## Proper Fractions, Improper Fractions, and Mixed Numbers

Read this text to see examples of proper and improper fractions using a number line.

#### Positive Proper Fractions

Fractions in which the whole number in the numerator is strictly less than the whole number in the denominator are called positive proper fractions. On the number line, proper fractions are located in the interval from $0$ to $1$. Positive proper fractions are always less than one.

The closed circle at 0 indicates that 0 is included, while the open circle at 1 indicates that 1 is not included.

Some examples of positive proper fractions are

$\dfrac{1}{2}, \dfrac{3}{5}, \dfrac{20}{27}$, and $\dfrac{106}{255}$

Note that $1 < 2,3 < 5,20 < 27$, and $106 < 225$.

#### Positive Improper Fractions

Positive Improper FractionsFractions in which the whole number in the numerator is greater than or equal to the whole number in the denominator are called positive improper fractions. On the number line, improper fractions lie to the right of (and including) $1$. Positive improper fractions are always greater than or equal to $1$.

Some examples of positive improper fractions are $\dfrac{3}{2}, \dfrac{8}{5}, \dfrac{4}{4}$, and $\dfrac{105}{16}$
Note that $3 \geq 2,8 \geq 5,4 \geq 4$, and $105 \geq 16$.

#### Positive Mixed Numbers

A number of the form

$\text{nonzero whole number + proper fraction}$

is called a positive mixed number. For example, $2 \dfrac{3}{5}$ is a mixed number. On the number line, mixed numbers are located in the interval to the right of (and including) $1$. Mixed numbers are always greater than or equal to $1$.

Source: Rice University, https://cnx.org/contents/XeVIW7Iw@4.6:3OiwYs1a@2/Proper-Fractions-Improper-Fractions-and-Mixed-Numbers