# Lesson Explainer: Circle Graphs Mathematics

In this explainer, we will learn how to use circle graphs to analyze data, communicate information, and get insights from this data.

### Definition: A Circle Graph

A circle graph, also called a pie chart, is a chart in the shape of a disc divided into sectors whose areas are proportional to the quantities they represent.

The whole disk represents the whole; that is, the sum of the sectors represents the whole or the total. If the quantities are expressed in percentages, this means that the sum of all sectors is 100%.

A sector representing half of the whole, or 50%, is then a half-disk.

A sector representing a quarter of a whole, or 25%, is then a quarter of a disk.

A sector representing three quarters of a whole, or 75%, is then three-quarters of a disk.

The sum of all the disks is the whole, or the total, that is, 100%.

Let us look at some examples.

### Example 1: Identifying the Largest Part in a Circle Graph

The pie chart shows the results of a survey of how students travel to school. What is the most common method of travel?

### Answer

The most common method of travel is the one that is represented by the largest sector. We see it is traveling by cab since it is represented by a sector that is half the whole circle. All the other sectors are smaller.

Hence, our answer is that the most common method of traveling to school is by cab.

### Example 2: Reading a Circle Graph

Nabil works in a bookstore. He made the following pie chart to represent the sales of different types of sports books. Which book sold 17 units?

### Answer

This pie chart gives the number of sport books sold according to the type of sport they are about. The quantities given are real numbers and not percentages of the total number of books sold. Therefore, the book that sold 17 units is “Football.”

### Example 3: Finding a Quantity by Reading a Circle Graph and Knowing the Total

The pie chart shows the results of a survey of what fruits students prefer. Given that 30 students completed the survey, how many students prefer peaches?

### Answer

The circle graph shows the different answers of students expressed in percentages. We know that 30 students in total answered. This means that the value of the whole is 30 students. 40% of the students prefer peaches. As 40% is , we need to find of 30.

This can be easily visualized on a double-line diagram.

We find that 40% of 30 is given by . (The double-line diagram shows that , which means that 12 and 30 relate to each other in the same way as 40 and 100.)

The number of students who prefer peaches is, therefore, 12.

### Example 4: Finding a Missing Value in a Circle Graph

The pie chart shows the results of a survey to find the most popular subject in a school. What percentage of student picked mathematics?

### Answer

In this question, we are given the different answers during a survey in percentages. One figure is, however, missing: the percentage of students who picked mathematics as their favorite subject.

To find this missing figure, we need to use the fact that the sum of all the percentages in the pie chart must be 100%, since it represents all the answers.

This gives, with the percentage of students who picked mathematics:

By subtracting 76 from each side of the equation, we find

The answer is, therefore, that 24% of students picked mathematics.

### Example 5: Finding a Missing Value in a Circle Graph and Analyzing the Data

The pie chart shows the results of a survey of what fruits students prefer. What fraction of students prefer oranges or peaches?

### Answer

We need to find the fraction of students who prefer either oranges or peaches. We know that 40% prefer oranges, but we do not have the figure for peaches. However, we know that the sum of the percentages is 100%. With the percentage of students who prefer peaches, we have and by subtracting 75 from each side,

Therefore, 25% of students prefer peaches. The percentage of students who prefer either oranges or peaches is thus . The fraction can be simplified by dividing both the numerator and the denominator by 5: .

The answer is, therefore, that is the fraction of students who prefer either oranges or peaches.

### Key Points

• A circle graph, also called a pie chart, is a chart in the shape of a disc divided into sectors whose areas are proportional to the quantities they represent.
• The whole disk represents the whole; that is, the sum of the sectors represents the whole or the total.
• If the quantities are expressed in percentages, the sum of all sectors has to be 100%.

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