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LESSON
Name
Date
7.1 Study Guide
For use with pages 329 –333
GOAL
Use a fraction to find the percent of a number.
VOCABULARY
Lesson 7.1
The word percent means “per hundred.” A percent is a ratio whose
denominator is 100. The symbol for percent is %.
EXAMPLE
1 Writing Percents as Fractions, Fractions as Percents
Write 80% and 4% as fractions in simplest form.
80
100
4
5
a. 80% ⫽ ᎏᎏ ⫽ ᎏᎏ
4
100
1
25
b. 4% ⫽ ᎏᎏ ⫽ ᎏᎏ
19
13
Write ᎏ20ᎏ and ᎏ5ᎏ0 as percents.
19
20
19 p 5
20 p 5
95
100
13
50
13 p 2
50 p 2
26
100
a. ᎏᎏ ⫽ ᎏᎏ ⫽ ᎏᎏ ⫽ 95%
b. ᎏᎏ ⫽ ᎏᎏ ⫽ ᎏᎏ ⫽ 26%
Exercises for Example 1
Write the percent as a fraction in simplest form, or write the fraction as
a percent.
1. 27%
13
20
3. ᎏᎏ
2. 90%
12
25
4. ᎏᎏ
Common Percents
1
10
20% ⫽ ᎏᎏ
1
5
25% ⫽ ᎏᎏ
1
4
30% ⫽ ᎏᎏ
40% ⫽ ᎏᎏ
2
5
50% ⫽ ᎏᎏ
1
2
60% ⫽ ᎏᎏ
3
5
70% ⫽ ᎏᎏ
3
4
80% ⫽ ᎏᎏ
4
5
90% ⫽ ᎏᎏ
9
10
100% ⫽ 1
10% ⫽ ᎏᎏ
75% ⫽ ᎏᎏ
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LESSON
Name
Date
7.1 Study Guide
Continued
EXAMPLE
For use with pages 329–333
2 Writing a Probability as a Percent
You randomly choose a letter from a bag that contains 20 letters. There are 5
vowels and the rest are consonants. What is the probability that you choose a
consonant? Write your answer as a percent.
15
20
P(consonant) ⫽ ᎏᎏ
⫽ 75%
Lesson 7.1
Solution
There are 20 possible outcomes, and 20 ⫺ 5 ⫽ 15 outcomes are favorable.
Write probability as a fraction.
Write fraction as a percent.
Answer: The probability that you choose a consonant is 75%.
Exercise for Example 2
5. You spin a spinner with 10 equal sections. One section is red, 4 sections are
blue, 3 sections are green, and 2 sections are white. Find the probability
that the spinner stops on blue. Write your answer as a percent.
EXAMPLE
3 Finding a Percent of a Number
In your town, it rained 30% of the days in April. How many days in April
did it rain?
Solution
3
To find 30% of the number of days in April, 30, use the fact that 30% ⫽ ᎏᎏ.
10
Then multiply.
3
10
90
⫽ ᎏᎏ
10
30% of 30 ⫽ ᎏᎏ p 30
⫽9
Write percent as a fraction.
Multiply.
Simplify.
Answer: It rained 9 days in April.
Exercises for Example 3
Find the percent of the number.
6. 60% of 5
7. 5% of 20
8. 10% of 10
9. 43% of 100
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LESSON
Name
Date
7.2 Study Guide
For use with pages 334 –339
GOAL
Use proportions to solve percent problems.
SOLVING PERCENT PROBLEMS
You can represent “a is p percent of b” using the proportion
p
a
ᎏᎏ ⫽ ᎏᎏ
b
100
p
100
where a is a part of the base b and p%, or ᎏᎏ, is the percent.
EXAMPLE
1 Finding a Percent
What percent of 9 is 3?
Solution
Lesson 7.2
p
a
ᎏᎏ ⫽ ᎏᎏ
100
b
p
3
ᎏᎏ ⫽ ᎏᎏ
100
9
p
3
100 p ᎏᎏ ⫽ 100 p ᎏᎏ
100
9
1
33 ᎏᎏ ⫽ p
3
1
Answer: 3 is 33 ᎏᎏ% of 9.
3
EXAMPLE
Write proportion.
Substitute 3 for a and 9 for b.
Multiply each side by 100.
Simplify.
2 Finding a Part of a Base
What number is 90% of 340?
