Hi Laurie,

I am going to solve a similar problem.

if shaded parts of a circle are $\large \frac25$ and the other is $\large \frac38$ what fraction is left

First I need to assume that the two shaded parts don't overlap.

The fraction of the circle that is shaded is the sum of $\large \frac25$ and $\large \frac38.$ To add the fractions I need a common denominator. The denominators are $5$ and $8$ so one common denominator is $5 \times 8 = 40.$ Now I need equivalent fractions to $\large \frac25$ and $\large \frac38$ both with denominators of $40.$

\[\frac25 = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}\]

and

\[\frac38 = \frac{3 \times 5}{8 \times 5} = \frac{15}{40}.\]

Thus

\[\frac25 + \frac38 = \frac{16}{40} + \frac{15}{40} = \frac{16 + 15}{40} = \frac{31}{40}.\]

The fraction of the circle that is not shaded is then

\[1 - \frac{31}{40} = \frac{40}{40} - \frac{31}{40} = \frac{9}{4}.\]

Now try your problem.

Penny