Pie charts are circular charts that are used to show how a whole group is divided into smaller portions.  The entire pie (or circle) represents the whole group or 100%.  Each slice (or section) of the graph represents a particular part of the group, with the pieces sized proportionally.  When you work with pie charts, you often work with percents, so it might be helpful to review the lesson on Percents.

Remember, whenever you work with a pie chart, all of the pieces add up to 100% (or, if you are working with fractions, they will add up to 1 whole).

When you look at any graph, the first thing to look at is the title: the graph below shows the distribution of grades in AP Biology.

Then next thing to look at in a pie chart are the labels on the "slices."  In the graph below, the labels also contain the percents represented by each slice (pie charts often include percents, but not always). In the graph below, we can see that 12% of grades are As, 30% are Bs, 28% are Cs, 15% are Ds, and 15% are Fs.  When working with pie charts, there is usually one additional piece of information given, and from there, you can figure out almost anything else.

Example: There are 33 students in a class.  Based on the graph above, how many students received Bs in AP Biology.

There are 33 students in the class.

30% of those students received Bs in AP Biology.

We need to find 30% of 33.

We can write an equation: $.30\times 33$ = 9.9 (round to 10 students)

Or, we can use a proportion:

\eqalign{\dfrac{\text{Students who got Bs}}{33 \text{ students}}&=\dfrac{30}{100}\\B \times 100 &= 30 \times 33\\100B&=990\\B&=9.9\\\text{Round to 10 students}}

Sometimes you will be asked to solve a problem that looks a little more complicated.  In those cases, it's usually easier to set up a proportion than to try to write an equation (though either method will work).

Example: Use the information in the graph above. 25 students failed AP Biology with an F.  How many students took AP Biology?

27 students failed AP Biology with an F.

15% of students failed AP Biology with an F.

We need to find the total number of students if 15% of students equals 27.

We can write an equation:

\eqalign{.15 \times t &=27\\.15t&=27\\\div.15&\quad \div .15\\t&= 180}

Or, we can use a proportion:

\eqalign{\dfrac{\text{Students who got Fs}}{\text{Total students}}&=\dfrac{\%}{100}\\\dfrac{27}{x}&=\dfrac{15}{100}\\27 \times 100 &= x \times 15\\2700&=15x\\x&=180\\\text{180 students took AP Biology}}

No matter how complicated the questions, pie charts just show you proportions or percents, so use fractions or percents to find the answers that you need.

#### Practice Problems:

Like everyone else, Annie has 24 hours in the day.  The pie chart above shows how she typically spends her day.  She spends $\dfrac{1}{12}$ of her day using the computer.  Use the chart to answer the questions below:

1. About what fraction of her time does Annie spend sleeping?
2. About how many hours a day does Annie spend on the computer?
3. About how many hours a day does Annie spend sleeping?
4. About what percent of her time does Annie spend sleeping?
5. About what percent of her time does Annie spend at school?
6. About how many hours does Annie spend in school each day?
7. About how many hours does Annie spend doing homework each day?
8. About what percent of her time does Annie spend on homework each day?
9. How many hours a day does Annie spend in school and doing homework?
10. What fraction of the day does Annie spend in school and doing homework?
11. What fraction of the day does Annie spend on the computer and doing homework?
12. What fraction of the day does Annie spend awake?