Chapter 1 Chapter 1 Resource Masters Resource Masters Contents Chapter Resources • Family Letter • Are You Ready Worksheets • Diagnostic Test • Pretest Language Arts Resources • Student Glossary Practice and Reinforcement • Facts Practice Leveled Lesson Resources • Explore • Reteach • Skills Practice • Homework Practice • Problem-Solving Practice • Enrich Technology Resources • Graphing Calculator Activity • Scientific Calculator Activity • Spreadsheet Activity Assessment Resources • Reflecting on the Chapter • Chapter Quizzes • Vocabulary Test • Chapter Tests • Standardized Test Practice • Extended-Response Test • Student Recording Sheet • Chapter Project Rubric Answer Pages Chapter Resource Masters are provided for every chapter in both print and digital formats.
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Teacher’s Guide to Using theChapter 1 Resource Masters
The Chapter 1 Resource Masters includes the core materials needed forChapter 1. These materials include information for families, student worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing from the online Teacher Edition.
Family ResourcesFamily Introduction to Course 3 (Available in Chapter 0)
• Talks about the focus of the grade level • Gives Web site information.
Family Letter • English and Spanish • Overview of the chapter • Key vocabulary • Provides at-home activities
Chapter ResourcesAre You Ready Worksheets • Use after the Are You Ready section in the Student Edition. • AL Review: Approaching-level students • Practice: On-level students • BL Apply: Beyond-level students
Chapter Diagnostic Test • Use to test skills needed for success in the upcoming chapter. • Retest approaching-level students after the Are You Ready? worksheets.
Chapter Pretest • Quick check of the upcoming chapter’s concepts to determine pacing • Use before the chapter to gauge students’ skill level. • Use to determine class grouping.
NAME ________________________________________ DATE _____________ PERIOD _____
Today we began Chapter 1: Rational Numbers and Percent. In this chapter, your student will learn how to add, subtract, multiply, and divide positive and negative fractions. Also, we will be applying percents to find discount, markup, and sales tax. Included in this letter are key vocabulary words and activities you can do with your student. You may also wish to log on to glencoe.com for other study help. If you have any questions or comments, feel free to contact me at school.
Sincerely,
_____________________
Rational Numberslike fractions Fractions that have the same denominator.
multiplicative inverses Two numbers with a product of 1.
rational numbers Any number that can be written as a fraction.
Percentcompound interest Interest paid on the initial principal and on interest earned in the past.
discount A decrease in price from the original price.
markup The increase in the wholesale price of an item sold.
percent of change The percent that an amount changes from its original amount.
simple interest The amount of money earned or paid on the initial principal of a savings account or loan.
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Write each fraction or mixed number as a decimal. 1. 3 − 5 2. 5 − 8 3. 9 − 20
4. 37 − 50 5. - 11 − 16 6. - 9 − 32
7. 3 1 − 5 8. 4 3 − 8 9. 5 − 33
10. - 7 − 9 11. -8 11 − 18 12. -9 11 − 30
Write each decimal as a fraction or mixed number in simplest form. 13. -0.8 14. 0.44 15. -1.35
16. 0. − 8 17. -1. − 5 18. 4. −− 45
19. POPULATION Refer to the table at the right. a. Express the fraction for Asian as a decimal.
b. Find the decimal equivalent for the fraction of the population that is African American.
c. Write the fraction for Hispanic as a decimal.
20. MEASUREMENTS Use the figure at the right. a. Write the width of the jellybean as a fraction. b. Write the width of the jellybean as a decimal.
Homework PracticeRational Numbers
in. 1
Population of Florida by RaceRace Fraction of
Total PopulationAsian 1 − 50
African American 4 − 25
Hispanic 1 − 5
Get ConnectedGet Connected For more examples, go to glencoe.com.
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Language Arts ResourcesStudent Glossary • Includes key vocabulary terms from the chapter • Students record definitions and/or examples for each term. • Students can use the page as a bookmark as they study the chapter
Practice and ReinforcementFacts Practice • Quick recall of concepts needed in the upcoming chapter • Use as a timed test to gauge student mastery of prior concepts.
examples, and exercises • Use for students who have been absent.
Skills Practice • Focuses on the computational nature of the lesson • Use as an additional practice. • Use as homework for second-day teaching.
Homework Practice • Mimics the types of problems found in the Practice
and Problem Solving of the Student Edition • Use as an additional practice. • Use as homework for second-day teaching.
Problem-Solving Practice • Includes word problems that apply the concepts of the lesson • Use as an additional practice. • Use as homework for second-day teaching.
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Enrich • Provides an extension of the concepts, offers a
historical or multicultural look at the concepts, or widens students’ perspectives on the mathematics
• For use with all levels of students
Technology Activities • Presents ways in which technology can be used with the
concepts in some of the lessons • Use as an alternative approach to teaching the concept. • Use as part of the lesson presentation.
Assessment Resources
Reflecting on Chapter 1 • Three open-ended questions • Allows students to write about mathematics
Chapter Quizzes • Free-response questions • One quiz for each multi-part lesson
Vocabulary Test • Includes a list of vocabulary words and questions to assess students’ knowledge of
those words • Use in conjunction with one of the Chapter Tests.
Chapter Tests • AL 1A-1B Approaching-level students Contains multiple choice questions • 2A-2B On-level students Contains both multiple-choice and free-response questions • BL 3A-3B Beyond-level students Contains free-response questions • Tests A and B are the same format with different numbers. Use when students are absent or for different rows.