Solution
p
a
ᎏᎏ ⫽ ᎏᎏ
100
b
a
90
ᎏᎏ ⫽ ᎏᎏ
340
100
a
90
340 p ᎏᎏ ⫽ 340 p ᎏᎏ
340
100
a ⫽ 306
Write proportion.
Substitute 340 for b and 90 for p.
Multiply each side by 340.
Simplify.
Answer: 306 is 90% of 340.
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LESSON
Name
Date
7.2 Study Guide
Continued
EXAMPLE
For use with pages 334–339
3 Finding a Base
In your school, 336 students play an instrument. The students who play an
instrument comprise 32% of the student body. How many students attend
your school?
Solution
In this situation, 336 is a part of the total number of students, which is the base.
p
a
ᎏᎏ ⫽ ᎏᎏ
b
100
336
32
ᎏᎏ ⫽ ᎏᎏ
b
100
336 p 100 ⫽ 32 p b
33,600 ⫽ 32b
1050 ⫽ b
Write proportion.
Substitute 336 for a and 32 for p.
Cross products property
Multiply.
Divide each side by 32.
Answer: There are 1050 students at your school.
Lesson 7.2
Exercises for Examples 1–3
Use a proportion to answer the question.
1. What percent of 12 is 3?
2. What percent of 25 is 20?
3. What percent of 90 is 42?
4. What percent of 85 is 17?
5. What number is 35% of 60?
6. What number is 12% of 125?
7. What number is 42% of 150?
8. What number is 8% of 625?
9. 300 is 24% of what number?
10. 15 is 60% of what number?
11. 20 is 40% of what number?
Copyright © McDougal Littell/Houghton Mifflin Company
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12. 70 is 35% of what number?
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LESSON
Name
Date
7.3 Study Guide
For use with pages 340 –344
GOAL
EXAMPLE
Use decimals to solve percent problems.
1 Writing Decimals as Percents
Write 0.35, 0.035, 5.7, and 0.001 as percents.
EXAMPLE
a. 0.35 ⫽ 0.35
b. 0.035 ⫽ 0.035
⫽ 35%
⫽ 3.5%
c. 5.7 ⫽ 5.70
d. 0.001 ⫽ 0.001
⫽ 570%
⫽ 0.1%
2 Writing Percents as Decimals
Write 53%, 560%, and 1.2% as decimals.
a. 53% ⫽ 53%
b. 560% ⫽ 560%
⫽ 0.53
c. 1.2% ⫽ 01.2%
⫽ 5.6
⫽ 0.012
Exercises for Examples 1 and 2
Write the decimal as a percent or the percent as a decimal.
EXAMPLE
1. 0.13
2. 15
3. 1.255
4. 0.0023
5. 61%
6. 4%
7. 0.05%
8. 212%
3 Writing Fractions as Percents
9
2
21
Write ᎏ32ᎏ, ᎏ9ᎏ, and ᎏ16ᎏ as percents.
Lesson 7.3
9
32
a. ᎏᎏ ⫽ 0.28125
Write fraction as a decimal.
⫽ 28.125%
Write decimal as a percent.
2
9
b. ᎏᎏ ⫽ 0.222. . .
w%
⫽ 22.2
21
16
c. ᎏᎏ ⫽ 1.3125
⫽ 131.25%
Write fraction as a decimal.
Write decimal as a percent.
Write fraction as a decimal.
Write decimal as a percent.
Exercises for Example 3
Write the fraction as a percent.
9
4
9. ᎏᎏ
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Chapter 7 Resource Book
3
2
10. ᎏᎏ
7
11
11. ᎏᎏ
3
40
12. ᎏᎏ
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LESSON
Name
Date
7.3 Study Guide
Continued
EXAMPLE
For use with pages 340–344
4 Finding a Percent of a Number
The average adult has 10 to 12 pints of blood. Human blood is 83% water. How
many pints of water are in 11 pints of human blood?
Solution
83% of 11 ⫽ 0.83 p 11
⫽ 9.13
Write percent as a decimal.
Multiply.
Answer: There are 9.13 pints of water in 11 pints of human blood.
Exercises for Example 4
Find the percent of the number.
13. 41% of 12
14. 207% of 300
15. 0.035% of 100
Lesson 7.3
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LESSON
Name
Date
7.4 Study Guide
For use with pages 345 –349
GOAL
Use equations to solve percent problems.
THE PERCENT EQUATION
You can represent “a is p percent of b” using the equation
a ⫽ p% p b
where a is a part of the base b and p% is the percent.
