Enter a mixed number such as 3 5/9 and convert it to a reduced improper fraction with the arithmetic shown.
Equivalent fraction forms should preserve the same rational value, and number-theory relationships should agree across factors, remainders, GCF, multiples, and prime structure. Use the connected tools to verify rather than relying on an isolated answer.
A mixed number combines a whole part and a fractional part, so negative values need an explicit sign convention. Convert the magnitude using whole × denominator + numerator, then apply the sign consistently to the final numerator. Avoid treating the fractional part as a separately signed value unless that is how the source expression is intentionally written.
The denominator cannot be zero. Once the improper numerator is formed, reduce numerator and denominator by their greatest common divisor when a simplified fraction is required. Reduction changes the representation but not the value, so it is useful to keep the unreduced intermediate numerator visible when checking classroom work or tracing a manual calculation.
An improper fraction is exact while its decimal representation may repeat or terminate only after several digits. For algebra, recipes, measurements, and fraction comparisons, preserve the exact numerator and denominator as the authoritative value. Use a decimal as a convenience for magnitude, not as a replacement when later operations depend on exact equality.
Divide the absolute improper numerator by the denominator to recover the whole-number quotient and remainder. The quotient should match the original whole magnitude and the remainder should match the original fractional numerator after simplification. This reverse check is especially useful when the whole number or numerator is large enough that a single multiplication error is hard to notice.
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