Horizons Pre-Algebra, Student Book
Pre-Algebra
Student Book
Author:
Shelly Chittam, M.S.
Managing Editor:
Alan Christopherson, M.S.
Editors:
Laura Messner, B.A.
Rachelle Wiersma, M.A.
Graphic Design & Illustration:
Ron A. Hartmann, B.A.
Alpha Omega Publications, Inc. • Rock Rapids, IA
i
Horizons Pre-Algebra, Student Bookii
©MMX by Alpha Omega Publications, Inc.®
804 N. 2nd Ave. E.
Rock Rapids, IA 51246-1759
All rights reserved.
No part of this publication may be reproduced, stored in an electronic retrieval system, or transmitted in any form by any means—electronic, mechanical, photocopy, recording
or otherwise—without the prior written permission of Alpha Omega Publications, Inc. Brief quotations may be used in literary review.
Printed in the United States of America
ISBN 978-0-7403-2244-0
Often students ask:
Who uses this stuff anyway?
I will NEVER be a math major. Why do I have to learn all this?
Will I ever have to use pre-algebra in the real world?
Math is a school subject that is used daily by people in their work, homes, and play. Many people use math in their jobs, even if those jobs do not require a college degree in mathematics. There is a very good chance you will have to use math on at least a pre-algebra level when you get a job.
While you may fi nd some of the topics in pre-algebra challenging, they will help you learn more about math and God’s carefully designed world. You do not know what plans God has for your life. You may be surprised in the directions God leads you and fi nd that you use math in ways you never expected.
Throughout this book, you will read interviews with several Christians who are using pre-algebra in their daily lives. None of these people were college math majors. Some of them have successful careers without earning a college degree. Whether or not God’s plan for your life includes college, math will play a role in your future.
“For I know the plans I have for you,” declares the LORD, “plans to prosper you and not to harm you, plans to give you hope and a future.”Jeremiah 29:11 NIV
1
Introduction to...
A Math Minute with......
21Horizons Pre-Algebra, Student Book
3 x 3 x 3 x 3 x 3 =
5 x 5 x 5 =
4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 =
7 x 7 x 7 x 7 x 7 x 7 =
12 x 12 x 12 x 12 =
8 x 8 x 8 x 8 x 8 x 8 x 8 =
Exponents Lesson 10
Expand and solve the following exponential expressions.
32 =23 =52 =33 =
Exponents tell how many times a number
is multiplied by itself. The number being
multiplied is called the base. The exponent is
written as a small number on the upper right
side of the base. In the expression 34 , the
number 4 is the base and the number 3 is the
exponent. 34 4 4 4 64= × × =
The answer to an exponential expression is
always a multiple of the base.
ACTIVITIES
CLASSWORK1
2
3
Write the expanded form expressions in exponential form. Do not solve them.
Write the following exponential expressions in expanded form and solve.
22 =
23 =
32 =
24 =
42 =
33 =
52 =
34 =
22 Horizons Pre-Algebra, Student Book
x
3
-4
5
-6
7
-8
9
2 -3 4 -5 6 -7 8 -9 10
4
5
Find the prime factorization of each number. Use the method of your choice.
Complete the multiplication chart, following the rules of signed numbers.
8
46
33
50
24
40
14
21
44
18
28
42
33Horizons Pre-Algebra, Student Book
Use the divisibility tests to determine which numbers are factors of the given numbers.
Lesson 15
Use the following divisibility tests to determine whether or not a number is divisible by another number.
Divisible by 2: any number ending in a 0, 2, 4, 6, or 8.
Divisible by 3: any number whose digits have a sum that is a multiple of 3. For example, 15 is divisible by 3 because 1 + 5 = 6 and 6 is a multiple of 3.
Divisible by 4: any number ending in 00, and any number whose fi nal two digits form a number that is a multiple of 4. For example, 128 is divisible by 4 because 28 is a multiple of 4. 4 × 7 = 28.
Divisible by 5: any number ending in a 0 or 5.
Divisible by 6: any even number whose digits have a sum that is a multiple of 3.
Divisible by 9: any number whose digits have a sum that is a multiple of 9. For example, 387 is divisible by 9 because 3 + 8 + 7 = 18 and 18 is a multiple of 9.
Divisible by 10: any number ending in a 0.