EXAMPLE
1 Finding a Part of a Base
In a recent year, about 7.3% of United States residents were 10 to 14 years old.
The total United States resident population that year was 284,797,000. About
how many United States residents were 10 to 14 years old?
Solution
To find the number of residents that were 10 to 14 years old, use the
percent equation.
a ⫽ p% p b
⫽ 7.3% p 284,797,000
⫽ 0.073 p 284,797,000
⫽ 20,790,181
Write percent equation.
Substitute 7.3 for p and 284,797,000 for b.
Write percent as a decimal.
Multiply.
Answer: About 20,790,181 United States residents were 10 to 14 years old.
Exercises for Example 1
Use the percent equation to answer the question.
EXAMPLE
1. What number is 30% of 60?
2. What number is 14% of 25?
3. What number is 0.5% of 6?
4. What number is 345% of 2?
2 Finding a Commission
A computer salesperson earns a 5.8% commission on every computer
package sold. The salesperson sells a computer package for $3500. What
is the commission?
Lesson 7.4
Solution
a ⫽ p% p b
⫽ 5.8% p 3500
⫽ 0.058 p 3500
⫽ 203
Write percent equation.
Substitute 5.8 for p and 3500 for b.
Write percent as a decimal.
Multiply.
Answer: The salesperson’s commission is $203.
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LESSON
Name
Date
7.4 Study Guide
Continued
For use with pages 345–349
Exercises for Example 2
5. In Example 2, find the commission if a computer package is sold for $2450.
6. In Example 2, find the commission if a computer package is sold for $900.
EXAMPLE
3 Finding a Percent
What percent of 600 is 25?
Solution
a ⫽ p% p b
25 ⫽ p% p 600
0.0416
w ⫽ p%
w% ⫽ p%
4.16
Write percent equation.
Substitute 25 for a and 600 for b.
Divide each side by 600.
Write decimal as a percent.
w% of 600.
Answer: 25 is 4.16
EXAMPLE
4 Finding a Base
In a recent year in the United States, 1,744,548 people ages 16 to 24 who had
graduated from high school within the previous 12 months were enrolled in
college. The college enrollment rate for the graduates was 63.3%. How many
16-to 24-year-old high school graduates in the previous 12 months were there?
Solution
a ⫽ p% p b
1,744,548 ⫽ 63.3% p b
1,744,548 ⫽ 0.633 p b
2,756,000 ⫽ b
Write percent equation.
Substitute 1,744,548 for a and 63.3 for p.
Write percent as a decimal.
Divide each side by 0.633.
Answer: There were 2,756,000 graduates.
Exercises for Examples 3 and 4
Use the percent equation to answer the question.
7. What percent of 8 is 1?
9. 60 is 3% of what number?
8. What percent of 20 is 35?
10. 51.75 is 115% of what number?
Lesson 7.4
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LESSON
Name
Date
Lesson 7.5
7.5 Study Guide
For use with pages 351–356
GOAL
Find a percent of change in a quantity.
VOCABULARY
A percent of change indicates how much a quantity increases or
decreases with respect to the original amount. If the new amount is
greater than the original amount, the percent of change is called a
percent of increase. If the new amount is less than the original
amount, the percent of change is called a percent of decrease.
EXAMPLE
1 Finding a Percent of Increase
Find the percent of increase from 40 to 44.
Solution
Amount of increase
Original amount
44 ⫺ 40
⫽ ᎏᎏ
40
4
⫽ ᎏᎏ
40
Substitute.
⫽ 0.1
Divide.
⫽ 10%
Write decimal as a percent.
p% ⫽ ᎏᎏᎏ
Write formula for percent of increase.
Subtract.
Answer: The percent of increase is 10%.
Exercises for Example 1
Find the percent of increase.
1. Original: 6
New: 10
EXAMPLE
2. Original: 50
New: 51
3. Original: 15
New: 30
2 Finding a Percent of Decrease
Find the percent of decrease from 250 to 175.
Solution
Amount of decrease
Original amount
250 ⫺ 175
⫽ ᎏᎏ
250
75
⫽ ᎏᎏ
250
3
⫽ ᎏᎏ
10
p% ⫽ ᎏᎏᎏ
⫽ 30%
Write formula for percent of decrease.
Substitute.
Subtract.
Simplify fraction.
Write fraction as a percent.
