1 Lesson 3.5.4 Circle Graphs and Percents Circle Graphs and Percents

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Lesson 3.5.4Lesson 3.5.4

Circle Graphs and Percents

Circle Graphs and Percents

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Lesson

3.5.4Circle Graphs and PercentsCircle Graphs and Percents

California Standard:Number Sense 1.4Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

What it means for you:You’ll use circle graphs to compare different percents

Key words:• percent• circle graph• 100%• compare

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Lesson

3.5.4

You’ll have seen circle graphs before in earlier grades.

Circle Graphs and PercentsCircle Graphs and Percents

Circle graphs are useful because they show clearly how the size of one group relates to another.

They’re often used to compare different percents.

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100% is Equal to the Whole Amount

Lesson

3.5.4

100% of something is all of it.


It’s important to remember this when you’re looking at questions about percents.

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Example 1

Solution follows…

Lesson

3.5.4

Yesenia has a number of marbles. 65% of the marbles are red. The rest are all blue. What percent of Yesenia’s marbles are blue?

Solution

All the marbles are either red or blue.

percent of red marbles + percent of blue marbles = all marbles


65% + percent of blue marbles = 100%

percent of blue marbles = 100% – 65%

= 35%

So 35% of Yesenia’s marbles are blue.

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Guided Practice

Solution follows…

Lesson

3.5.4

1. 47% of students in a school are boys. What percent are girls? 100% – 47% = 53%

100% – 18% = 82%

100% – 29% = 71%

100% – (30 + 40)% = 30%


2. A store took a survey of customers’ ages. 29% said they were under 15. What percent were aged 15 or over?

3. 18% of a class of 6th graders have a pet dog. What percent of the class don’t have a dog?

4. A bag contains a number of colored counters. All the counters are either blue, green, or yellow. 30% of the counters are blue, and 40% of the counters are green. What percent of the counters are yellow?

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Guided Practice

Solution follows…

Lesson

3.5.4

5. Mrs. Goldman’s garden has only red, white, and blue flowers. 37% of the flowers are red, and 39% of the flowers are white. What percent of the flowers are blue?

100% – (37 + 39)% = 24%

100% – (27 + 41)% = 32%


6. Visitors to a movie theater were asked which of 3 types of movie they liked best. This table shows the results. What is the missing percent?

Action 27%

Comedy 41%

Romance ?

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Circle Graphs Are Often Divided into Percents

Lesson

3.5.4

Circle graphs show how a total splits into different parts.


The girls section is larger.

The two sections represent the boys and the girls.

The whole circle represents the whole class.

This means the class has more girls than boys.

This graph represents a math class split into boys and girls.

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Lesson


When a circle graph shows percents, the whole circle represents 100%.

A section that represents a certain percent fills that percent of the circle.

100%

50%25%

25%

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Example 2

Solution follows…

Lesson

3.5.4

This circle graph shows the results of a survey to find which out of apples, bananas, and oranges students liked best.

Solution

The whole circle represents 100%, so the total value of all the sections must be 100%.

Call the percent of students who like bananas best b%.

Then 25 + 35 + b = 100

60 + b = 100


What percent of the students like bananas best?

b = 100 – 60 = 40

So 40% of the students like bananas best.

The total of all sections is 100%

25 + 35 = 60

Subtract 60 from both sides

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Guided Practice

Solution follows…

Lesson

3.5.4

In Exercises 7–10, find the missing value in each circle graph.

7. 8.

9.

100% – 50% = 50% 100% – (55 + 30)% = 15%

100% – (31 + 24)% = 45%


10.

100% – (34 + 19 + 21)% = 26%

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Guided Practice

Solution follows…

Lesson

3.5.4

A survey asked people which of three drinks they prefer. This graph shows the number of people who said they prefer each drink.

11. How many people answered the survey?20 + 20 + 10 = 50 people

12. What fraction of these people preferred each drink?


13. What percent of these people preferred each drink?Water: (1 ÷ 5) × 100 = 20%, Juice: (2 ÷ 5) × 100 = 40%, Milk: (2 ÷ 5) × 100 = 40%

Water: , Juice: , Milk:=1050

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=2050

25

=2050

25

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Guided Practice

Solution follows…

Lesson

3.5.4

This graph shows the number of insects a scientist counted for a study.

14. How many insects were there in total?125 + 75 + 125 + 175 = 500 insects


15. What percent of each type of insect were there?Crickets: (125 ÷ 500) × 100 = 25%, Wasps: (75 ÷ 500) × 100 = 15%, Bees: (125 ÷ 500) × 100 = 25%, Butterflies: (175 ÷ 500) × 100 = 35%

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You Can Turn Percents on Circle Graphs into Numbers

Lesson

3.5.4

If you know how many units make up the full 100% of a circle graph, then you can work out how many each section represents.