Standardized Test Practice • Test is cumulative. • Includes multiple-choice and short-response questions
NAME ________________________________________ DATE _____________ PERIOD _____
Read each question. Then fill in the correct answer. 1. Write –5 7 − 8 as a decimal. A. –0.875 B. –4.125 C. –4.375 D. –5.875 2. Write –2.18 as a fraction in simplest form. F. –2 18 − 100 G. –2 9 − 50 H. –1 41 − 50 I. –1 82 − 100 3. Find –4 3 − 5 – (–4 3 − 5 ). Write in simplest form. A. 9 1 − 5 B. 0 C. –1 1 − 5 D. –8 2 − 5 4. Find 2 − 5 + 3 − 8 . Write in simplest form. F. 1 − 8 G. 3 − 20 H. 5 − 13 I. 31 − 40 5. GEOMETRY Find the area of a square with sides that measure 1 3 − 8 inches. A. 1 9 − 64 in2 B. 1 57 − 64 in2 C. 2 3 − 4 in2 D. 5 1 − 2 in2
6. A number cube is rolled twice. Find P(odd and even). F. 1 G. 1 − 2 H. 1 − 4 I. 1 − 8 7. What is the multiplicative inverse of 11 − 7 ? A. 7 − 11 B. – 7 − 11 C. – 11 − 7 D. –77 8. BAKING Jose needs 1 2 − 3 cups of flour for a cake recipe. How many cakes can he make for the school carnival if he has 15 cups of flour? F. 25 G. 16 2 − 3 H. 13 1 − 3 I. 9 9. Write 98% as a decimal.
A Triangular Line DesignConnect each pair of equivalent rational numbers with a straight line segment. Although you will draw only straight lines, the finished design will appear curved!
722 13
16 711
120
118
112
116
130
513
13 3
7 38
19
18
341
4
59
78
16
23
12
15
17
0.03
0.428571
0.318
0.333
0.666
0.166
0.875
0.5
0.8125
0.11
0.384615
0.375
0.142857
0.6363
0.083
0.05
0.2
0.250.05
0.750.125
0.06250.5
Enrich
Chapter 1 16
Course 3
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Use this recording sheet with pages 86-87 of the Student Edition.Fill in the correct answer. For gridded-response questions, write your answers in the boxes on the answer grid and fill in the bubbles to match your answers.
1. A B C D
2.
3. F G H I
4. A B C D
5. F G H I
6. A B C D
7.
8. F G H I
9.
10. A B C D
11.
12. F G H I
Extended ResponseRecord your answers for Exercise 13 on the back of this paper.
Materiales: papel, lápiz, regla, cuatro artículos del hogar como un clip, una cuchara, etc.
• Dividan el papel en cuatro trozos.
• Escriban el nombre de cada uno de los artículos del hogar en cada papel.
• Midan las dimensiones de cada artículo al 1 − 8 de pulgada más cercano y escriban la longitud en el papel correspondiente.
• Ordenen los artículos de menor a mayor según las longitudes medidas.
• Coloquen los trozos de papel correspondientes en el mismo orden y comparen las fracciones.
Actividad concreta
• Elijan tres páginas de un periódico.
• Para cada página, escriban un porcentaje que represente la cantidad de espacio empleado en promociones y un porcentaje de la cantidad de espacio empleado en artículos.
• Escriban cada porcentaje como fracción y luego sumen el par de fracciones de cada página.
Are You ReadyAre You Readyfor Chapter 1?for Chapter 1?
Practice
Get ConnectedGet Connected For more examples, go to glencoe.com.
Add, subtract, multiply, or divide.
1. –22 + 35
2. 44 – (–12)
3. –11(–12)
4. –33 ÷ (–11)
5. FOOTBALL Milo is a running back on his middle school football team. On his first running play he netted –8 yards, and on his second running play he netted –6 yards. What is the average of his two carries?
6. TEMPERATURE The high temperature for the day was 77° while the low was 52°. What is the difference between the high and low temperature for the day?
Solve each proportion.
7. - 6 − 7 = m −
21
8. 10 − n = 2 − 3
9. 18 − 24
= p −
4
10. 12 − p = 1 − 3
11. 12 − 4 = 75 − n
12. 64 − 48
= 36 − y
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
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NAME ________________________________________ DATE _____________ PERIOD _____
Are You ReadyAre You Readyfor Chapter 1?for Chapter 1?
Apply 1. AUTOMOBILES Killian’s tire is leaking
air. The change in the amount of air is –2 cubic inches per minute. At this rate, how many minutes will it be before the total change is –16 cubic inches?
2. STOCKS Helen owns stock in the Do Well company. Over the past 4 days, the value of her stock fell $5 each day. What is the total change in the price of her stock during these four days?
3. TENNIS Louis played tennis while in middle school. The table shows the number of wins and losses he had in each of the three years. How many matches did Louis win during his middle school career?
Grade Wins Losses6th 12 37th 9 88th 11 2
4. DEBT Kenneth wanted to buy a skateboard but found that he did not have enough money. To make his purchase, he borrowed $5 from Dontrell, $2 from Serena, and $27 from Linda. If he did not owe any money to start with, what is the total change in his debt?
5. TEMPERATURE During the course of a 6-hour period the temperature dropped 18°. What was the average change in temperature per hour?
6. SCIENCE A microscope slide shows 35 red blood cells out of 60 blood cells. Write and solve a proportion to find how many red blood cells would be expected in a sample of the same blood that has 840 blood cells.
5. BALLOON RIDES Dakota is taking a balloon ride. The balloon first ascends to 850 feet and then descends 75 feet. What is the current height of the balloon?
6. SHOPPING Toni had $45 dollars to spend. She bought a book for $13 and then found a ten dollar bill on her way home. How much money did she have when she got home?
Solve each proportion.
