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Get NordVPN →Fraction Calculator (add, subtract, multiply, divide)
Enter two fractions (numerator over denominator) and an operation. The calculator returns the result in lowest terms, plus its decimal value and mixed-number form when applicable. Uses BigInt for exact arbitrary-size results.
Result (simplified)
5
4
- Decimal
- 1.25
- Mixed number
- 11/4
Related tools
How it works
How fraction operations work
Addition/subtraction: convert to a common denominator first. a/b ± c/d = (ad ± bc) / bd. Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6.
Multiplication: a/b × c/d = (ac) / (bd). Cross-cancellation simplifies before multiplying. Example: 2/3 × 9/10 = (2×9)/(3×10) = 18/30 = 3/5.
Division: invert the second fraction and multiply. a/b ÷ c/d = a/b × d/c = (ad) / (bc). Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3.
Why simplify
A fraction is in lowest terms when numerator and denominator share no common factors greater than 1. We use the Euclidean algorithm to find their GCD and divide both by it.
Example: 18/30 has GCD 6, so simplifies to 3/5. Mathematically equivalent but easier to read and work with.
We also normalize the sign: a positive numerator is conventional. So −3/−5 simplifies to 3/5; 3/−5 to −3/5.
Mixed numbers
When the numerator's absolute value exceeds the denominator's, the fraction can be expressed as a whole number plus a proper fraction. Example: 7/3 = 2⅓ (since 7 = 2×3 + 1).
Mixed numbers are common in everyday measurements (recipes, lumber dimensions, music time signatures) but less common in math/science where improper fractions are simpler to manipulate. We show both representations.
Frequently asked questions
›Can I enter negative fractions?
Yes. Use a minus sign on either numerator or denominator. The calculator normalizes to a single negative sign in the numerator.
›Why is 1/2 + 1/3 = 5/6 and not 2/5?
You can't add fractions by adding numerators and denominators separately. You must first find a common denominator. 1/2 = 3/6, 1/3 = 2/6, so 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
›Does this support whole numbers as fractions?
Yes. Enter whole = whole/1. So 5 + 1/2 = 5/1 + 1/2 = 11/2 = 5½.
›What's the largest fraction this handles?
We use BigInt internally, so arithmetic on numerators and denominators of essentially any size is exact. Display is limited to whatever your screen fits.
›Why is the decimal sometimes not exact?
Some fractions don't have exact decimal representations (1/3 = 0.3333…). We display up to 8 decimal places. The fraction itself is exact; the decimal is an approximation.
›Can I divide by zero?
No. Division by zero (or any fraction with a zero numerator as divisor) is undefined. The calculator returns no result for that case.
›Where do mixed numbers come from?
Improper fractions (numerator ≥ denominator). 7/3 = 2 + 1/3 = 2⅓. Both forms are equivalent; choose based on context (math: improper, recipes: mixed).
›Does the data leave my browser?
No. Calculation runs locally; nothing is sent to a server.
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