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:

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