## Basic College Mathematics (9th Edition)

Proper fractions have a numerator that is smaller than the denominator, while improper fractions have a numerator that is greater than or equal to the denominator. An example of an improper fraction is three-halves: $\displaystyle \frac{3 \leftarrow numerator}{2\leftarrow denominator}$ To convert an improper fraction to a mixed number, you first need to divide the numerator by the denominator (e.g. $3\div 2$) and find the remainder: $~~~~1$ $2\overline{)~~3~}$ $~-2$ $~~\overline{~~1~~}$ In this example, the remainder is $1$ and the quotient is also $1$. Next we write the quotient as the whole number and the remainder as the numerator of the fraction part. The denominator stays the same. Thus the fraction becomes: $\displaystyle 1\frac{1}{2}$