calculator, Average Calculator, Discount Calculator, or Tip Calculator.
Accuracy & Sources
Last reviewed: August 2026. Formula source: Standard fraction arithmetic (fractions.Fraction, Python standard library). All calculations run in your browser. No data is sent to any server.
Frequently Asked Questions
Cross-multiply to get a common denominator: a/b + c/d = (a×d + c×b) / (b×d), then simplify the result. For example, 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. This calculator does that automatically — just enter both fractions and pick Add.
This calculator always reduces every result to lowest terms automatically — you'll never get an answer like 2/8 that could be simplified further; it's always shown as 1/4. Simplify mode additionally tells you the GCD (greatest common divisor) used to reduce your original fraction, in case you want to see that step explicitly.
Flip the second fraction upside down (its reciprocal) and multiply: a/b ÷ c/d = a/b × d/c. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12, which simplifies to 5/6.
Exact math only. Every operation uses whole-number numerator/denominator arithmetic with no rounding at any step — the fraction result is always exact, even for values like 1/3 whose decimal form repeats forever. The decimal shown alongside the result is purely for reference and is never used to calculate the fraction itself.
It's rejected with a clear error — a fraction with a zero denominator isn't a valid number. Dividing by a fraction that equals zero (like 0/5) is also specifically rejected in Divide mode, since division by zero is undefined.
Yes — enter a negative numerator, a negative denominator, or both. The result is always shown with the sign on the numerator and a positive denominator (so -1/2 and 1/-2 both display as -1/2), which is the standard convention for writing a negative fraction.
A mixed number writes a value greater than one whole as a whole number plus a proper fraction — 7/3 as a mixed number is 2 1/3. This calculator shows the mixed-number form whenever the result has a whole-number part; for a result already less than one (like 5/6), there's no whole part to show separately, so only the fraction is shown.