Lesson 5 Introduction Solve Problems with Percentkarladavis.weebly.com/.../5/37452469/lesson_5_solve... · Picture It You can use a bar model to solve the problem. 80 0% 10% 20% 30%

©Curriculum Associates, LLC Copying is not permitted.40 Lesson 5 Solve Problems with Percent

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IntroductionLesson 5Solve Problems with Percent

You have learned how to make tables of equivalent ratios to solve problems. Take a look at this problem.

On the first math test, Keiko answered 19 out of 25 questions correctly. On the second test she got 17 out of 20 correct. On which test did she get a better grade?

Use the math you already know to help solve the problem.

a. Write a ratio in fraction form to compare the number correct to the total questions

for each test.

b. Can you compare these two ratios as they are written? Explain why or why not.

c. Look at the table. How are 50, 75, and 100 related to 25?

What do you need to do to complete the table?

Now complete the table.

d. How are 40, 60, 80 and 100 related to 20?

Use this information to complete a table of equivalent ratios for the second test.

e. Look at the two tables. Which ratios can you use to compare the test results? Why?

f. On which test did Keiko get a better grade? Explain.

Test 1Number Correct 19

Total 25 50 75 100

Test 2Number Correct 17

Total 20 40 60 80 100

MGSE 6.RP.3c

©Curriculum Associates, LLC Copying is not permitted. 41Lesson 5 Solve Problems with Percent

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The ratios on the previous page, 76 ··· 100 and 85 ··· 100 , can be expressed as fractions, decimals and

percents. A percent is a rate “for every 100” or “per 100.“ The symbol % signifies percent.

Base-ten models can be used to represent fractions, decimals, and percents.

Fraction: 76 ··· 100 Fraction: 85 ··· 100

Decimal: 0.76 Decimal: 0.85

Percent: 76% Percent: 85%

Here are some fractions, decimals, and percents that you will see and use often.

Fraction 1 ··· 100 1 ·· 10 1 ·· 4 or 25 ··· 100 1 ·· 2 or 50 ··· 100 3 ·· 4 or 75 ··· 100 1 ·· 1 or 100 ··· 100

Decimal 0.01 0.1 or 0.10 0.25 0.5 or 0.50 0.75 1.00

Percent 1% 10% 25% 50% 75% 100%

Sometimes it is easier to use an equivalent fraction when given a decimal or percent.

Example: What is 0.25 · 80?

Think: What is 1 ·· 4 of 80? 80 4 4 5 20

Reflect1 Why do you think percents are used to compare ratios when the wholes are di� erent?

Modeled and Guided Instruction

Learn About


Lesson 5

Percent of a Number

Read the problem below. Then explore different ways to solve problems involving percent of a number.

At Madison Middle School, 60% of the 800 students participate in music. How many students participate in music?

Picture It You can use a bar model to solve the problem.

80

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

80 80 80 80 80 80 80 80 80

The bar model shows 800 students divided into 10 groups of 80. Each group of 80 represents 10%.

Model It You can write an expression to find the number of students.

Use words: 60% of 800

Use numbers: 60 ··· 100 . 800

Remember: of means to multiply.


Connect It Now you will solve the problem from the previous page using a bar model and related expression.

2 In the bar model, how many groups of 80 make up 60%? What is the total number of students in these groups?

3 Using your answer to number 2, what is 60% of 800 students?

4 The expression from the previous page is shown below. Fill in the blanks to show how to multiply.

60 ··· 100 • 800 ··· 1 5 or

5 Explain how to � nd a percent of a number.

6 Imagine that 55% of the 800 students participate in music instead of 60%. How could you use the idea of halves with the bar model to � nd 55% of 800?

Try It Use what you’ve just learned about the percent of a number to solve these problems. Show your work on a separate sheet of paper.

7 Charlie wants a new pair of shoes that cost $40. His mom pays 75% of the cost and Charlie pays 25%. How much do they each pay?

8 A school will have a fall festival if at least 40% of the 500 students plan to attend. How many students must agree to attend in order for the school to have the festival?

Modeled and Guided Instruction

Learn About


Lesson 5

Finding the Whole

Read the problem below. Then explore different ways to find the whole when a part and the percent are given.

Eric wants to buy a video game that costs $24, but he only wants to spend 40% of his savings. How much must Eric save in order to buy the game?

Picture It You can use a double number line to find the whole when a part and the percent are given.

$ dollars 0 6 ?

0 10 100% percent

24

20 30 40 50 60 70 80 90

Model It You can make a table of equivalent ratios to find the whole when a part and the percent are given.

$ dollars 6 12 ?

