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Applied MathematicsLevel 3

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2 • Applied Mathematics

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Applied Mathematics • 3

Hi, my name is EdWIN. I will be your guidethrough Applied Mathematics Level 3. Together we willproceed through this course at your speed. Look forme to pop up throughout your lessons to give youhelpful tips, suggestions, and maybe even a pop quizquestion or two. Don’t worry, you can find the answersto pop quiz questions at the end of the course.

Now, don’t get nervous. I know how many of youfeel about mathematics, especially when the word“fraction” is mentioned. We will cover one topic at atime and I will be there to give you examples to helpyou along.

If the content of the lesson is something that youunderstand, you should be able to work through it at afaster pace. On the other hand, if the material isdifficult, read the text several times and then try towork the exercises one at a time. After you try oneproblem, look at the solution. You can learn byreviewing each step that is provided in the solutionand by concentrating on the process being illustrated.Now let’s think positive; no negative attitudes allowed!!

INTRODUCTION

Hi, I’m EdWIN


Applied Mathematics is a course designed to helpyou solve problems that arise in the workplace withappropriate mathematical techniques. It is importantthat you not only have basic mathematical skills, butthat you are able to apply them to problems that ariseon your job. The intention of this level of AppliedMathematics is for you to be able to solve simple,straightforward problems using one type ofmathematical operation and possibly one unitconversion involving either money or time. Addition,subtraction, multiplication, and division of wholenumbers and/or monetary units are reviewed in thislevel. Addition and subtraction involving both positiveand negative values are discussed. Also, this level brieflycovers conversions between fractions, decimals, andpercents.

INTRODUCTION


LESSON 1 Review of Basic Mathematical Operations

LESSON 2 Introduction to Problem Solving

LESSON 3 Addition and Subtraction of Monetary Units

LESSON 4 Multiplication of Monetary Units

LESSON 5 Division of Monetary Units

LESSON 6 Practice Session with Practical Problems

LESSON 7 Addition and Subtraction of Signed Numbers

LESSON 8 Conversions Involving Whole Numbers, Fractions,Decimals, and Percents

LESSON 9 Posttest

REFERENCES Workplace Problem Solving GlossaryTest-Taking TipsFormula Sheet

OUTLINE


REVIEW OF BASIC MATHEMATICALOPERATIONS

Let’s begin by taking a pretest on the skills thatyou should already know. You should know how toadd, subtract, multiply, and divide using your calculatoras needed. It is assumed that you understand thedifference between the notation for dollars and centsas well as how to make basic conversions of time, forexample, converting days to weeks and hours tominutes.

See if you are ready for this level by completingthe pretest. The answers will be provided on the pagesfollowing the test. You should be able to complete allof the problems. If you cannot, please review these skillsbefore you begin this course. There will be reviewexercises provided after the pretest. Good luck!

LESSON 1

I like thinking aboutdollars and cents!


EXERCISE - PRETEST

Instructions: Solve these problems involving addition, subtraction, multiplication, anddivision.

1. 4 + 5 =________ 2. 15 ÷ 3 =________

3. 8 - 3 =________ 4. 7 × 3 =________

Instructions: Fill in the blank.

5. 7 days = ________ week(s)

6. 1 hour = ________ minute(s)

7. 1 year = ________ day(s)

8. 1 minute = ________ second(s)

Instructions: Answer the following questions.

9. What is the purpose of the “Clear” key on the calculator? (Theremay be a key with “CE” on it and a key with “C” on it.)

10. How many cents are in one dollar?

LESSON 1


11. How do you represent 4 cents in dollars?

Instructions: Calculate answers for the following problems on your calculator.

12. 4.52 + 0.08 =________ 13. 7.3 × 0.2 =________

14. 1.8 ÷ 0.06 =________ 15. 0.124 - 0.008 =________

LESSON 1


ANSWERS TO PRETEST

1. 4 + 5 =________ 2. 15 ÷ 3 =________

Answer: 9 Answer: 5

3. 8 - 3 =________ 4. 7 × 3 =________

Answer: 5 Answer: 21

5. 7 days = ________ week(s)

Answer: 1

6. 1 hour = ________ minute(s)

Answer: 60

7. 1 year = ________ day(s)

Answer: 365

8. 1 minute = ________ second(s)

Answer: 60

LESSON 1


9. What is the purpose of the “clear” key on the calculator? (There isusually a key with “CE” on it and a key with “C” on it.)

Answer: The “CE” clears your last entry. The “C” clears the wholeproblem. Some calculators have “AC” which clears allof the problem and “C” clears the last entry. You shouldlearn your calculator functions.

10. How many cents are in one dollar?

Answer: 100

11. How do you represent 4 cents in dollars?

Answer: $.04

12. 4.52 + 0.08 =________ 13. 7.3 × 0.2 =________

Answer: 4.6 Answer: 1.46

14. 1.8 ÷ 0.06 =________ 15. 0.124 - 0.008 =________

Answer: 30 Answer: .116

Note: If you solved all of the problems on the pretest correctly, you should begin Lesson2. If, however, you had any wrong answers, you should spend time practicing basicoperations using a calculator and converting time and money measurements. ReviewExercises are optional.

