A mixed number is a combination of a whole number and a fraction.
For example, you and your friends ate \(2\frac{3}{8}\) pizzas last night.
We can convert this mixed number to a fraction:
\[2\frac{3}{8}\text{ pizzas}=2\text{ whole pizzas}+3\text{ more slices}\]
If each pizza has 8 slices we have
\[\begin{align}2\frac{3}{8}\text{ pizzas}&=2\times\frac{8}{8}\text{ pizzas}+\frac{3}{8}\text{ pizzas}\\ &=2\times8\text{ slices}+3\text{ slices}\\ &=16\text{ slices}+3\text{ slices}\\ &=19\text{ slices}\end{align}\]
Each slice is \(\frac{1}{8}\) of a pizza so
\[2\frac{3}{8}\text{ pizzas}=\frac{19}{8}\text{ pizzas}\]
The mixed number \(2\frac{3}{8}\) can be expressed as the fraction \(\frac{19}{8}\)
Your guests ate \(1\frac{2}{3}\) blueberry pies for dessert at your place last night.
If each slice is \(\frac{1}{3}\) of a pie, and they ate one slice each, how many of your guests had blueberry pie last night?
\[1\frac{2}{3}\text{ blueberry pies}=1\times\frac{3}{3}+\frac{2}{3} blueberry pies\]
\[\frac{3}{3} + \frac{2}{3} = \frac{(3+2)}{3} = \frac{5}{3} = \frac{(5\times1)}{3}\text{ pies} = 5 \text{ slices}\]
5 of your guests had one slice of blueberry pie each last night.
The mixed number \(1\frac{2}{3}\) can be expressed as the fraction \(\frac{5}{3}\)
Because a mixed number is a whole number and a fraction, when a mixed number is converted to a fraction it is always an improper fraction. (An improper fraction has enough parts to make one whole or more; a proper fraction is less than one whole.)