7. 3 − 7 = 9 − w
8. p −
8 = 5 −
4
9. 25 − 60
= t − 12
10. 35 − 50
= y −
10
11. 7 − 9 = 70 − m
12. 64 − n = 16 − 4
13. 45 − 60
= n − 12
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
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NAME ________________________________________ DATE _____________ PERIOD _____
Add, subtract, multiply, or divide. Write in simplest form.
1. - 3 − 4 · 8 −
9
2. - 2 − 5 + 4 −
5
3. 3 1 − 3 ÷ 5 −
6
4. 1 − 6 - (- 1 −
3 )
5. Write 13.1% as a decimal.
6. 17 is what percent of 68?
7. BUSINESS A paint store buys a gallon of paint at a wholesale price and then prices it to sell at a 50% markup. If a gallon of paint costs the store $16, what is the selling price of the gallon of paint?
8. SPORTS A sporting goods store is advertising a 30% off sale on soccer balls. Panna wants to buy a soccer ball that originally costs $44.50. Find the sale price of the soccer ball.
9. ANIMALS Dorie’s kitten weighed 14 ounces when she brought it home. One year later that same kitten weighed 30 ounces. Find the percent of change in the kitten’s weight. Round to the nearest tenth.
10. COAT Lorrene bought a coat for $67.20 that was on sale for 20% off. What was the original price of the coat?
11. PET FOOD The pet store’s food stock went from 1,500 cans of food to 1,200 cans in one week. What was the percent of decrease?
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NAME ________________________________________ DATE _____________ PERIOD _____
This is an alphabetical list of new vocabulary terms you will learn in Chapter 1. Fold the page vertically and use it as a bookmark. As you study the chapter, write each term’s definition or description in as few words as possible.
Vocabulary Word Definition/Description/Example
compound interest
discount
like fractions
markup
multiplicative inverses
percent equation
percent of change
percent proportion
rational number
simple interest
Fold over
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NAME ________________________________________ DATE _____________ PERIOD _____
1. ASTRONOMY The pull of gravity on the surface of Mars is 0.38 that of Earth. Write 0.38 as a fraction in simplest form.
2. ENERGY Nuclear power provided 78% of the energy used in France in 2005. Write 0.78 as a fraction in simplest form.
3. WEIGHTS AND MEASURES One pint is
about 5 − 9 liter. Write 5 −
9 liter as a decimal.
4. WEIGHTS AND MEASURES One inch is 25.4 millimeters. Write 25.4 millimeters as a mixed number in simplest form.
5. EDUCATION A local middle school has 47 computers and 174 students. What is the number of students per computer at the school? Write your answer as both a mixed number in simplest form and a decimal rounded to the nearest tenth.
6. BASEBALL In the 2008 season, the Florida Marlins won 84 out of 162 games. What was the ratio of wins to total games? Write your answer as both a fraction in simplest form and a decimal rounded to the nearest thousandth.
7. COLLEGES AND UNIVERSITIES Recently, a small college had an enrollment of 1,342 students and a total of 215 faculty. What was the student-faculty ratio for this college? Write your answer as both a mixed number in simplest form and a decimal rounded to the nearest hundredth.
8. BASKETBALL In the 2007–2008 season, Dwayne Wade made 439 field goals out of 937 attempts. What was Dwayne Wade’s ratio of successful field goals to attempts? Write your answer as both a fraction in simplest form and a decimal rounded to the nearest thousandth.
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NAME ________________________________________ DATE _____________ PERIOD _____
A Triangular Line DesignConnect each pair of equivalent rational numbers with a straight line segment. Although you will draw only straight lines, the finished design will appear curved!
722
1316
711
120
118
112
116
130
513
13
37
38
19
18
34
14
59
78
16
23
12
15
17
0.03
0.428571
0.318
0.333
0.666
0.166
0.875
0.5
0.8125
0.11
0.384615
0.375
0.142857
0.6363
0.083
0.05
0.2
0.25 0.05 0.750.1250.0625 0.5
Enrich
Chapter 1 16 Course 3
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NAME ________________________________________ DATE _____________ PERIOD _____
Fractions that have the same denominator are called like fractions. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator.
Example 1 Find 1 − 5 + (- 4 −
5 ) . Write in simplest form.
1 − 5 + (- 4 −
5 ) = 1 + (-4) −
5 Add the numerators. The denominators are the same.
= -3 − 5 or - 3 −
5 Simplify.
Fractions with unlike denominators are called unlike fractions. To add or subtract unlike fractions, rename the fractions using prime fractors to ! nd the least common denominator. Then add or subtract as with like fractions.
Magic SquaresA magic square is an arrangement of numbers such that the rows, columns, and diagonals all have the same sum. In this magic square, the magic sum is 15.
Find the magic sum for each square in Exercises 1–5. Then fill in the empty cells.
1. 2. 3.
22 3
21 3
23
98
34
54
14
12
2
-2
1
12
4. 5.
14
23
1
1
1
1
112
712
13
112
16
13
381
34
14
116
916
18
1316
12
6. Arrange these numbers to make a magic square.
1 − 2 1 −
3 2 −
3 1 −
4 3 −
4
1 − 6 1 −
12 5 −
12 7 −
12
8
5
27
613
49Column Row
Diagonal
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NAME ________________________________________ DATE _____________ PERIOD _____
AReteachProblem-Solving Investigation: Look for a Pattern
You may need to look for a pattern to solve a problem.
Understand Determine what information is given in the problem and what you need to ! nd.
Plan Select a strategy including a possible estimate.
Solve Solve the problem by carrying out your plan.
Check Examine your answer to see if it seems reasonable.