LESSON 1


REVIEW EXERCISES

These problems are intended to provide practice in conversions of time and money.

1. 52 weeks =________ year(s)

2. 60 seconds =________ minute(s)

3. 14 days =________ week(s)

4. 1 hour =________ minute(s)

5. 1 minute =________ second(s)

6. 1 hour =________ second(s)

7. 1 day =________ hour(s)

8. 23 cents =________ of a dollar

9. 52 cents = $________

10. $4.63 =________ cents

LESSON 1


8. 23 cents =________of a dollar

Answer: 0.23

9. 52 cents = $________

Answer: $0.52

10. $4.63 = ________cents

Answer: 463

ANSWERS TO REVIEW EXERCISE

1. 52 weeks =________ year(s)

Answer: 1

2. 60 seconds =________ minute(s)

Answer: 1

3. 14 days =________ week(s)

Answer: 2

4. 1 hour =________minute(s)

Answer: 60

5. 1 minute =________second(s)

Answer: 60

6. 1 hour =________second(s)

Answer: 3,600

7. 1 day =________hour(s)

Answer: 24

LESSON 1


INTRODUCTION TO PROBLEM SOLVING

How did you do on the pretest? I hope you areready to move on and tackle problem solving. A strategyoften used in problem solving is the use of estimationas a tool to predict answers and to check results.Estimation is the practice of judging an approximatevalue, size, or cost.

By using estimation, you can determine if ananswer is reasonable compared to what you alreadyknow. If your answer to a problem indicates an airplaneflew at 5 miles an hour or a car is able to get 200 milesper gallon, you should recognize that there is an errorand rethink your process to solve the problem.

The practice of rounding numbers, which we willbe discussing in detail later in this course, is often usedin estimation. The following example shows howestimation could be used to speed up the calculationprocess and to check your answers.

A word problem indicates you are to find the totalnumber of hours Joe worked if his time cards showed48 hours for week one and 41 hours for week two. Youmight estimate the number of hours by adding therounded 50 plus 40 to approximate 90 hours. Joeactually worked 48 plus 41 which equals 89 hours. Theestimate of 90 hours was close to the actual 89 hours.If your answer was not close to your estimate, youshould check your work. It is easy to touch the wrongkey on a calculator, so always think about your answersto make sure they make sense.

LESSON 2

We will tackle problemsolving together


Estimation may also be helpful in determiningwhich operation to use. For instance, read the followingword problem:

Five crates weigh 200 lb Each crate weighs the same amount.How many lb does each crate weigh?

If you had no idea which mathematical operation to use, youcould estimate an answer by asking yourself if the answer shouldbe larger or smaller than the facts given. By adding, 5 plus 200,you get 205 lb which is more than the total 5 crates weigh; bymultiplying 5 times 200, you get 1,000 lb which is also morethan the total 5 crates weigh. Your estimates should let you knowthese are the wrong operations. The correct operation is divisionindicated by the key words how many does each.

200 divided by 5 equals 40 lb

This is a reasonable answer for each crate to weigh.

LESSON 2


Now, let’s review four steps that make problem solving much easier to do. Read andbecome familiar with these four steps before we actually begin working a problem.

Problem solving is generally divided into four parts:• define the problem• decide on a plan to solve the problem• carry out the plan• examine the outcome to see if it is reasonable

1) Define the Problem• What am I being asked to do or find?• What information have I been given?• Is there other information that I need to know or need to find?• Will a sketch help?• Can I restate the problem in my own words?• Are there any key words?

2) Decide on a Plan• What operations do I need to perform and in what order?• On which numbers do I perform these operations?

3) Carry Out the Plan

4) Examine the Outcome• Is this a reasonable outcome?• Does the outcome make sense in the original problem?• If I estimated the answer, would it be close to the result?• Does the outcome fall outside any limits in the problem? Is it too large or too

small?

LESSON 2


Before we begin working problems, I have a list of key words that indicate the operationthat will be needed. There is also a Workplace Problem Solving Glossary located at the endof the course.

LESSON 2

ADDITIONadded toadditionalall togethercombinedgain ofhow many all togetherhow many in allhow much all togetherin allincrease ofincreased bymore thanplussumtotal

SUBTRACTIONchangedecreasedecreased bydifferencedroppedhave lefthow many morehow many lesshow many lefthow many fewerhow many remainhow much morehow much lesslessless thanloss ofminusremainingsavetake away

MULTIPLICATIONdoublehow many in all (with equal numbers)how much (with equal amounts)of (with fractions and percents)producttimestotal (of equal numbers)tripletwicetwice as much

DIVISIONdivided bydivided equallydivided intoevenlyhow many in eachhow many pergoes intoquotientwhat’s half

OPERATION SYMBOLS+ ADDITION- SUBTRACTION× MULTIPLICATION÷ DIVISION

(Multiplication may be indicated in several ways

i.e., •, ×, ( ). In this course we will use ×.)

