Fraction Calculator

Add, subtract, multiply, and divide fractions with Euclidean GCD simplification to lowest terms, mixed numbers, decimals, and percentages.

Category: Math

How to Use Fraction Calculator

  1. Enter the numerator and non-zero denominator for Fraction 1 and Fraction 2 (zero numerators and negative values are supported).
  2. Choose your arithmetic operation: Addition (+), Subtraction (−), Multiplication (×), or Division (÷).
  3. Click Calculate to view the unsimplified result, GCD divisor, reduced lowest terms, mixed number form, decimal value, and percentage.

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Frequently Asked Questions

How do you add or subtract two fractions with different denominators?

To add or subtract a/b and c/d, cross-multiply to form a common denominator (b × d): (a × d ± c × b) / (b × d), then divide both the resulting numerator and denominator by their Greatest Common Divisor (GCD) to reduce the fraction to lowest terms.

How do you multiply and divide fractions?

To multiply two fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = (a × c) / (b × d). To divide by a fraction, multiply the first fraction by the reciprocal of the second fraction: (a/b) ÷ (c/d) = (a × d) / (b × c), provided c ≠ 0.

How does the calculator simplify improper fractions into mixed numbers?

After reducing a fraction to lowest terms (simNum / simDen) using the Euclidean GCD algorithm, if |simNum| > simDen and simDen > 1, the calculator divides simNum by simDen. The integer quotient becomes the whole number part and the remainder over simDen forms the proper fractional part (for example, 5/4 = 1 1/4).

How are negative signs in denominators handled?

In standard rational canonical form, the denominator of a reduced fraction is always kept strictly positive. If a calculation produces a negative denominator (such as 3 / -4), the calculator normalizes the sign to the numerator (-3/4), and if both are negative (-3 / -4), it simplifies to +3/4.

Can I enter 0 as a numerator or decimal numbers inside a fraction?

Yes. A numerator of 0 is valid and simplifies cleanly to 0/1 (0). Denominators cannot be 0 ( nor can the second fraction's numerator be 0 during division). If you enter decimal values in a numerator or denominator (such as 1.5 / 2.5), the engine scales both by powers of 10 before GCD reduction (yielding 3/5).