Example 1
The Ferris wheel located at Navy Pier in Chicago stands 150 feet tall and can
carry 240 people. It takes 7 1 − 2 minutes to make one revolution, 15 minutes to make
two revolutions, and 22 1 − 2 minutes to make three revolutions. If this pattern
continues, how many minutes will it take to make six revolutions?
Understand You know the time it takes to make the first three revolutions.
Plan Look for a pattern in the number of minutes. Then continue the pattern to find how many minutes it takes to make six revolutions.
Solve Complete the information for the first, second, and third revolutions. Continue the pattern to solve the problem.
First Revolution
SecondRevolution
ThirdRevolution
FourthRevolution
FifthRevolution
SixthRevolution
7 1 − 2 min 15 min 22 1 −
2 min 30 min 37 1 −
2 min 45 min
It takes 45 minutes to make six revolutions.
Check Check your pattern to make sure the answer is correct.
Exercises
Look for a pattern. Then use the pattern to solve each problem.
1. COOKING A muffin recipe calls for 2 1 − 2 cups of flour for every 2 −
3 cup of sugar. How many
cups of flour should be used when 4 cups of sugar are used?
2. FUNDRAISER There were 256 people at a fundraiser. When the event was over, half of the people who remained left every 5 minutes. How long after the event ended did the last person leave?
ASkills PracticeProblem-Solving Investigation: Look for a Pattern
Look for a pattern in Exercises 1–6.
1. YARN A knitting shop is having a yarn sale. One skein sells for $1.00, 2 skeins sell for $1.50, and 3 skeins sell for $2.00. If this pattern continues, how many skeins of yarn can you buy for $5.00?
2. BIOLOGY Biologists place sensors in 8 concentric circles to track the movement of grizzly bears throughout Yellowstone National Park. Four sensors are placed in the inner circle. Eight sensors are placed in the next circle. Sixteen sensors are placed in the third circle, and so on. If the pattern continues, how many sensors are needed in all?
3. HONOR STUDENTS A local high school displays pictures of the honor students from each school year on the office wall. The top row has 9 pictures displayed. The next 3 rows have 7, 10, and 8 pictures displayed. The pattern continues to the bottom row, which has 14 pictures in it. How many rows of pictures are there on the office wall?
4. EARNING MONEY Penny is holding a car wash. The table
shows what part of a car she can wash in 1 − 4 hour. How many
cars can she wash in 3 hours?
5. GEOMETRY Find the perimeters of the next two figures in the pattern. The length of each side of each small square is 3 feet.
6. HOT TUBS A hot tub holds 520 gallons of water when it is full. A hose fills
the tub at a rate of 6 1 − 2 gallons every five minutes. How long will it take to
1. GEOMETRY Draw the next two angles in the pattern.
10°20°
30° 40°
a.
c.
b.
d.
2. ANALYZE TABLES A falling object continues to fall faster until it hits the ground. How far will an object fall during the fifth second?
Time Period Distance Fallen
1st Second 16 feet
2nd Second 48 feet
3rd Second 80 feet
4th Second 112 feet
Use any strategy to solve Exercises3–6. Some strategies are shown below.
PROBLEM-SOLVING STRATEGIES • Look for a pattern • Work backward • Guess, check, and revise • Choose an operation
3. YARD WORK Denzel can mow 1 − 8 of his
yard every 7 minutes. If he has 40 minutes to mow 3 −
4 of the yard, will he
have enough time?
4. READING Ling read 175 pages by 1:00 P.M., 210 pages by 2:00 P.M., and 245 pages by 3:00 P.M. If she continues reading at this rate, how many pages will Ling have read by 4:00 P.M.?
5. MOVIES The land area of Alaska is about 570 thousand square miles. The land area of Washington, D.C., is
about 3 − 50
square mile. How many times
larger is Alaska than Washington, D.C.?
6. U.S. PRESIDENTS President Clinton served 5 two-year terms as governor of Arkansas and 2 four-year terms as President of the United States. How many total years did he serve in these two government offices?
Homework PracticeProblem-Solving Investigation: Look for a Pattern
1-2
Get ConnectedGet Connected For more examples, go to glencoe.com.
AProblem-Solving PracticeProblem Solving Investigation: Look for a Pattern
Look for a pattern. Then use the pattern to solve each problem.
ENTERTAINMENT For Exercises 1 and 2, use the information at the right, which shows the ticket prices at a skating rink.
Number of People in
Group
Total Cost per Group
1 $1.002 $2.003 $2.904 $3.705 $4.40
1. Describe the pattern used to calculate the cost for a group after 2 people.
2. If the pattern continues, what would the cost be for a group of 8 skaters?
3. RUNNING Evie wants to train to run a marathon. For the first four weeks, she ran 3, 6, 9, and 12 miles. If the pattern continues, how many miles will she run in the 6th week of training?
4. AGRICULTURE In a vegetable garden, the second row is 8 inches from the first row, the third row is 10 inches from the second row, the fourth row is 14 inches from the third row, and the fifth row is 20 inches from the fourth row. If the pattern continues, how far will the eighth row be from the seventh row?
5. GEOMETRY Draw the next two figures in the pattern.
6. BIOLOGY A newborn seal pup weighs 4 pounds at the end of the first week, 8 pounds at the end of the second week, 16 pounds at the end of the third week, and 32 pounds at the end of the fourth week. If this growth pattern continues, how many weeks old will the seal pup be before it weighs over 100 pounds?
32. TEST SCORES On a science test, Ali answered 38 of the 40 questions
correctly, Jamar answered 9 − 10
of the questions correctly, and Paco
answered 92.5% of the questions correctly. Write Ali’s and Jamar’s scores as percents and list the students in order from the least to the highest score.
