# Mixed numbers and improper fractions review

CCSS Math: 4.NF.B.3
Review how to rewrite mixed numbers as improper fractions and improper fractions as mixed numbers.  Then, try some practice problems.

## What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Below are examples of improper fractions:
$\dfrac94, \dfrac55, \dfrac73$

## What is a mixed number?

A mixed number is a number consisting of a whole number and a proper fraction.
Below are examples of mixed numbers:
$4\dfrac12, 1\dfrac38, 12\dfrac56$

## Rewriting a mixed number as an improper fraction

Rewrite $3\dfrac45$ as an improper fraction.
$3\dfrac45=\blueD3+\greenD{\dfrac45}$
$\phantom{3\dfrac45}=\blueD1+\blueD1+\blueD1+\greenD{\dfrac45}$
$\phantom{3\dfrac45}=\blueD{\dfrac55}+\blueD{\dfrac55}+\blueD{\dfrac55}+\greenD{\dfrac45}$
$\phantom{3\dfrac45}=\dfrac{\blueD5+\blueD5+\blueD5+\greenD4}5$
${3\dfrac45}=\dfrac{19}5$
Rewrite $\dfrac{10}3$ as a mixed number.
$\dfrac33=1\text{ whole}$
So, let's see how many wholes we can get out of $\dfrac{10}3$.
$\dfrac{10}3=\dfrac{\blueD3+\blueD3+\blueD3+\greenD1}3$
$\phantom{\dfrac{10}3}=\blueD{\dfrac33}+\blueD{\dfrac33}+\blueD{\dfrac33}+\greenD{\dfrac13}$
$\phantom{\dfrac{10}3}=\blueD1+\blueD1+\blueD1+\greenD{\dfrac13}$
$\dfrac{10}3=\blueD3\greenD{\dfrac13}$