Proper fractions

A proper fraction is a rational number of the form $\frac{a}{b}$, where $a$ and $b$ are integers, $b \neq 0$, and $|a| < |b|$. Proper fractions represent numbers strictly between $-1$ and $1$ (excluding $0$ if $a = 0$).

Important properties

• The absolute value of the numerator is less than the absolute value of the denominator.

• Proper fractions are always less than 1 in absolute value.

• They cannot be simplified to a whole number or to 1.

• Every proper fraction is already less than one whole.