1-2B
Get ConnectedGet Connected For more examples, go to glencoe.com.
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NAME ________________________________________ DATE _____________ PERIOD _____
1. BASKETBALL In a recent season, Deanne Nolan of the WNBA team the Detroit Shock made 39% of her 3-point shots. Write this percent as a decimal.
2. POPULATION From 2000 to 2006, the population of New York City increased by 3%. Write this percent as a decimal.
3. BASEBALL Recently, the Chicago White Sox had a team batting average of 0.263. Write this decimal as a percent.
4. POPULATION In 2006, 4.4% of people in the U.S were of Asian descent. Write this percent as a decimal.
5. INTERNET Internet access in the U.S. has increased dramatically in recent years. If 110 out of every 200 households has Internet access, what percent of households has Internet access?
6. VOTING The data below show the rate of voter turnout in three U.S presidential elections. Order the rates from least to greatest as percents.
Year Rate of Turnout
1996 49.1%
2000 0.513
2004 553 − 1,000
7. LAND Florida makes up approximately 0.015 of the land mass of the United States. Write this decimal as a percent.
8. READING Over the summer, Chang
read 7 − 8 of the books that Alaqua read
during the previous school year. Write this fraction as a percent.
Block Party 1. This model is made up of 27 cubes and has a length of 3 cubes,
a width of 3 cubes, and a height of 3 cubes. The entire model will be painted yellow, then cut apart into individual cubes.
What percent of the cubes will be painted yellow on:
0 sides? 1 side? 2 sides?
3 sides? 4 sides? 5 sides?
6 sides?
2. This model is made up of 64 cubes and has a length of 4 cubes, a width of 4 cubes, and a height of 4 cubes. The entire model will be painted orange, then cut apart into individual cubes.
What percent of the cubes will be painted orange on:
0 sides? 1 side? 2 sides?
3 sides? 4 sides? 5 sides?
6 sides?
3. This model is made up of 125 cubes and has a length of 5 cubes, a width of 5 cubes, and a height of 5 cubes. The entire model will be painted purple, then cut apart into individual cubes.
What percent of the cubes will be painted purple on:
0 sides? 1 side? 2 sides?
3 sides? 4 sides? 5 sides?
6 sides?
1-2B
Enrich
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NAME ________________________________________ DATE _____________ PERIOD _____
.ReteachAlgebra: The Percent Proportion and EquationC
1-2
In a percent proportion, one ratio compares a part to the whole. The other ratio is the equivalent percent written as a fraction with a denominator of 100.
part −
whole = percent
A percent equation is an equivalent form of a percent proportion in which the percent is written as a decimal.
part = percent • whole
12 is what percent of 60?
METHOD 1 Use the percent proportion.part
whole 12 − 60
= p −
100 } percent Write the percent proportion.
12 • 100 = 60 • p Find the cross products.
1,200 = 60p Multiply.
1200 − 60
= 60p
− 60
Divide each side by 60.
20 = p Simplify.
So, 12 is 20% of 60.
METHOD 2 Use the percent equation.
part = percent • whole
12 = p • 60 Write the percent equation.
12 − 60
= 60p
− 60
Divide each side by 60.
0.2 = p Simplify.
Since 0.2 = 20%, 12 is 20% of 60. Note that the answer, a decimal, must be converted to a percent.
Exercises
Solve each problem using a percent proportion. 1. 3 is what percent of 10? 2. What number is 15% of 40?
3. 24 is 75% of what number? 4. 45 is what percent of 60?
Solve each problem using a percent equation. 5. Find 30% of 70. 6. 52 is what percent 65?
.Homework PracticeAlgebra: The Percent Proportion and Equation
Solve each problem using a percent proportion.
1. 6 is what percent of 24? 2. 125 is what percent of 375?
3. What is 20% of 80? 4. What is 14% of 440?
5. 28 is 35% of what number? 6. 63 is 63% of what number?
7. GAMES Before discarding, Carolee has 4 green cards, 3 red cards, 3 orange cards, and 1 gold card. If she discards the gold card, what percent of her remaining cards are red?
Solve each problem using a percent equation.
8. 4% of what number is 7? 9. 85 is 10% of what number?
10. Find 3 1 − 2 % of 250. 11. What is 7 1 −
4 % of 56?
12. 560 is what percent of 420? 13. 2 1 − 5 % of what number is 44?
14. MUSIC In a recent survey, 47% of teens said they use the Internet to download music. If there were 300 teens surveyed, how many use the Internet to download music?
1-2C
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In Exercises 1–4, use a percent proportion. In Exercises 5-8, use a percent equation.
Problem-Solving PracticeAlgebra: The Percent Proportion and Equation
1. DINING OUT Trevor and Michelle’s restaurant bill comes to $35.50. They are planning to tip the waiter 20%. How much money should they leave for a tip?
2. CHESS The local chess club has 60 members. Twenty-four of the members are younger than twenty. What percent of the members of the chess club are younger than twenty?
3. TENNIS In the city of Bridgeport, 75% of the parks have tennis courts. If 18 parks have tennis courts, how many parks does Bridgeport have altogether?
4. COLLEGE There are 175 students in twelfth grade at Silverado High School. A survey shows that 64% of them are planning to attend college. How many Silverado twelfth-grade students are planning to attend college?
5 SPORTS In the 2007-2008 season, the Tampa Bay Buccaneers won 9 out of 16 games in the regular season. What percent of their games did they win? Round to the nearest tenth if necessary.
6. GOLF On a recent round of golf, Shana made par on 15 out of 18 holes. On what percent of holes did Shana make par? Round to the nearest tenth if necessary.