SYMBOLS$ DOLLAR¢ CENT% PERCENT# NUMBER@ ATº DEGREE

Key Words for Word Problems


Examples: Addition and subtraction

In an average year, the Smith Co. sells 123,000 washers and95,000 dryers. What is the total number of appliances sold inan average year?

Define the Problem

I have 123,000 washers and 95,000 dryers. The problem asks forthe total which is a key word for addition. (You do not have towrite a definition of the problem. Most people complete thisstep mentally.)

Decide on a Plan

I will add 123,000 to 95,000. (Again, this is often the thinkingprocess, though some people like to jot numbers down, makesketches, etc.)

Carry Out the Plan

123,000 + 95,000 = 218,000

Examine the Outcome

Ask: Does the answer make sense?

218,000 is a reasonable answer. Let’s suppose for a minute that Ihad subtracted:

123,000 - 95,000 = 28,000

28,000 would be less than either the number of washers or dryers.This would not make sense. Asking this question is one of themost important steps in solving problems and is often omitted.We all make mistakes and this gives you an opportunity to catchthem. So, slow down, take your time, and most importantly...think!

LESSON 2


Last week, Carrie worked 8 hours more than her usual 35 hours.What was the total number of hours she worked?

Define the Problem

Again, I am asked for a total. I want to know how many hoursCarrie worked.

Decide on a Plan

“Total” and “more than” indicate addition is the appropriateoperation.

Carry Out the Plan

35 hours + 8 more hours = 43 total hours

Examine the Outcome

This answer makes sense because it is more than her usual hoursworked, and it is a reasonable number of hours a person couldwork.

LESSON 2


When a corrugated box company begins production at 8:00a.m., the temperature in the plant is 58° F. At critical locations,the temperature must be brought up to at least 70° F by usingspace heaters. This represents a change of how many degrees.

Define the Problem and Decide on a Plan

I read the problem and locate “change” as a key word. Change isa key word for subtraction. The problem asks for the change intemperature from 58° F to 70° F.

Carry Out Plan

70° - 58° = 12° F

Examine the Outcome

This is a change of 12° which is a reasonable difference for thespace heaters to accomplish.

You work at a bookstore. A shipment of 82 boxes of paperbackshas just arrived. Each box holds 40 books. How many bookswere in the shipment?

Define the Problem

I read through the problem and have 82 boxes with 40 books ineach one. I see “how many” as key words. I get confused becauseI see the words “how many” under addition and multiplicationon my key word list.

LESSON 2


Decide on a Plan

I draw a sketch to help me.

I have 82 boxes. Each box has 40 books in them. I can either add40+40+40+40... +40, 82 times but since “how many” with equalnumbers (each box has 40 books) indicates multiplication, I couldmultiply 40 × 82. This seems easier.

Carry out the Plan

82 × 40 = 3,280

Examine the Outcome

I have 3,280 books in all. My answer has to be more than 40because there are 40 in each box and more than 82 if there wereat least 1 book in each box. It seems reasonable to me that thereare 3,280 books.

LESSON 2

Sometimes drawing apicture of the problemhelps me know how to

solve it.


A woman earns $135 a week. What are her total earnings for14 weeks?

Define the Problem

I want to know how much money she earns in 14 weeks.

Decide on a Plan

The key word “total” implies addition, but addition of equalamounts (the same $135 every week) indicates multiplication.You can add $135 + 135 + 135... 14 times or multiply.

Carry Out the Plan

$135 × 14 = $540

Examine the Outcome

$540 is not much money for 14 weeks! I better try that again.

$135 × 14 = $1,890

$1,890. Now, that’s better! I must have missed a key when Ientered this problem the first time. I told you it is smart to thinkabout your answers.

LESSON 2


Now that we have looked at some examples, it istime for you to try some problems. I will work theanswers out following the problems. But, don’t peek.Solving word problems takes time and effort. The onlyway you will learn is to practice. Go back and reviewthe examples if you are having difficulty. Practicing willhelp you score higher on the ACT™ WorkKeys®

Applied Mathematics assessment. So, hang in there!

LESSON 2

Don’t peek at theanswers!


EXERCISE - BASIC OPERATIONS IN PROBLEM SOLVING

Instructions: Use your calculator and the steps for problem solving to answer the followingquestions. Remember, look for key words and make sure your answers makesense.

Bill is employed by the Flower and Shrub LandscapingCompany. His employer sends him to the seed store to buygrass seed which cost $3 per pound (lb) after tax.

1. If Bill buys 12 pounds of seed, how much will it cost?

2. If Bill’s employer sends $50, how much change will he expect whenBill returns?

LESSON 2


3. The company is presently landscaping an area of 7,200 sq ft. If apound of seed will cover 900 sq ft, how many pounds of seed willbe needed to cover this area?

4. How many pounds of seed will Bill have left after a 5,400 sq ft areahas been sown?

5. How many more sq ft would this left over seed cover?

LESSON 2


6. You need 458 brake linings to fill a customer’s order. You havealready boxed 229. How many more do you need to box?

7. An employee worked 8 hours on Monday, 5 hours on Tuesday, 10hours on Wednesday, 9 hours on Thursday, and 7 hours on Friday.How many hours did he work during this week?

