rational number

A rational number is any number you can write as one integer divided by another — a ratio, which is where the name comes from. Cutting a pizza into 8 slices and taking 3 gives 3/8; sharing 7 cookies among 2 people gives 7/2. Wherever you split or share whole things evenly, rational numbers appear.

Precisely, a rational number is any number expressible as a/b where a and b are integers and b is not zero. The denominator can never be zero, because dividing by zero has no meaning. The same rational number has infinitely many disguises — 1/2, 2/4, and 50/100 are all equal — and each rational has a unique form in lowest terms, where numerator and denominator share no common factor.

Rationals are closed under addition, subtraction, multiplication, and division by anything nonzero, so ordinary arithmetic never leaves the set. In decimal form, a number is rational exactly when its expansion either terminates (like 0.75) or eventually repeats forever (like 0.333… = 1/3). Every integer is rational too, since n equals n/1.