7. DRIVING TEST On the written portion of her driving test, Sara answered 84% of the questions correctly. If Sara answered 42 questions correctly, how many questions were on the driving test?
8. EDUCATION In a certain small town, 65% of the adults are college graduates. How many of the 240 adults living in the town are college graduates?
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The Cost of UsingThe percent proportion can be used to describe the percent by which something depreciates, or loses its value during the course of time.
In 2006, the average purchase price of a new compact automobile was $17,000. One year later, the compact automobile that was purchased new in 2006 typically was worth $11,500. By what percent did the automobile depreciate during the first year of ownership?
First find the amount of decrease.
$17,000 - $11,500 = $5,500
Then write and solve the percent proportion.
$5,500 is what percent of $17,000?
5,500 −
17,000 = r −
100
550,000 = 17,000r
32.4 ≈ r
The automobile depreciated about 32.4%, or about 1 − 3 of its value, during the first year of
ownership.
Exercises
Advertisements such as these regularly appear in the classified pages of newspapers. Find the percent of depreciation in each advertisement. Round to the nearest tenth if necessary.
1. For sale: Venus 2 dr, 5 speed, air, sport wheels, mint. Bought new 8 months ago for $9,600, yours for $7,200. Must sell—baby on way.
2. For sale: Washer/dryer combo. Antique white, electric, like new—18 mos. old. Paid $950, asking $500.
3. For sale: Mars 4 dr, auto, air, ABS, the works. 1 year old—12,400 mi. Purchase price—$16,000. Your price—$12,800 firm.
4. For sale: Dishwasher, 2 racks, full factory warranty. Never used—won in contest. List: $840. I will deliver for $588 cash.
5. For sale: Mountain bike. 20-inch frame. 26 × 1.60 new tires. Used but not abused. Bought last summer for $320. $150 or best offer.
6. For sale: Personal Computer. Intex processor. 8.0 GB hard drive. 56X CD-ROM drive. 17-inch monitor. Color inkjet printer with lots of software. $2,200 new—yours for $895.
11. TRAVEL Theodore is staying at the Comfy Hotel. The hotel charges $145 a night for a room.
a. He has a coupon to receive an additional 15% off. What is the cost of the room before tax?
b. After he receives the discount, how much will his total bill be if there is an 8% tax?
12. AUTOMOBILES Tayshia is buying a new car. The sales person tells her she will get a goodwill discount of 5% but then will have to pay an 8.75% sales tax.
a. If the car Tayshia wants to buy costs $35,000 without the discount, what will the cost be after the discount but before the tax?
b. After she receives the discount, how much will her total bill be after taxes?
13. SHOPPING Rosa knows that her mother buys bolts of fabric for her sewing shop wholesale. If a bolt of fabric costs $150 dollars and the markup is 20%, what is the selling price of a bolt of fabric?
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1. SPORTS Hector wants to buy a new football. He initially thought it would cost $36, but when he went to the sporting goods store it was discounted 20%. What is the sale price of the football?
2. RESTAURANT Camilla had lunch with her friend Cleavon. Before tax, the bill is $15.45. How much will the bill be if there is a 7.4% sales tax?
3. PHARMACY At Health First Pharmacy, the wholesale price of an asthma medicine is $126. What is the selling price, if the percentage of markup is 42%?
4. SHOPPING Upon entering EZ-Mart, Kyle sees the following sign. What should he pay for a sweater originally selling for $32.50?
Everything in the store 10% off!
5. CARNIVAL A ride ticket usually costs $1.50, but if you buy 10 tickets, you get a 5% discount. Find the sale price of 10 tickets which would normally cost $15.
6. SURFBOARD A surf board that costs $112 is on sale for 12% off, and the sales tax is 5.5%. What is the total cost of the surf board?
7. TELEVISION At Total Viewing, the wholesale price of a 52-inch television is $1,950. What does it cost to buy the television if the store’s markup is 15% and the sales tax is 7.5%?
8. BAKERY It costs Mr. Goody $0.85 to make a loaf of bread. What does it cost to buy the loaf if Mr. Goody’s markup is 22% and the sales tax is 8%?
Problem-Solving PracticeDiscount, Markup, and Sales Tax
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Party Time!It is football season and you decide to have a party. The table contains a list of items you want to buy for your party. The table also indicates the quantity of each item needed and the unit cost for the item. If there is a * next to the unit price, the item will be discounted 5%. If there is a ** next to the unit price, the item will be discounted 10%.
Use the table to solve each problem.Round all answers to the nearest cent. 1. What is your cost for all of the food items before
tax?
2. What is your cost for all of the non-food items before tax?
3. What is your total cost before tax?
4. Suppose you live on the border between Cook County and Lake County. If the sales tax is 7% for non-food items in Lake County and 10% for non-food items in Cook County, how much will you save if you travel across the border from Cook County to Lake County to buy the party items?
5. Research the sales tax on food in your area. Is the sales tax the same on all items purchased in a supermarket, or does the tax vary depending on the item? Is the sales tax the same throughout your county or state?
Suppose you are the owner of a shop that sells casual clothes. Your store often has sales where every item is discounted by the same percent. Use your calculator to find the sales price of each item so that you can have new signs printed that show the sale prices.
The Moonlight Madness Sale will offer customers 25% off. Find the sale prices.
Step 1 Store the amount of the discount in the variable x.
25
Step 2 Enter the current price of each item in a list.
Item Regular Price
1 Cotton Sweater 29.99
2 Denim Jacket 36.29
3 Team Sweatshirt 24.89
4 Sport Socks 3-Pack 6.59
5 T-Shirt 7.99
[MEM] 6
In L1 enter each regular price.
