## Converting between improper fractions and mixed numbers

### Changing a mixed number into an improper fraction.

Consider the mixed number $1\frac{3}{5}$. Here is how you can imagine $1\frac{3}{5}$ on a number line.

$1\frac{3}{5}$ means each whole number is cut into five pieces and there are three additional fractional pieces. Therefore there are eight fractional pieces in $1\frac{3}{5}$.

$1\frac{3}{5}\,=\,\frac{8}{5}$

A second way to think of this goes as follows:

$1\frac{3}{5}\,=\,1\,+\,\frac{3}{5}\,=\,\frac{5}{5}\,+\,\frac{3}{5}\,=\,\frac{8}{5}$

### Changing an improper fraction into a mixed number.

We can also change in improper fraction into a mixed number. Here is how…

The fraction $\frac{8}{3}$ means you have 8 fractional pieces and each three fractional pieces equals one whole. Look at the picture of $\frac{8}{3}$.

You can see that $\frac{8}{3}$ is equal to 2 wholes plus $\frac{2}{3}$ left over. This means

$\frac{8}{3}\,=\,2\frac{2}{3}$

A second way to think of this goes as follows:

$\frac{8}{3}\,=\,\frac{3}{3}\,+\,\frac{3}{3}\,+\,\frac{2}{3}\,=\,1\,+\,1\,+\,\frac{2}{3}\,=\,2\frac{2}{3}$

### Explore with this GeoGebra applet:

Duane Habecker, Created with GeoGebra

 1. Change each improper fraction into a mixed number. (Use the applet above to check your answer.) a) $\frac{11}{3} =$ b) $\frac{21}{8} =$ c) $\frac{7}{4} =$ d) $\frac{20}{5} =$ 2. Change each mixed number into an improper fraction. (Use the applet above to check your answer.) a) $2\frac{2}{3} =$ b) $5\frac{1}{4} =$ c) $8\frac{1}{2} =$ d) $2\frac{6}{7} =$ 3. Use words to describe what the picture would look like for the improper fraction $\frac{16}{3}$. Draw a sketch of the number line for $\frac{16}{3}$. Confirm your thoughts by setting the sliders to $\frac{16}{3}$.

# Self-Check

Q1: Change $4\frac{1}{3}$ into an improper fraction. [show answer]

Q2: Change $3\frac{4}{5}$ into an improper fraction. [show answer]

Q3: Change $\frac{16}{5}$ into a mixed number. [show answer]

Q4: Change $\frac{14}{4}$ into a mixed number. [show answer]