Answer: The percent of decrease is 30%.
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Name
Date
Lesson 7.5
7.5 Study Guide
Continued
For use with pages 351–356
Exercises for Example 2
Find the percent of decrease.
4. Original: 40
New: 30
EXAMPLE
5. Original: 55
New: 23
6. Original: 9000
New: 8982
3 Using a Percent of Increase
In 1999, total attendance at United States symphony orchestras was 30,800,000.
Attendance increased by about 2.9% from 1999 to 2000. What was the
approximate attendance in the year 2000?
Solution
To find the attendance in the year 2000, you need to increase the attendance in
1999 by 2.9%.
2000 attendance
⫽
1999 attendance
⫹
Amount of increase
⫽ 30,800,000 ⫹ 2.9% p 30,800,000
⫽ 30,800,000 ⫹ 0.029 p 30,800,000
⫽ 31,693,200
Substitute.
Write percent as a decimal.
Evaluate.
Answer: The attendance at symphony orchestras in 2000 was about 31,693,200.
EXAMPLE
4 Finding a New Amount
Your 5K time for the first race of the cross country season was 25 minutes.
Your time for the last race of the season decreased by 12% from the first
race time. What was your last race time of the season?
Solution
Last race time ⫽ First race time p (100% ⫺ p%)
⫽ 25 p (100% ⫺ 12%)
⫽ 25 p 88%
⫽ 25 p 0.88
⫽ 22
Substitute.
Subtract.
Write percent as a decimal.
Multiply.
Answer: It took you 22 minutes to run the last 5K race of the season.
Exercises for Examples 3 and 4
Find the new amount.
7. Increase 60 by 85%.
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Pre-Algebra
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8. Decrease 80 by 0.5%.
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LESSON
Name
Date
7.6 Study Guide
For use with pages 357–361
GOAL
Find markups, discounts, sales tax, and tips.
VOCABULARY
EXAMPLE
Lesson 7.6
An increase from the wholesale price of an item to the retail price is
a markup.
A decrease from the original price of an item to the sale price is
a discount.
1 Finding a Retail Price
A store buys DVD players for $50. The store marks up the price by 110%. What
is the retail price of a DVD player?
Solution
Method 1: Add the markup to the wholesale price.
Retail price ⫽ Wholesale price ⫹ Markup
⫽ 50 ⫹ 110% p 50
Substitute.
⫽ 50 ⫹ 1.1 p 50
Write 110% as a decimal.
⫽ 50 ⫹ 55 ⫽ 105
Multiply. Then add.
Method 2: Multiply the wholesale price by (100% ⫹ Markup percent).
Retail price ⫽ Wholesale price p (100% ⫹ Markup percent)
⫽ 50 p (100% ⫹ 110%)
Substitute.
⫽ 50 p 210%
Add percents.
⫽ 50 p 2.1 ⫽ 105
Write 210% as a decimal. Then multiply.
Answer: The retail price of a DVD player is $105.
Exercise for Example 1
1. In Example 1, what is the retail price of a DVD player if the markup
percent is 125%?
EXAMPLE
2 Finding a Sale Price
Haircuts are 35% off for a limited time. The original price of a haircut is $20.
What is the sale price?
Solution
Method 1: Subtract the discount from the original price.
Sale price ⫽ Original price ⫺ Discount
⫽ 20 ⫺ 35% p 20
⫽ 20 ⫺ 0.35 p 20
⫽ 20 ⫺ 7
⫽ 13
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All rights reserved.
Substitute.
Write 35% as a decimal.
Multiply.
Subtract.
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LESSON
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Date
7.6 Study Guide
Continued
For use with pages 357–361
Method 2: Multiply the original price by (100% ⫺ Discount percent).
Lesson 7.6
Sale price ⫽ Original price p (100% ⫺ Discount percent)
⫽ 20 p (100% ⫺ 35%)
Substitute.
⫽ 20 p 65%
Subtract percents.
⫽ 20 p 0.65 ⫽ 13
Write 65% as a decimal. Then multiply.
Answer: The sale price of a haircut is $13.
Exercise for Example 2
2. In Example 2, what is the sale price of a haircut if the discount percent
is 55%?
EXAMPLE
3 Using Sales Tax and Tips
The bill for your family’s restaurant meal is $47. You leave an 18% tip. The
sales tax is 7%. What is the total cost of the meal?
Solution
Sales tax and tip are calculated using a percent of the purchase price. These
amounts are then added to the purchase price.
