Introduction

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Think It Through

Lesson 4B Understand Percent

Lesson 4BUnderstand Percent

The word percent means parts per 100 or for each 100. A percent describes an amount by showing it as part of 100. Percent amounts are written using this symbol: %.

Look at the model below. 50 out of 100 parts are shaded. You already know how to show this amount as a fraction and a decimal. You can also show the amount as a percent.

Fraction:

Decimal: 0.50

Percent: 50% Read this as 50 percent.

50100

In the model below, 5 out of 100 parts are shaded. Compare it to the number shaded in the model above.

Fraction:

Decimal: 0.05 < 0.50

Percent: 5% < 50% 5 percent is less than 50 percent.

5100

50100<

Think You compare percents just as you compare decimals and fractions.

Circle all the numbers on the page that are percents.

What is percent? 

5.NS.6

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A percent compares a part to the whole, just as a fraction can. Percent means parts per

100, so 25% means 25 parts per 100, or 25 ··· 100 . You can always write a percent as a fraction

using 100 as the denominator.

100 of 100 parts 65 of 100 parts 4 of 100 parts 21 of 100 parts

100% 65% 4% 21%

• Percent is a way to describe a part of the whole, when the whole is 100. For example, if you take a test with 100 questions and you get 90 questions correct, you got 90 percent of the questions correct.

90 out of 100 correct 90100

correct 90% correct

One whole describes all or 100% in every percent situation. If you know that you got 90% of the test questions correct, you know that you got 10% of the questions incorrect.

• Percent is also a way to describe groups or parts even when the whole may not be equal to 100. Suppose you know that 45% of the students in your town ride a bus to school. You don’t know the number of students that ride a bus to school, but you know that a little less than half of the students do.

Reflect

1 A bicyclist has traveled 20% of the total distance from home to school. Is that less

than 1 ·· 4 of the distance, exactly 1 ·· 4 , or more than 1 ·· 4 ? Explain how you know.

Think A percent compares a part to the whole.

I can see that 50% is

equal to 1 ··

2 and 25%

is equal to 1 ·· 4 .

Guided Instruction

Think About

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Lesson 4B

Solving Percent Problems

Lesson 4B Understand Percent

2 Reina is making a paper chain, and 35% of the links in the chain are green. Shade the model below to show 35%.

3 If the chain has 100 links, how many of the links are green?

4 What fraction can you write for the amount of the model that is shaded?

5 Some of the links in the chain are blue. Can 75% of the links be blue? Explain.

Now try these two problems.

6 Shade the model at the right to show 60%.

7 What percent of the model is not shaded?

Let’s Explore the Idea Use a model to help you think about percent problems.

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Let’s Talk About It Solve the problems below as a group.

8 The model on the previous page shows 35%. Write a decimal that names the same amount. Explain how you found your answer.

9 Think about designing your own paper chain that follows these rules:

• It has 3 colors of links.

• Each color of links is greater than 10% of the chain.

Shade the model at the right to show the percent of each color of your design.

10 Complete the table below for the paper chain you designed in problem 9.

ColorNumber of Links in a

100-Link ChainPercent Fraction Decimal

Try It Another Way Work with your group to relate percents and circle graphs.

11 A survey asked if people have been to Lake Michigan. The circle

graph shows the results. Which response did about 3 ·· 4 of the

people give, Yes or No?

Complete the equation: 3 ·· 4 5 ··· 100

12 About what percent of the people surveyed answered Yes?

Have you visitedLake Michigan?

Yes

No