ACTIVITIES
CLASSWORK1
2
3
Use the divisibility tests to identify each number as prime or composite.
Simplify the following expressions, following the proper order of operations.
Divisibility Tests
125 127 129 131
135 137 139 141
12 3 4 2 5 4− × + × + =
( ) ( )13 2 7 8 5− + ÷ − =
2 33 2 6 3+ − ÷ =
( )23 7 4 5 2 3+ ÷ ÷ + × =
( )35 10 2 7 9 2+ ÷ − ÷ + =
3 2 01 2 3 4 8 4+ − × + ÷ =
2 3 4 5 6 9 10
627
564
747
900
432
822
537
34 Horizons Pre-Algebra, Student Book
4
5
Find the prime factorization of each number. Use exponents where appropriate.
Solve. Remember to label your answers.
Ric has the following activities planned for the school year: Back-to-school party – $5, discipleship training class – $30, fl ag football – $5, Christmas party – $10, winter ski retreat – $120, basketball game – $16, dodge ball tournament – $5, spring break race around town – $30, baseball game – $11, summer retreat – $200. If he wants to give parents the option of paying for activities in twelve equal monthly payments, how much is due each month?
Ric gives the teenagers the option of doing odd jobs around the church in the evenings and on Saturdays. He gives them a $5 discount on their activity fees for every hour they work. If a teenager volunteers at the church for 2 hours each weekend for 4 weekends each month, will the discount be enough to cover the teen’s activity expenses?
30 32 33
34 35 36
38 39 40
RiRic c has the fofollllowing activivitities planneded f for the schchooool year: Back-to-school party – $5, didiscipleshipip t training clclasass – $30, fl fl a ag g football – – $ $5, Christmas party – $10, winter ski retreat – – $120, basksketetball game e – $16, dododgege ball tournament – $5, spring break race arououndnd town – $3$30,0, baseball l gagame – $1111, summer retreat – $200. If he wants to give paparerents the opoptition of payiyingng for activititieies in twelve equal monthly payments, how much isis due each h month?
Ric gives s ththe teenagerers the option of doing odd jobs around the church in the evenings and onon S Saturdaysys. . H He gives them a $5 discount on their activity fees for every hour they y workrk. If a teenenagager volunteers at the church for 2 hours each weekend for 4 weekendnds s eaeach month, , wiwill the discount be enough to cover the teen’s activity expenses?
177Horizons Pre-Algebra, Student Book
The graph above shows the number of hurricanes that hit the United States mainland each decade from 1931 to 2000. Use this graph to answer questions 1 and 2.
1. How many hurricanes hit the United States mainland from 1931 to 2000?A. 112B. 115C. 118D. 120E. 122
2. During what 2-decade period was the average (arithmetic mean) hurricane hits equal to 13 per decade?A. 1981-2000B. 1971-1990C. 1961-1980D. 1951-1970E. 1941-1960
26
24
22
20
18
16
14
12
10
8
6
4
2
0
1931-1940 1941-1950 1951-1960 1961-1970 1971-1980 1981-1990 1991-2000
Number of Hurricanes
Test Skills 8It’s College Test Prep Time!
178 Horizons Pre-Algebra, Student Book
What is your occupation? I am a professional landscaper.
Where do you work? I own my own landscaping business.
Did you attend college? If so, what was yourmajor? No.
What parts of your job require the use of math? I calculate the square footage of lots. I make precise
measurements for sod installations and landscape design. I also do my own invoicing and billing.
What is the biggest “problem” you have faced thatrequired the use of math to solve? The most diffi cult
problems involve designing and building walls out of landscape block. I begin by measuring the desired length and height of the walls. I also measure the length and height of the landscape blocks. I use these measurements to calculate the number of landscape block needed to build the wall, taking into consideration the space between the blocks. The problem becomes more challenging if the wall is curved instead of straight.
Are there any other interesting math uses you have experienced? In my job I often use estimations. When bidding for a job, I estimate the area of the lot, determine the number of visits needed to complete the job, and give an estimate of the total price. For landscape maintenance jobs I will make multiple trips over several months to mow, trim, etc. Additionally I calculate the average cost per month over a one-year period. This allows the customer to pay less during the months when they have many services done. It also provides me with an income during the winter months when little landscaping takes place.