8. A new machine sorts 28 parts per minute. How many minutes willit take the machine to sort 952 parts?

LESSON 2


9. Gary has 4 shipping crates in which to package 240 boxes of cereal.If each crate should contain the same number of boxes, how manyboxes of cereal should he put in each?

10. You work for a suit manufacturer. You have an order for 3,345 suitsand you already have sent a partial shipment of 2,390. How manysuits remain to be shipped?

11. A sewing machine operator makes 125 articles per day. How manyarticles does she make in a five-day work week?

LESSON 2


12. At your workplace, there are 103 people on the day shift and only43 people on the night shift. How many people are employed alltogether?

13. At the grocery store, your purchases total thirteen dollars after taxis added. If you hand the cashier a twenty dollar bill, how muchchange should you receive?

14. You are paid $6.00 per hour. How much will you earn in a 42-hourwork week?

LESSON 2


ANSWERS TO EXERCISE

Bill is employed by the Flower and Shrub LandscapingCompany. His employer sends him to the seed store to buygrass seed which cost $3 per pound after tax.

1. If Bill buys 12 pounds of seed, how much will it cost?

Answer: Key words – how much (of equal amounts, each lb costs$3)

$3 (per lb) × 12 (lb)

$36 total cost

This is a reasonable answer, but $1.50 would not havebeen since 1 lb costs $3. $2,000 would also beunreasonable because no one would pay $2,000 for 12lb of grass seed.

2. If Bill’s employer sends $50, how much change will he expect whenBill returns?

Answer: Key words – how much change

$50 (money sent) - $36 (cost for seed)

$14 change received

The answer must be less than $50 since Bill has a total of$50. $14 is reasonable since he spent $36 of the $50.

LESSON 2


3. The company is presently landscaping an area of 7,200 sq ft. If apound of seed will cover 900 sq ft, how many pounds of seed willbe needed to cover this area?

Answer: Key words – how many pounds will cover area. Thismay be confusing, since “how many” is a key word foraddition and multiplication, but it does not say “howmany in all.” So, a sketch may be helpful to determinewhat operation is needed.

Sketch of process... total area is 7,200 sq ft• 1 lb covers 900 sq ft or one small area...• 2 lb covers 1,800 sq ft or two small areas...

This process is dividing up the total 7,200 sq ft. The keywords “how many in each” are implied.

teeFerauqS0027

009 009 009 009

009 009 009 009

7,200 ÷ 900 = 8 lb will be needed and this is areasonable answer.

LESSON 2


4. How many pounds of seed will Bill have left if a 5,400 sq ft area hasbeen sown?

Answer: Bill had 12 pounds of seed (from initial information).Use the same thought process as in problem 3.

Key word – left

5,400 ÷ 900 = 6 lb used12 (total lb in original problem)

- 6 (lb used for 5,400 sq ft)6 lb left

The answer is reasonable. If more than 12 lb were left,that would have been impossible and you would reworkthe problem.

5. How many more sq ft would this left over seed cover?

Answer: First, let’s define the problem. We want to know howmany sq ft the 6 pounds of left over seed would cover.

Now, decide on a plan.

If 1 pound covers 900 square feet, then 2 pounds woulddouble that coverage. This sounds like we need tomultiply. If we carry out this plan, 6 × 900 = 5,400 sq ft.

So, 5,400 more sq ft could be covered.

6. You need 458 brake linings to fill a customer’s order. You havealready boxed 229. How many more do you need to box?

Answer: Key words – how many more

458 (total) -229 (already boxed)

229 left to box

LESSON 2


7. An employee worked 8 hours on Monday, 5 hours on Tuesday, 10hours on Wednesday, 9 hours on Thursday, and 7 hours on Friday.How many hours did he work during this week?

Answer: Key words – how many

Since the hours per day are not equal, the operation isaddition.

8 + 5 + 10 + 9 + 7 = 39 hours worked

39 hours is a reasonable work week

8. A new machine sorts 28 parts per minute. How many minutes willit take the machine to sort 952 parts?

Answer: Key words – per minute

Since you are given a total amount (952 parts) and thekey words - imply division or multiplication...952 ÷ 28 = 34 (minutes)

It would take 34 minutes to sort 952 parts.

You can check your answer:

28 (parts per minute) × 34 (minutes)

952 parts

LESSON 2


LESSON 2

9. Gary has 4 shipping crates in which to package 240 boxes of cereal.If each crate should contain the same number of boxes, how manyboxes of cereal should he put in each crate?

Answer: Key words – how many in each

A sketch of the problem also helps to determine theoperation.

240 ÷ 4 = 60 boxes in each crate

You can visualize the answer to see that 60 boxes percrate would evenly divide 240 boxes of cereal.

10. You work for a suit manufacturer. You have an order for 3,345 suitsand you already have sent a partial shipment of 2,390. How manysuits remain to be shipped?