50%25%

25%

If this graph represents 200 people…

…so 25% = 50 people

…then 100% = 200 people…

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Example 3

Solution follows…

Lesson

3.5.4

Chris, Martina, and D’Andre each ran for student body president. A total of 150 students voted in the election, and the outcome of the election is shown in the circle graph. How many students voted for Martina?

Solution

The circle graph tells you 40% of the students voted for Martina. You know that the whole circle graph represents 150 students.

So the number of students who voted for Martina is


40% of 150 = 0.4 × 150 = 60

A total of 60 students voted for Martina.

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Guided Practice

Solution follows…

Lesson

3.5.4

16. This graph shows the results of a survey of students’ favorite school subjects. 80 students were surveyed. Find the number of students that liked each subject best.

Math – 0.45 × 80 = 36, English – 0.30 × 80 = 24, Science – 0.25 × 80 = 20


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Guided Practice

Solution follows…

Lesson

3.5.4

17. The percents of games won, lost, and tied by a soccer team out of their last 40 games are shown on this graph. How many of the games did they win, lose, and tie?


Won – 0.60 × 40 = 24, Tied – 0.15 × 40 = 6, Lost – 0.25 × 40 = 10

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Guided Practice

Solution follows…

Lesson

3.5.4

18. This graph shows the percent of each color of balloon at a party. There were a total of 200 balloons at the party. Find how many of each color of balloon were at the party.

Red – 0.48 × 200 = 96, White – 0.27 × 200 = 54, Blue – 0.25 × 200 = 50


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Guided Practice

Solution follows…

Lesson

3.5.4

19. 300 people were surveyed as to which of 4 types of animals they liked the best. This graph shows the results. How many people in the survey liked each type of animal?


Dog – 0.30 × 300 = 90, Cat – 0.28 × 300 = 84, Goldfish – 0.24 × 300 = 72, Rat – 0.18 × 300 = 54

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Independent Practice

Solution follows…

Lesson

3.5.4

The percents must add up to 100%. This means that the percent who go to the reading club is: 100 – 15 – 10 – 40 – 10 = 100 – 75 = 25%


1. A group of sixth-grade students each go to one of 5 clubs after school on Tuesdays. The table shows what percent of the students go to each club.

Acting Club 15%

Reading Club ?%

Debate Club 10%

Music Club 40%

Recycling Club 10%

What percent of the students go to the reading club? Explain your answer.

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Solution follows…

Lesson

3.5.4

Cabbage: 25%


2. A group of people were asked which of 3 vegetables they like best. This graph shows the results. Calculate the missing percent.

3. 300 people were questioned. Find the number of people who said they like each vegetable.

Carrots – 99, Spinach – 126, Cabbage – 75

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Solution follows…

Lesson

3.5.4

Cleveland: 38%


4. A town held a vote to decide who to build a statue of. The results are shown on this graph. Find the missing percent.

5. 250 people voted. Figure out how many people voted for each choice.

Washington – 90, Lincoln – 65, Cleveland – 95

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Solution follows…

Lesson

3.5.4

Red: 28%


6. This graph shows the colors of cars in the school parking lot. What percent of the cars are red?

7. If there are 175 cars in the lot, how many of each color are there?

Red – 49, Blue – 42, Silver – 49, Other – 35

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8. This graph shows the results of a survey asking people about their favorite season. Figure out the missing percent.


Solution follows…

Lesson

3.5.4

Winter: 24%


9. The survey questioned 325 people. How many said they like each season the best?

Spring – 91, Summer – 104, Fall – 52, Winter – 78

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Solution follows…

Lesson

3.5.4

150 acres


10. How many acres of corn are there?

11. Which section of the graph represents each crop? Explain your answer.The smallest section of the graph represents the crop with the least land, so A represents lettuce. B is the largest part of the graph, so it represents the crop with the largest area, the corn. So C represents the tomatoes.

Mr. Benson has 300 acres of land on his farm. He grows corn, lettuce, and tomatoes. There are 60 acres of lettuce and 90 acres of tomatoes. The graph shows how the land on the farm is divided between the three crops.

12. What percent of the land is used for each crop?Corn: 50%, Lettuce: 20%, Tomatoes: 30%

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Solution follows…

Lesson

3.5.4

500 sixth-graders were asked which of four sports they liked best. This graph shows the results.

13. How many students said they liked cycling best?100 students

15. What percent of the students preferred each sport?Swimming – 35%, Running – 30%, Cycling – 20%, Tennis – 15%


14. Write down what fraction of the sixth-graders preferred each sport.

Swimming: = , Running: = , Cycling: = , Tennis: = 175500

720

150500

310

75500

15

100500

320

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Round UpRound Up

Circle graphs are useful for giving out information.

Lesson


People who don’t know much about math can still understand what it means when one part of the circle is bigger than another.

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1 Lesson 3.5.4 Circle Graphs and Percents Circle Graphs and Percents