Exact arithmetic with numerator and denominator parts

Fractions stay exact because the calculator works with numerators and denominators directly. Addition and subtraction need comparable denominator units; multiplication and division can use direct products.

Enter fractions cleanly

Enter numerator and denominator for each fraction.
Choose the operation.
Put negative signs on numerators when possible.
Never use a zero denominator.
Read the reduced result.

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Exact fraction operation rules

The operation decides whether the calculator cross-multiplies, multiplies directly, or flips the second fraction.

Addition

\frac{a}{b} + \frac{c}{d} = \frac{a \times d + c \times b}{b \times d}

Subtraction

\frac{a}{b} - \frac{c}{d} = \frac{a \times d - c \times b}{b \times d}

Multiplication

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Division

\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}, c \neq 0

Simplification

result = \frac{n / g}{d / g}, g = gcd (| n |, | d |)

How to read the result

Lowest terms have no shared factor larger than 1.
The denominator is kept positive.
Improper fractions are exact and may be converted with the mixed-number calculator.
A negative result carries one sign, not two.

FAQ

Why does addition need a common denominator?

The numerators only count comparable parts after both fractions use the same denominator units.

Why is the final fraction simplified?

Dividing numerator and denominator by their greatest common divisor gives the same exact value in lowest terms.

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