Answer: Key word – remain

3,345 (ordered) - 2,390 (sent)

955 suits remain to be shipped


11. A sewing machine operator makes 125 articles per day. How manyarticles does she make in a five-day work week?

Answer: Key words – how many (equal amounts)

125 × 5 = 625 articles per week

12. At your workplace, there are 103 people on the day shift and only43 people on the night shift. How many people are employed alltogether?

Answer: Key words – How many (and) all together

103 (day) + 43 (night) = 146 people all together

This number is reasonable. It is more than the numberof people working on either shift, yet it is not double thenumber of day shift workers (since you know less peoplework at night).

13. At the grocery store, your purchases total thirteen dollars after taxis added. If you hand the cashier a twenty dollar bill, how muchchange should you receive?

Answer: Key word – change

$20 - $13 = $7

14. You are paid $6 per hour. How much will you earn in a 42-hourwork week?

Answer: Key words – how much (equal amounts)

$6 × 42 = $252

LESSON 2


LESSON 3

ADDITION AND SUBTRACTION OFMONETARY UNITS

Congratulations!! You have now made it throughLesson 2!

Lesson 3 will begin with some addition andsubtraction of monetary units. Money, of course, hasdecimals. Since the American monetary system has 100cents in one dollar, the decimals in money are basedon hundredths or two decimal places. Five dollars andfive cents is written $5.05. When we add or subtractwith decimals, we should always line up the decimals.For example, $5.05 + $42.50 would be written:

$5.05+ $42.50

Addition or subtraction would then be carried outnormally, carefully lining up the decimal in the answer.

$5.05+ $42.50

$47.55

Congratulations!


A whole number has a decimal at the end. $42 isreally $42.00. So, adding $42 to $5.05 would actuallylook like:

$5.05+ $42.00

$47.05

But, your calculator will keep the decimals linedup so you don’t have to concentrate on it. You willneed to know how to enter the data you have to solveproblems appropriately.

Cents are written with 2 decimal places. 3¢ iswritten as $.03. (Don’t let the period at the end of thesentence confuse you.)

LESSON 3


EXERCISE – ADDING AND SUBTRACTING MONETARY UNITS

Instructions: Use your calculator to add or subtract the following problems. Write youranswers in monetary units ($0.00)

1. $37.52 + $0.04 =________ 2. $27.89 - $25 =________

3. $0.04 + 2¢ =________ 4. $25 - 3¢ =________

5. $10 - 42¢ =________ 6. $142.80 + $31 =________

7. 21¢ - 7¢ =________ 8. $78.21 - $78.20 =________

9. $1 - 23¢ =________ 10. $1,422.85 + $784.13 =________

LESSON 3


Pop Quiz: Name the 4 steps that are suggested for problem solving. List atleast one question you should ask yourself to complete each step.

Step 1

Question to help complete Step 1

Step 2


Step 3


Step 4


LESSON 3


ANSWERS TO EXERCISE

1. $37.52 + $0.04 =________ 2. $27.89 - $25 =________

Answer: $37.56 Answer: $2.89

3. $0.04 + 2¢ =________ 4. $25 - 3¢ =________

Answer: $0.06 Answer: $24.97Be sure to enter 2¢as .02

5. $10 - 42¢ =________ 6. $142.80 + $31 =________


7. 21¢ - 7¢ =________ 8. $78.21 - $78.20 =________

Answer: 14¢ or $0.14 Answer: 1¢ or $0.01

9. $1 - 23¢ =________ 10. $1,422.85 + $784.13 =________

Answer: 77¢ or $0.77 Answer: $2,206.98

LESSON 3


MULTIPLICATION OF MONETARY UNITS

Now, multiplication of decimals is a little differentthan addition and subtraction if you are not using acalculator. When we multiply using money, we typicallyuse decimals.

If you did not have a calculator to multiply$45.36 × 12, we would place the numbers up anddown, not being concerned where any decimals mightbe. When we multiply $45.36 × 12, we must carefullyline up our numbers in the calculation as illustrated:

$45.36 × 12

9072 453654432

Now, count the number of decimal places in theoriginal problem. There are two numbers... 3 and 6...to the right of the decimal. Count back two placesfrom the right in the last line or result of themultiplication problem. The decimal goes between the3 and 4.

$544.32 will be your answer.

LESSON 4

See what happens whenyou don’t keep track of

decimals!


In this course, you will not be required to manuallydo the mathematical operations. You need to know howto use your calculator and since this course focuses onyour problem solving skills, it is OK to use thatcalculator! When multiplying it does not matter whatnumber you enter first on your calculator:

$2.32 × 5 = $11.605 × $2.32 still equals $11.60

One important fact you should remember is thatmoney only has two numbers to the right of thedecimal. As stated before, there are 100 cents in onedollar, so cents are represented by two decimal places(showing hundredths of dollars).

Examples:

52¢ = $0.524¢ = $.04

(Sometimes a zero is placed in the one dollar placeand sometimes it is omitted. Do not let this variationconfuse you. $0.04 and $.04 represent 4 cents.)