Press after each price.
Step 3 Enter a formula in L2 to calculate the sale price.sale price = regular price - (discount %)(regular price)
[TEXT] " Done
[STAT] 1 x
[STAT] 1 [TEXT] " Done
The sale price for each item is displayed in L2.
Use the list of data to answer the questions below.
1. List the sale prices for the Moonlight Madness Sale.
2. Explain why the formula for L2 correctly calculates the sale price.
3. Use the same lists, L1 and L2, to find sale prices when the discount rate is 35%. (Hint: Store a new value in x.)
4. Add a new item: a suede jacket priced at $99.59. What is its sale price when the discount is 35%?
5. Create a new list, L3, to find the amount of the discount for each item at 35% off.
Find the simple interest for $600 invested at 8.5% for 6 months.
Notice the time is given in months. Six months is 6 − 12
or 1 − 2 year.
I = prt Write the simple interest formula.
I = 600 · 0.085 · 1 − 2 Replace p with 600, r with 0.085, and t with 1 −
2 .
I = 25.50 Simplify.
The simple interest is $25.50.
Find the total amount in an account where $136 is invested at 7.5% compounded annually for 2 years.
First Year
I = prt Write the simple interest formula.
I = 136 · 0.075 · 1 Replace p with 136, r with 0.075, and t with 1.
I = 10.20 Simplify.
136 + 10.20 = 146.20 Add the amount invested and the interest.
Second Year
I = prt Write the simple interest formula.
I = 146.20 · 0.075 · 1 Replace p with 146.20, r with 0.075, and t with 1.
I = 10.97 Simplify.
The amount in the account after two years is $146.20 + $10.97 or $157.17.
Exercises
Find the simple interest to the nearest cent.
1. $300 at 5% for 2 years 2. $650 at 8% for 3 years
3. $575 at 4.5% for 4 years 4. $735 at 7% for 2 1 − 2 years
Find the total amount in each account to the nearest cent, if the interest is compounded annually.
5. $250 at 5% for 3 years 6. $425 at 6% for 2 years
7. $945 at 7.25% for 4 years 8. $2,680 at 9.1% for 2 years
To ! nd simple interest, use the formula I = prt. Interest I is the amount of money paid or earned. Principal p is the amount of money invested or borrowed. Rate r is the annual interest rate expressed as a decimal. Time t is the time in years.
1. $350 at 5% for 4 years 2. $750 at 6.5% for 3 years
3. $925 at 4.75% for 3 months 4. $2,050 at 7.65% for 36 months
Find the total amount in each account to the nearest cent, assuming simple interest.
5. $1,500 at 6% for 5 years 6. $4,010 at 5.2% for 4 years
7. $16,000 at 3 1 − 4 % for 42 months 8. $3,200 at 6 2 −
3 % for 5 1 −
2 years
Find the total amount in each account to the nearest cent if the interest is compounded annually.
9. $320 at 2.5% for 4 years 10. $1,100 at 5% for 4 years
11. $70 at 6 1 − 4 % for 2 years 12. $470 at 6.6% for 24 months
13. HOUSING Mrs. Landry bought a house for $35,000 in 1975. She sold the house for $161,000 in 2005. Find the simple interest rate for the value of the house.
14. CARS Brent’s older brother took out a 4-year loan for $16,000 to buy a car. If the simple interest rate was 8%, how much total will he pay for the car including interest?
15. SAVINGS What is the total amount of money in an account where $300 is invested at an interest rate of 4.5% compounded annually for 5 years?
16. CREDIT Reed borrowed $3,200 from the credit union at an interest rate of 7%. The interest is compounded annually. Suppose he made no payments, how much does he owe at the end of the 3 years?
Homework PracticeFinancial Literacy: InterestB
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1. SAVINGS ACCOUNT How much interest will be earned in 3 years from $730 placed in a savings account at 6.5% simple interest?
2. INVESTMENTS Salvador’s investment of $2,200 in the stock market earned $528 in two years. Find the simple interest rate for this investment.
3. SAVINGS ACCOUNT Lonnie places $950 in a savings account that earns 5.75% interest compounded annually. Find the total amount in the account after five years.
4. INHERITANCE William’s inheritance from his great uncle came to $225,000 after taxes. If William invests this money in a savings account at 7.3% simple interest, how much will he earn from the account each year?
5. RETIREMENT Han has $410,000 in a retirement account that earns $15,785 each year. Find the simple interest rate for this investment.
6. COLLEGE FUND When Jin was born, her parents put $8,000 into a college fund account that earned 9% interest compounded annually. Find the total amount in the account after 2 years.
7. MONEY Leora won $800,000 in a state lottery. After paying $320,000 in taxes, she invested the remaining money in a savings account at 4.25% interest compounded annually. What is the total amount of money in her account after 4 years?
8. SAVINGS Mona has an account with a balance of $738. She originally opened the account with a $500 deposit and a simple interest rate of 5.6%. If there were no deposits or withdrawals, how long ago was the account opened?
Does Compounding Really Make a Difference?Does it really make a difference whether an investment earns simple interest or compound interest? Suppose you invest $10,000 in a savings account paying 7% interest for 9 years. Using the ideas you have already learned about interest, you can answer the question.
There are formulas for both simple interest and compound interest that will predict the balance in your savings account. For simple interest, the formula is A = p + prt. For compound interest, the formula is A = p(1 + r)t. A is the balance in the account at the end of a given time period, p is the amount of money invested, r is the interest rate expressed as a decimal, and t is the length of time written in years. In the example, p = $10,000, r = 7%, and t = 9 years. Use a calculator with a power key to find the value of A.