% percent 10 20 100

Start with the ratio 24 to 40.

Find half of both quantities in 24 to 40: 12 to 20

Find half of both quantities in 12 to 20: 6 to 10

0 10% percent

40 4 4 5 10 and 24 4 4 5 6

24

$24 is 40% of Eric’s savings.

?

100% represents the total amount of Eric’s savings.


Connect It Now you will solve the problem from the previous page using the double number line and the table.

9 Look at the table and the double number line. How many dollars is 10% of the

total? How many times greater than 10% is 100%? So,

how many times greater than $6 is the dollar amount that equals 100%?

10 Look at the double number line. Using the ratio 6 to 10, explain how you can � nd an equivalent ratio that has 100 as the second quantity.

11 How much does Eric have to save in order to buy the game?

12 What does the answer to the problem mean? Fill in the blanks to help you understand.

10 • 5 100% and 10 • $6 5 $

If $24 is 40%, then $ is 100%.

So, 40% of $ is $24.

13 You can use what you know about � nding percent of a number to check your answer. Fill in the blanks.

40% of $60

40 ··· 100 • 60 ·· 1 5 or $

14 How can you � nd the whole when you know part and the percent?

Try It Use what you’ve just learned about finding the whole to solve this problem. Show your work on a separate sheet of paper.

15 150 students at York Middle School took part in the school clean up. This is 30% of

the school’s total students. How many students go to York Middle School?

Practice

©Curriculum Associates, LLC Copying is not permitted.46

Guided Practice

Lesson 5 Solve Problems with Percent

Lesson 5

Solving Problems with Percent

Study the example below. Then solve problems 16–18.

Example

At Sydney’s school, 300 of the 500 girls and 450 of the 600 boys attend the Spring Carnival. Which group has greater attendance?

Look at how you can use equivalent ratios and percents to solve the problem.

Solution

16 Cesar turned in his third research report. His teacher said that Cesar had completed 20% of the reports for the school year. How many research reports will he do during the school year?

Show your work.

Solution

The boys have better attendance because 75% > 60%.

Girls Boys

300 ···· 500 5 60 ···· 100 450 ···· 600 5 75 ···· 100

60% 75%

If you find equivalent ratios with the denominator of 100, you can use percents.

Pair/ShareWhy can’t you say, “450 . 300, so the boys have better attendance?”

Pair/Share

Suppose you think of

20% as 20 ··· 100 or 1 ·· 5 .

How can you solve the

problem using 1 ·· 5

instead of 20%?

How can you use an equivalent ratios table to help you solve the problem?


17 Nia answered 80% of the 40 questions on a test correctly. How many correct answers did she have?

Show your work.

Solution

18 Andrei’s grandfather o� ered to give him a gift of 50% of the amount of money he saved in one year. Andrei saved $120 dollars. How much did his grandfather give him as a gift?

A $50

B $60

C $120

D $180

Mitch chose D as the correct answer. How did he get that answer?

I think that it would be easy to solve this problem using a fraction.

Pair/ShareDid you use a fraction or a decimal to solve this problem? Why?

Pair/ShareHow can you show that your answer is 50% of 120?

When you write a number equation from a word equation, what symbol do you use for the word “of?”

Independent Practice

Practice


Solving Problems with Percent

Lesson 5

Solve the problems.

1 Jason’s father bought a computer for $800. He made equal payments of 25% of the total cost. How much was each payment?

A $25

B $32

C $200

D $400

2 Antonio has read 147 pages of a book. He has completed 70% of the book. How many more pages does he need to read to � nish the book?

pages

3 During the basketball season, Cory made 21 of the 60 baskets she attempted. Krista made 16 of the 40 baskets she attempted. Paula made 17 of the 50 baskets she attempted. Write the names of the players in order from the least percentage of baskets made to the greatest percentage of baskets made.

Least GreatestName Name Name

Self Check


Go back and see what you can check off on the Self Check on page 1.

4 Jackson’s mom limits the amount of time he is allowed to play video games. After Jackson plays for 9 minutes, his mom tells him that he has used up 30% of his time. How many more minutes can Jackson play before he uses all of his time?

Show your work.

Answer Jackson can play more minutes.

5 Ashley has sold 70% of the 20 candy bars she is supposed to sell for her softball team. How many candy bars does she have left to sell?

Show your work.

Answer Ashley has more candy bars to sell.

Documents

Lesson 5 Introduction Solve Problems with Percentkarladavis.weebly.com/.../5/37452469/lesson_5_solve... · Picture It You can use a bar model to solve the problem. 80 0% 10% 20% 30%