LESSON 4


If our answer was $363.180, in calculatingmonetary units, we would need to round to the nearestcent. (Two places to the right of the decimal point.)Two places past the decimal would be the 8. Now, lookat the next number, the number to the right of the 8.If that number is a 5 or larger, round the eight up to a9. If it is less than 5, the number 8 stays the same. Inthis case, 0 is less than 5 so the answer is $363.18.

Let’s multiply this monetary problem and roundthe answer appropriately.

$48 × .002 =

Answer:

24 8 .× =0 0

The display should indicate .096.

.096 rounds to $.10

Note that some calculators may use * for

multiplication.

Since we have 3 decimals places in our originalproblem, a zero was placed in front of the nine resultingin 3 decimal places in our answer. But, we know moneyis represented by 2 decimal places. Therefore, we mustround the answer to 2 decimal places. The first twodecimal places are .09 but we must look at the thirddecimal place, .096. If this number is 5 or larger (which6 is), we round the 9 up to 10 which makes our answer$0.10.

LESSON 4


Now, let’s work some practice problems. Theanswers will be on the following page. You should useyour calculator, but be sure you round answers whenappropriate.

LESSON 4

Pop Quiz: Whatmathematical operation isindicated by the keywords “have left”?


EXERCISE - MULTIPLYING MONETARY UNITS

Instructions: Use your calculator to multiply the following problems, but be sure you roundanswers when appropriate.

1. $.24 × 6 =________ 2. $.97 × 21 =________

3. $13.65 × 2.03 =________ 4. $3.69 × .740 =________

5. $456.92 × 6.943 =________ 6. $7.68 × 8 =________

7. $3.46 × 3.9 =________ 8. $27.95 × 1.5 =________

9. $47.82 × .890 =________ 10. $125 × .20 =________

LESSON 4


ANSWERS TO EXERCISE

1. $.24 × 6 =________ 2. $.97 × 21 =________


3. $13.65 × 2.03 =________ 4. $3.69 × .740 =________


5. $456.92 × 6.943 =________ 6. $7.68 × 8 =________

Answer: $3,172.40 Answer: $61.44

7. $3.46 × 3.9 =________ 8. $27.95 × 1.5 =________


9. $47.82 × .890 =________ 10. $125 × .20 =________

Answer: $42.56 Answer: $25 or $25.00

LESSON 4


DIVISION OF MONETARY UNITS

I hope you did well on the multiplication. Now,let’s look at division. You should know how to do simpledivision like:

9 ÷ 3 = 3

Even problems like:

450 ÷ 90 = 5

should not be difficult using your calculator. But,what if your answer is not a whole number? I wantto quickly make sure you know about remainders.

When you have a problem like:

429 ÷ 9

you will have a remainder.

The correct answer will be 47 with a remainder of

6 (sometimes written 47R6). It might be written 47

6

9.

(The remainder 6, is placed as a fraction over thenumber that you divided by which was 9.) You shouldalways reduce fractions which we will discuss later.

LESSON 5


When you use a calculator, your display reads47.6666667. (Calculators vary: some may have moreor fewer decimal places displayed.) Try entering 429 ÷9 =. Did you get 47.6666667? Your calculator may ormay not round the decimal. The answer should berounded to two decimal places if we are dividingmonetary units such as $429.

47.666

In this case, the 3rd position to the right of thedecimal is greater than 5, so we round the second placeup to 7.

Your answer is $47.67.

Let’s discuss the rounding process further. If youwanted to round 47.666 to the nearest whole number,you would look at the first place after the decimal.47.666

Since we are rounding in order to make a wholenumber, we want to know if the ones place (the placewe are rounding to), 47.666 rounds up to an 8 or staysa 7, dependent upon the number right of ones place.If that number (to the right) is 5 or greater, we roundup and eliminate any numbers to the right. So in thisproblem, the 7 is rounded up to an 8 making 47.666round to the whole number 48. If the number to theright where you are rounding is less than 5, the 7 staysthe same, numbers to the right are eliminated, and theanswer is $47.

LESSON 5

To round or not to round,that is the question!


If you have not understood the rounding process,this can be very confusing. So, let’s practice some more.If you have mastered this concept, please skip ahead tothe division problems.

To round 51.293 to the nearest whole number,look at the 2 (51.293) to see if the 1 (ones place) roundsup or stays the same. The 2 is less than 5, so 1 remainsthe same and the nearest whole number to 51.293 is51.

To round 51.293 to the nearest hundredths place(like monetary units), look at the 3 (51.293) to see ifthe 9 (hundredths place) rounds up or stays the same.The 3 is less than 5, so 9 remains the same and therounded number is 51.29 or $51.29 if we are referringto money.

To round 51.297 to the nearest hundredths place(like monetary units), look at the 7 (51.297) to see ifthe 9 (hundredths place) rounds up or stays the same.The 7 is greater than 5, so 9 rounds up to a 10 and therounded number becomes 51.30 or $51.30 if we arereferring to money.

Suppose you want to round $2,585.98 to thenearest dollar or whole number, look at the 9 (2,585.98)to see if the 5 (ones place) rounds up or stays the same.The 9 is greater than 5, so 5 rounds up to a 6 and thenearest whole number is 2,586. Now, let’s think aboutour answer because 98 cents is almost one dollar. If weare going to drop the change from $2,585.98, we wouldbe closer to the original amount to round up to $2,586than to $2,585. Right?

