Mixed numbers show up everywhere from recipes to construction plans, but adding, subtracting, multiplying, or dividing them by hand means juggling whole numbers and fractions at the same time. This calculator converts everything to improper fractions first, applies the operation, and simplifies the result — showing every step along the way.
How the Mixed Number Calculator works
Every mixed number, fraction, or whole number you enter is first converted to an improper fraction (numerator over denominator, with the whole number folded in). Addition and subtraction use a common denominator formed by multiplying the two denominators together; multiplication multiplies numerators and denominators directly; division multiplies by the reciprocal of the second fraction. The raw result is then reduced to lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD), and finally converted back into a mixed number for the headline result.
Inputs and what they mean
Both inputs accept the same three formats: a mixed number like "2 1/3" (a space or hyphen between the whole number and the fraction both work), a bare fraction like "7/3", or a plain whole number like "5". Negative values are supported with a leading minus sign, e.g. "-2 1/3". The operation selector supports addition, subtraction, multiplication, and division — division by a fraction whose numerator is zero is undefined and is called out directly in the result.
Limits and edge cases
A denominator of zero (e.g. typing "1/0") is rejected as invalid, since division by zero is undefined. Dividing by a second value that equals zero is likewise flagged as an undefined result rather than silently returning zero or infinity. Very large denominators can make some fully-reduced results hard to express with a nice recognizable fraction symbol (like ½ or ⅓) — in that case the calculator falls back to plain numerator/denominator text instead of a Unicode glyph. This tool handles rational numbers only; it does not evaluate general decimal or irrational inputs beyond a simple decimal-to-fraction conversion.