A Math Minute with... Mike L. – Professional Landscaper
183Horizons Pre-Algebra, Student Book
Lesson 83
List everything you know to be true about the diagram below. Include the perimeter and area.
Given: DCBA▱ ; DC = 5; CB = 5
A rectangle is a parallelogram with four congruent angles. Because a rectangle is a parallelogram, the formulas for perimeter and area remain the same.
A square is a rectangle with four congruent sides. Because a square has four congruent angles and four congruent sides, the formulas for perimeter and area can be simplifi ed as follows:P = 4s, where s is the length of a sideA = s2, where s is the length of a side
List everything you know to be true about the diagram below. Find the perimeter and area.
D C
BA
Given: DCBA▱ ; DC = 7; CB = 4What you know:It is a parallelogram. It is rectangle.
AB DCP ,AD BCP , AB DC≅ , AD BC≅Each of the angles is equal to 360° ÷ 4 = 90°.
Perimeter is 2(7) + 2(4) = 14 + 8 = 22 units.The area is 7(4) = 28 square units.
ACTIVITIES
CLASSWORK1
2 List everything you know to be true about the diagrams below. Include the perimeter and area.
Rectangles and Squares
W X
YZ
W X
YZ
D C
BA
Given: WXYZ▱ ;12
4WX = ; 14
2XY =
Given: WXYZ▱ ; 12
4WX =
184 Horizons Pre-Algebra, Student Book
3
4
5
Complete the chart to show simple interest.
Complete the chart to show probability and odds.
Solve.
Mike offers his customers an annual lawn care plan. He charges $0.01 per square foot of grass per month for 12 months to cover mowing, edging, and blowing. What should Mike charge each month for the rectangular yard pictured below? What is the total cost of an annual contract for this lawn? If Mike’s contract includes 20 lawn care visits, what is the average cost per visit? (All measurements are given in feet.)
What percent of the above lot is covered with grass? Round your answer to the nearest tenth of a percent.
Scenario
Principal
$1,500
$3,900
$5,200 9.9% 8
4.5% 5
6.9% 3
Interestrate
Amount of InterestTime, in years
Multiple of 7
Multiple of 11
Odds (infavor of E)
P(E)Number ofPossible
Outcomes
DesiredEvent(E)
Odds(Against E)
Choosing an integer from
1 to 50
Choosing an integer from
1 to 100
50
40
108
100
25
20Driveway
House
325Horizons Pre-Algebra, Student Book
w
Find the area of the fi gure below.
A regular octagon has a piece removed as shown.
A regular polygon is a polygon with all sides congruent and all angles equal. There is an alternate formula for fi nding the area of a regular polygon if you know the length of the apothem – the perpendicular distance from the center of the polygon to a side.
Use the formula 2aPA = , where a is the apothem
and P is the perimeter.
To fi nd the area of irregular polygons, you may divide the polygon into known shapes and add the individual areas, fi nd the area of the entire region and subtract the missing areas, or use a combination of the two methods.
Find the area of the fi gure below.
Without the triangle removed, the fi gure would be a regular hexagon with P = 6(2) = 12.The area of the entire hexagon is
( )3 12
26 3A = =
The area of the missing triangle is
( ) ( )12
2 3 3A = =
Subtract this from the original hexagon to get the area of the given fi gure.
6 3 3 5 3 sq. unitsA = − =
ACTIVITIES
CLASSWORK1
2 Find the area of the fi gure below.
Lesson 148Area of Regular Polygons
A regular pentagon has a piece removed as shown.
2.6 cm2.4 cm
2 cm
2
2
2
2
2
2
2
2 cm1.4 cm
1.7 cm
3
326 Horizons Pre-Algebra, Student Book
3
4
Find the area of each shaded region.
A square with a regular hexagon removed An equilateral triangle with a square removed
Solve.
The air fl ow velocity in an air conditioner duct is calculated using the formula ( )2
576 i
i
q
id
vπ
= , where v
i is the air velocity in feet per minute, q
i is the air fl ow in cubic feet
per minute, and di is the diameter of the duct in inches. Calculate the air fl ow
velocity for a system blowing 1600 cubic feet per minute through a duct with a 12-inch diameter. Use 3.14 for the value of π. Round your answer to the nearest tenth.
What is the velocity in feet per second? Round your answer to the nearest tenth.
1 ft.
5 ft.
3
2 in. 8 in.
in.