LESSON 5


In negotiating with a customer, you need to round$2,585.98 to the nearest hundreds place (nothundredths place). Look at the 8 right of hundredsplace (2,585.98) to see if the 5 (hundreds place) roundsup or stays the same. The 8 is greater than 5, so 5 roundsup and the number nearest hundreds becomes $2,600.Again, $85.98 is close to one hundred dollars making585.98 closer to $600 than $500.

That said, let’s look at some problems involvingdecimals.

Example:

45.2 ÷ 3.2

When dividing, always enter into your calculator first, the numberyou are dividing into (the first number listed). This is called thedividend. Then enter the number you are dividing by (the secondnumber listed). This is called the divisor. When we begin wordproblems you will have to decide which number is the divisor(the number that must be entered second). In this case, 3.2 is thedivisor.

45.2 ÷ 3.2 = 14.125

LESSON 5


Let’s do a couple more problems together, and thenyou can practice on your own.

79.8 ÷ .24 =

Answer: 332.5

$86.75 ÷ .5 =

Answer: $173.50

Notice the added zero to 173.5 to make 50 centssince we are working with money.

Now work the following problems on your own.The page following the problems will have the answers.If you get stuck, refer to the solutions. But, before youpractice... it is time for a pop quiz.

LESSON 5

EdWIN


Pop Quiz: List as many “key words” for mathematical operations as you canremember without referring to your list.

Addition Multiplication

Subtraction Division

LESSON 5


EXERCISE – DIVISION OF MONETARY UNITS

Instructions: Use your calculator to solve the following problems. Round answers if necessaryto the nearest hundredth.

1. $24 ÷ 8 = _________ 2. $12, 096 ÷ 3 =_________

3. $848 ÷ 16 =_________ 4. $93 ÷ 7 =_________

5. $78,906 ÷ 46 =_________ 6. $2,817 ÷ 6 =_________

7. $850.86 ÷ 58 =_________ 8. $3,840,214.72 ÷ 732 =_________

9. $12.16 ÷ .04 =_________ 10. $1,893.72 ÷ .17 =_________

LESSON 5


ANSWERS TO EXERCISE

1. $24 ÷ 8 = _________ 2. $12, 096 ÷ 3 =_________

Answer: $3 or $3.00 Answer: $4,032or $4,032.00

3. $848 ÷ 16 =_________ 4. $93 ÷ 7 =_________

Answer: $53 or $53.00 Answer: $13.2913.2857 rounds up

5. $78,906 ÷ 46 =_________ 6. $2,817 ÷ 6 =_________

Answer: $1,715.35 Answer: $469.501,715.3478 rounds up

7. $850.86 ÷ 58 =_________ 8. $3,840,214.72 ÷ 732 =_________

Answer: $14.67 Answer: $5,246.195,246.19497stays the same

9. $12.16 ÷ .04 =_________ 10. $1,893.72 ÷ .17 =_________

Answer: 304 Answer: 11,139.5311,139.529rounds up

LESSON 5


PRACTICE SESSION WITH PRACTICALPROBLEMS

Before we move on, we need to practice using whatwe have learned. The following pages contain practicalproblems and solutions using skills we have discussed.Refer to Lesson 2 if you have forgotten the 4 steps forproblem solving. If you are having difficulty with aproblem, look for word clues that indicate an operation.Again, you may need to review key words listed inLesson 2. In cases where word clues are not obvious,restate the question in your own words trying to usekey words such as total, in all, difference, for each, etc.,to determine which words best fit the meaning of thequestion.

Another way to determine which operation youneed to solve word problems is to use the given infor-mation such as:

• If the given information includes a total value, theoperation is most likely subtraction or division.

• If the problem asks for a total, the operation is alwaysaddition or multiplication. Multiplication is ashortcut for addition and should be used when thenumbers being totaled are the same.

Remember, you can always refer to the answers ifyou really get stuck. Good luck!

LESSON 6

This is key informationfor problem solving


EXERCISE - PRACTICAL APPLICATIONS

Instructions: Perform the indicated operations using your calculator. Remember the foursteps to problem solving. All monetary answers should be rounded appropriately.Don’t forget to examine your answers to make sure they make sense.

1. Your plant runs two assembly lines. Line A produces 427 units perhour and line B produces 519 units per hour. How many more unitsper hour does Line B produce than Line A?

2. Fly Away travel agency is advertising an eight day and seven nightstay in Cancun for $749. If this is a savings of $120, what was theprevious price?

LESSON 6


3. There are 156 cases of bolts in inventory. If 75 cases are shippedout, how many cases are left?

4. You work at the local recycling center. In the last three weeks, 67 lb,42 lb, and 74 lb of aluminum cans were brought in. How many lb ofaluminum were recycled during this three week period?

5. Your department is responsible for roadside litter pickup. This yearyou have been alloted $57,000 for this purpose. The first monthyou spent $5,600 removing trash from county roads. How muchmoney do you have left for the rest of the year?

