How the Fraction Calculator works.
use common denominators for ±; multiply reciprocals for ÷n₁/n₂ and n₃/n₄ are the input fractions; denominators n₂ and n₄ must be positive.
Worked example
One half plus one third is five sixths after using denominator six.
What the result means
The reduced numerator and denominator represent the same ratio.
Edge cases
A denominator cannot be zero, and division requires a nonzero second numerator.
Input contract and fraction signs
Enter whole-number numerators and positive whole-number denominators. A negative sign belongs in the numerator, so −3/4 is valid while a negative or zero denominator is rejected. Decimal entries such as 1.5/2 are not silently rounded because this calculator is for exact integer fractions. Use the operation control to choose addition, subtraction, multiplication, or division before reading the reduced result.
Adding and subtracting with a common denominator
Addition and subtraction first create a common denominator. For 1/2 + 1/3, cross-multiply to obtain (1 × 3 + 1 × 2) / (2 × 3) = 5/6. For subtraction, the second cross-product is subtracted instead. Do not add or subtract denominators directly: 1/2 + 1/3 is not 2/5.
Multiplication, division and the reciprocal
Multiplication uses numerator × numerator and denominator × denominator before reduction. Division multiplies the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a × d)/(b × c). The second numerator cannot be zero during division because its reciprocal would require division by zero. Keep the order of the two fractions when dividing because fraction division is not commutative.
Reduction and decimal interpretation
After the selected operation, the numerator and denominator are divided by their greatest common divisor so the displayed fraction is in lowest terms. A negative result keeps its sign in the numerator and the denominator remains positive. The decimal detail is the reduced fraction evaluated numerically; a rounded decimal can hide a repeating value, so preserve the exact fraction when it is the required answer.
Boundary checks and safe integer limits
Zero is valid in a numerator and produces a zero fraction when the operation is otherwise defined. Every denominator must be greater than zero, and division by a fraction whose numerator is zero is rejected. Inputs and intermediate cross-products must remain within JavaScript’s safe-integer range; the calculator reports an error rather than presenting an exact-looking fraction after integer precision has been lost.
Scope and common mistakes
This calculator performs arithmetic on two numeric fractions. It does not parse mixed-number text such as 1 1/2, simplify algebraic expressions with variables, choose measurement units, or decide how quantities should be combined in a real problem. Convert mixed numbers to improper fractions first, keep units compatible, verify the selected operation, and retain the unreduced inputs when another person must reproduce the work.
What this calculator does not include.
The calculator uses numeric inputs and is not a symbolic algebra system.
Fraction Calculator questions.
Which numbers can I enter in a fraction?
Enter whole-number numerators and positive whole-number denominators. Numerators may be negative or zero. Denominators cannot be zero, and decimal inputs are rejected instead of being rounded to integers.
Why do addition and subtraction need a common denominator?
Fractions can be added or subtracted only when their parts refer to the same-sized unit. The calculator cross-multiplies to create an equivalent common denominator, combines the numerators, and then reduces the result.
How does division of fractions work?
Dividing by c/d is the same as multiplying by its reciprocal d/c. The calculator therefore multiplies the first numerator by the second denominator and the first denominator by the second numerator. A second numerator of zero is rejected because its reciprocal is undefined.
Does the calculator reduce the answer?
Yes. It divides the result numerator and denominator by their greatest common divisor, keeps any negative sign in the numerator, and displays a positive denominator. It also shows a decimal value for comparison.
Why can the decimal look rounded while the fraction is exact?
Some fractions have repeating decimal expansions that cannot be displayed completely. The reduced fraction preserves the exact ratio within the supported safe-integer range, while the decimal detail is formatted for readable display.
Can I enter mixed numbers or algebraic fractions?
No. Convert a mixed number such as 1 1/2 to the improper fraction 3/2 before using the calculator. The page handles two numeric fractions only and does not parse variables, symbolic expressions, or measurement-unit conversions.