Total ⫽ Food bill ⫹ Sales tax ⫹ Tip
⫽ 47 ⫹ 7% p 47 ⫹ 18% p 47
Substitute.
⫽ 47 ⫹ 0.07 p 47 ⫹ 0.18 p 47
Write 7% and 18% as decimals.
⫽ 47 ⫹ 3.29 ⫹ 8.46 ⫽ 58.75
Multiply. Then add.
Answer: The total cost of the meal is $58.75.
EXAMPLE
4 Finding an Original Amount
There is a 40% off sale on CDs. You buy a CD for $12.95. What is the
original price?
Solution
Let x represent the original price.
Sale price ⫽ Original price p (100% ⫺ Discount percent)
12.95 ⫽ x p (100% ⫺ 40%)
Substitute.
12.95 ⫽ x p 60%
Subtract percents.
12.95 ⫽ 0.6x
Write 60% as a decimal.
21.58 ≈ x
Divide each side by 0.6.
Answer: The original price of the CD is about $21.58.
Exercises for Examples 3 and 4
3. In Example 3, find the total cost of the meal if the sales tax is 6% and the
tip is 15%.
4. A store marks up the wholesale price of a skateboard by 112%. The retail
price is $35. What is the wholesale price of the skateboard?
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LESSON
Name
Date
7.7 Study Guide
For use with pages 362–367
GOAL
Calculate interest earned and account balances.
VOCABULARY
The amount earned or paid for the use of money is called interest.
The amount of money deposited or borrowed is the principal. Interest
that is earned or paid only on the principal is called simple interest.
The percent of the principal earned or paid per year is the annual
interest rate.
The balance A of an account that earns simple annual interest is the
sum of the principal P and the interest Prt.
Compound interest is interest that is earned on both the principal and
any interest that has been earned previously.
EXAMPLE
1 Finding Simple Interest
You purchase a bond for $450. The bond earns 6.5% simple annual interest.
How much interest will the bond earn after 10 years?
Lesson 7.7
Solution
I ⫽ Prt
⫽ (450)(0.065)(10)
⫽ 292.5
Write simple interest formula.
Substitute 450 for P, 0.065 for r, and 10 for t.
Multiply.
Answer: The bond will earn $292.50 in interest after 10 years.
EXAMPLE
2 Finding an Interest Rate
You deposit $600 into an account that earns simple annual interest. After
18 months, the balance is $648.60. Find the annual interest rate.
Solution
A ⫽ P(1 ⫹ rt)
冤
Write formula for finding balance.
冢 冣冥
3
648.60 ⫽ 600 1 ⫹ r ᎏᎏ
2
Substitute. 18 months ⫽ ᎏᎏ years ⫽ ᎏᎏ years
18
12
3
2
648.60 ⫽ 600 ⫹ 900r
48.60 ⫽ 900r
0.054 ⫽ r
Distributive property
Subtract 600 from each side.
Divide each side by 900.
Answer: The annual interest rate is 5.4%.
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Name
Date
7.7 Study Guide
Continued
For use with pages 362–367
Exercises for Examples 1 and 2
1. A $1600 bond earns 5.2% simple annual interest. What is the interest
earned after 3 years?
Find the unknown quantity for an account that earns simple annual interest.
2. A ⫽ $5037.50, P ⫽ $5000, r ⫽ 3%, t ⫽ ____
?
3. A ⫽ $1337.50, P ⫽ ____,
? r ⫽ 4%, t ⫽ 21 months
EXAMPLE
3 Calculating Compound Interest
You deposit $2000 into an account that earns 3.6% interest compounded
annually. Find the balance after 5 years.
Lesson 7.7
Solution
A ⫽ P(1 ⫹ r)t
⫽ 2000(1 ⫹ 0.036)5
≈ 2386.87
Write formula.
Substitute.
Use a calculator.
Answer: The balance of the account after 5 years is about $2386.87.
Exercises for Example 3
For an account that earns interest compounded annually, find the balance of
the account. Round your answer to the nearest cent.
4. P ⫽ $35, r ⫽ 2.5%, t ⫽ 10 years
5. P ⫽ $100, r ⫽ 7.5%, t ⫽ 4 years
6. P ⫽ $2000, r ⫽ 5.4%, t ⫽ 7 years
7. P ⫽ $20, r ⫽ 8.2%, t ⫽ 8 years
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