Division and Percentages:

Pie Charts

In this lesson, you will practice interpreting pie charts. What is a pie?

This is an image of a pumpkin pie. There is a wedge shaped piece removed from the pie.

A pie is a food dish that usually contains either fruit, meat, or vegetables and has a bottom and sometimes a top made out of pastry. It is usually round and divided into triangle-like slices, starting from the center to the outside edge. The picture above is of a pumpkin pie.

A pie chart is a round graph that uses pie-shaped wedges to represent the percentages of the whole.

Video Source (09:04 mins) | Transcript

Pie charts help us see how things compare to each other.

The bigger the slice of the pie chart, the higher the percentage of the whole it represents. The smaller the slice in the pie chart, the lower the percentage. The following pie chart represents the favorite colors of a group of people. The largest group of people represented by this pie chart like the color blue. Yellow is the least liked of the group.

The practice problems in this section help walk you through how to find percentages using data and a pie chart. You will need to know how to do this for the application activity.

Additional Information

Division:
If we want to convert a certain number of hours in a day to a percentage, we would divide that number by 24 hours. For example, if we wanted to know how much of the day is represented by 8.4 hours, we would divide 8.4 hours by 24 hours. The result is

$\frac{8.4 \text { hours}}{24 \text { hours}}=0.35$

Which we can write as 35%.

Notice that if we are dividing to calculate a percentage, the units in the numerator (hours) needs to be the same as the units in the denominator (hours). You can think of the units (hours) as “canceling” each other out.
Multiplication:
If we know that something is, say, 35% of a whole, then we can multiply 35% (or 0.35) by the total amount to find out how much 35% is of the total. For example, we learned that Daniel spends 35% of his day at work. This means that the number of hours he spent at work is:

0.35 × 24 hours = 8.4 hours.

Practice Problems

Answer the following questions.

The following chart shows how Daniel, a PathwayConnect student, uses his time in a typical weekday.

This is a pie chart divided into 8 wedges of various sizes. The title of the chart says Daniels Daily Activities. Starting on the upper right hand wedge and going clockwise around the pie chart we have a wedge that is about a quarter of the circle labeled sleep and 25%. Next is a very small sliver sized wedge labeled shower and dress and 1%. Next is a slightly larger wedge labeled scripture study prayer and 4%. Next is a similar sized wedge labeled Travel and 5%. The next wedge is a little larger than a quarter of the circle and labeled work and 35%. The next medium sized wedge is labeled Cooking Eating and 15%. The next wedge is a bit smaller and labeled homework and 6%. The last wedge at the top left of the circle is labeled Time with Family Friends and does not have a percentage associated with it. It is a medium sized wedge a little larger than the homework wedge but a little smaller than the cooking eating wedge.

Everything Daniel does is represented in one of the slices in the chart, and the size of the slices indicates the percentage of time he does each activity. Larger slices indicate a greater amount of time.

Every day is comprised of 24 hours. This represents all (or 100%) of Daniel's time. So, the percentages of the slices on a pie chart must add up to 100%.

The word "percent" comes from Latin words that mean "for every hundred" or "one part in every hundred." You may find that you are already very familiar with percents. For examples, tithing represents 10% of our income, or 10 parts in every 100. So, a tithe (or 10%) of $200 would be $20.

Consider Daniel's pie chart as you complete the following questions.

When compared to the other activities, in what activity does Daniel spend the greatest portion of his time?
On what activity does Daniel spend the least amount of time?
What percentage of time does Daniel spend either sleeping or working?
What percentage of time is Daniel with family and friends?
How many hours does Daniel spend at work?

Solutions

Work (Written Solution)

Daniel spends more time working than he does in any other activity. He works 35% of the time. 35% is greater than any other percentage illustrated on the graph.

Suppose we divided the day into 100 equal parts, Daniel would spend 35 of those working. If we were to consider all of Daniel’s time in a day, it would be 100% of his time. He spends 35% of his time working.
Shower and Dress (Written Solution)

The smallest slice of the pie chart represents the percentage of time Daniel spends showering and dressing. The chart indicates that Daniel spent 1% of his day doing these things.
60% (Solution Video | Transcript | Written Solution)

The total percentage of time Daniel spends either sleeping or working can be calculated by adding the percentage of time he spends sleeping to the percentage of time he spends working. Daniel spends 25% of his time sleeping and 35% of his time working. Combining these, we get

25% + 35% = 60%

Notice that more than half of his time is spent either sleeping or working. Half of his time would be represented by 50%. Since 60% is greater than 50%, he spends more than half of his time either sleeping or working.
9% (Written Solution)

If we think about all the things Daniel can do in a day, all of this time must add up to 100%. When we think in terms of percentages, 100% represents the whole (or the entire amount.)

Daniel spends 25% of his time sleeping, 1% showering and dressing, 4% in scripture study and prayer, 5% travelling, 35% at work, 15% cooking and eating, and 6% doing homework. If we add these up, we find the total percentage of time he spends on these activities is:

25% + 1% + 4% + 5% + 35% + 15% + 6% = 91%.

The entire day is represented by 100%. So, if a full day is 100%, and 91% of the time is spent on other activities, the amount of time Daniel spends with family and friends is:
100% − 91% = 9%.
8.4 hours (Solution Video | Transcript | Written Solution)

In a full day, there are 24 hours. This represents 100% of the time Daniel has. The portion of the day that Daniel spends at work is 35%.

We want to know what portion of Daniel’s day is spent at work. In math, including with story problems, the word “of” can be a hint that we need to multiply. Notice what happens when we express the sentence “Daniel spends 35% of 24 hours at work.” In this case, the word “of” suggests multiplication.

We can convert this percentage to hours by multiplying 35% by 24 hours. Before we do this multiplication, it is helpful to rewrite 35% as 0.35.

We divide 35 by 100 to get 0.35. 35% and 0.35 are two ways to represent the same value.

Next, we multiply this by the total number of hours in a day:

0.35 × 24 hours = 8.4 hours

Daniel spends 8.4 hours each day at work.