Simple Interest Compound Interest
A = p + prt A = p(1 + r)t
A = 10,000 + 10,000(0.07)(9) A = 10,000(1 + 0.07) 9
A = 10,000 + 6,300 A = 10,000(1.07) 9
A = 16,300 A = 18,384.59
Since $18,384.59 − $16,300 = $2,084.59, your investment will earn $2,084.59 dollars more if it earns compound interest.
Find the balance in your account for the given values of p, r, and t using both the simple interest formula and the compound interest formula. Round to the nearest dollar. Then tell how much more interest you will earn on your investment if it earns compound interest.
1. p = $3,000 2. p = $5,000r = 5% r = 6.5%t = 6 years t = 4.5 years
3. p = $400 4. p = $1,600r = 8% r = 3.5%t = 10 years t = 8 years
Enrich
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You can use the percent key, , to solve equations involving simple interest.
Find the simple interest to the nearest cent from $265 invested at 5.15% for 2 years.
Use the formula I = prt: interest = principal × rate × time.
I = $265 × 5.15% × 2
Keys: 265 5.15 2
Display: 265∗5.15%∗2 27.295
The interest is $27.30.
Exercises
Find the simple interest to the nearest cent.
1. $1,000 at 6.75% for 5 years 2. $535 at 8.2% for 6 months
3. $257 at 15% for 2.5 years 4. $48.67 at 12.25% for 30 months
5. Terry put $500 in a savings account that earned 5.125% simple interest. She has not made any deposits or withdrawals for 7 years. How much interest has she earned?
6. How much money will be in Terry’s account at the end of 15 years if she does not make any deposits or withdrawals?
7. Suppose you deposit $200 in an account that earns 10% simple interest. How many months will it take to earn $50 in interest?
8. How much money would you have to deposit in an account that earns 8.375% simple interest to earn $1,000 in interest in 18 months?
Two months ago, the bicycle shop sold 50 bicycles. Last month, 55 bicycles were sold. Find the percent of change. State whether the percent of change is an increase or a decrease.
Step 1 Subtract to find the amount of change.
55 - 50 = 5 final amount - original amount
Step 2 Write a ratio that compares the amount of change to the original number of bicycles. Express the ratio as a percent.
percent of change = amount of change −−
original amount Definition of percent of change
= 5 − 50
Substitution
= 0.1 Divide. Use a calculator.
Step 3 The decimal 0.1 written as a percent is 10%. Since the percent of change is positive, it is a percent of increase.
Exercises
Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease.
7. POLLS In a presidential poll taken last week, 182 people said they would vote for the democratic candidate. This week, when the poll was taken again, 150 people said they would vote for the democratic candidate. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
8. TRAFFIC The Florida Department of Transportation wanted to know how many vehicles passed through a particular intersection weekly. During the first week, 470 vehicles passed through the intersection. During the second week, 600 vehicles passed through the intersection. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
9. COMMISSION Nino works at a furniture store. Last week he earned $130 in commission. This week he earned $90 in commission. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
D
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1. CLUBS Last year the chess club had 20 members. This year the club has 15 members. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
2. READING During Todd’s junior year in high school, he read 15 books. In his senior year, he read 18 books. Find the percent of change. Round to the nearest tenth, if necessary. State whether the change is an increase or decrease.
3. INCOME La’Rae earned $612 last week and $820 this week. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
4. SOFTBALL Eileen plays softball. Last year she had 34 extra base hits. This year she had 21. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
5. TRAVEL Micha is on vacation. Yesterday he traveled 512 miles. Today he traveled 212 miles. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
6. GROWTH Last year Becca was 48 inches tall. This year she is 52 inches tall. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
7. PRICING The table shows the change in price of three items sold at Eisenbach’s Grocery Store. Find the percent of change in the price of potatoes. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.
Item Old Price New PriceBeans $2.75 per lb $2.20 per lbPotatoes $4.00 per lb $3.30 per lbTomatoes $5.15 per lb $5.00 per lb
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Florida’s Population GrowthThe table to the right shows the estimated population of Florida at the beginning of the indicated decades.
Year Population(millions)
Increase in
Population(millions)
Percent of Change inPopulation
1950 2.771 X X1960 4.9521970 6.7911980 9.7471990 12.9382000 15.982
1. Without doing any calculations, explain how you know that the percent of change in the population from decade to decade is always increasing.
2. Complete the table. Round the percent of change in population to the nearest tenth, if necessary.
3. In which decade did the total population increase the most? In which decade did the total population increase the least?
4. What would you estimate the population of Florida to be in the year 2010 if you knew the percent of change in population was 23.3%? How close is your answer to the actual estimate? Round your answer to the nearest tenth, if necessary.
5. Research and write a few paragraphs explaining why the population of Florida has grown so quickly over the last half of the twentieth century. What do you think will happen over the first half of the twenty-first century? Explain.
1. Write about one new thing you learned in this chapter.
2. Create a problem in which an item is advertised as being on sale. Then explain how to find the percent of change in the price.
3. Write about the concepts of markup, discount, and selling price. Provide real-world examples of where these concepts are used.
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Contents Chapter 0 Start Smart Chapter 1 Rational Numbers and Percent Chapter 2 Expressions and Functions Chapter 3 Linear Functions and Systems of Equations Chapter 4 Equations and Inequalities Chapter 5 Operations on Real Numbers Chapter 6 Angles and Lines Chapter 7 Similar Triangles and the Pythagorean Theorem Chapter 8 Data Analysis Chapter 9 Units of Measure Chapter 10 Measurement: Area and Volume Chapter 11 Properties and Multi-Step Equations and InequalitiesChapter 12 Nonlinear Functions and Polynomials