LESSON 6


6. In a given month, your pay checks vary each payday. How muchdid you earn all together if your checks were $115, $126, $125, and$124?

7. Your department uses 120 file folders per week. You are told to buysupplies and to get enough for 2 months. How many file foldersshould you buy? (Assume 4 weeks equals 1 month.)

8. You take four prospective buyers out to lunch and everyone ordersthe sirloin steak for $8.99. What is the cost of lunch? (Assume taxis included.)

LESSON 6


9. A woman earns $135 a week. What are her total earnings for 14weeks?

10. A car dealership is advertising a 1994 Dodge Spirit for no moneydown and $225 per month for 5 years. What is the cost of this carbased upon this information?

11. You work at an electronics store. One day you sold 6 VCRs costing$249 each. What was the total amount of your sales?

LESSON 6


12. Last year your recycling center took in 12,700 lb of glass. The glasswas sold to a local bottle manufacturer for $.15 per lb. How muchmoney did the recycling center receive for the glass?

13. A shipping clerk mailed 15 cartons to each of 740 customers. Whatwas the total number of cartons mailed?

14. A textile worker is paid $7.50 per hour overtime. One week he putsin 8 hours overtime. How much overtime pay does he earn?

LESSON 6


15. A tree nursery received a contract with the city for planting treesin the three city parks. In all, 720 trees are to be planted, with eachpark receiving an equal number of trees. How many trees will beplanted in each park?

16. A box contains 6 rolls of tape and sells for $1.86. What is the costof one roll of tape?

17. You have been told to order 500 legal pads for your office. They aresold in packs of 15. How many packs do you need to order?

LESSON 6


18. A man purchases a piece of lumber that is 192 inches long. Howmany 16 inch long pieces can be cut from it? (Assume there is nowaste from cutting.)

19. A vial contains 150 cc of penicillin. How many 5 cc injections canbe administered from the vial?

20. You are volunteering at a local Habitat for Humanity house. Thepaint can you are to use indicates a gallon of paint covers 300 sq ft.How many gallons of paint will you need to cover 1,100 sq ft?

LESSON 6


21. You work at a shoe manufacturing plant. You have an order for 78pairs of shoes that need to be boxed for shipment. If each boxholds 4 pairs of shoes, how many boxes will you need to fill theorder?

22. There are 24 Mars bars in a case. How many cases would you needto hold 4,032 Mars bars?

23. A 12-foot board of lumber costs $1.92. What is the cost of onefoot?

LESSON 6


24. A new copier can produce 600 copies of a document in 5 minutes.How many copies does it make per minute?

25. Your office uses 200 pencils per month. You are told to requisitionenough pencils for the next month. If pencils come in boxes of 25,how many boxes do you need to requisition?

26. While selling Girl Scout Cookies, each of the 17 Girl Scouts sold51 cases of cookies. How many cases of Girl Scout Cookies didthe troop sell?

LESSON 6


27. A sofa normally sells for $225. A customer can save $43 by payingfor the sofa in cash. What is the cash price of the sofa?

28. During a fund raiser, 37 employees donated $7.25 each. How muchmoney was raised from the employees?

29. Your company purchased 7 laser printers for $8,721.86. If eachprinter costs the same amount, how much did each printer cost?

LESSON 6


30. A drill usually costs $29.95. This week it is on sale for $21.86. Whatis the difference in price?

LESSON 6

What a bargain!


ANSWERS TO EXERCISE

1. Your plant runs two assembly lines. Line A produces 427 units perhour and line B produces 519 units per hour. How many more unitsper hour does Line B produce than Line A?

Answer: Key words – how many more

519 - 427 = 92 units

It makes sense that one line produces 92 more thanthe other line. It would not, however, make sense if weincorrectly added and found one line made 946 morethan the other; this is more than either group produced.Always examine your outcome.

2. Fly Away travel agency is advertising an eight day and seven nightstay in Cancun for $749. If this is a savings of $120, what was theprevious price?

Answer: No key word is obvious. Ask yourself if the giveninformation provides a total amount. Remember a giventotal amount indicates division or subtraction. If you arelooking for a total amount, multiply or add.

Well, $749 is a total price of the trip, but the questionasked for a previous total price, before the savings.Eliminate 8 days and 7 nights from your processingbecause the question does not address time, only price.

$749 + $120 (savings) = $869 (previous price)

LESSON 6


3. There are 156 cases of bolts in inventory. If 75 cases are shippedout, how many cases are left?

Answer: Key words – how many left

156 - 75 (shipped) = 81 cases left

4. You work at the local recycling center. In the last three weeks, 67lb, 42 lb, and 74 lb of aluminum cans were brought in. How many lbof aluminum were recycled during this three week period?

Answer: Key words – how many (amounts not equal)

67 + 42 + 74 = 183 lb of aluminum

5. Your department is responsible for roadside litter pickup. This yearyou have been alloted $57,000 for this purpose. The first monthyou spent $5,600 removing trash from county roads. How muchmoney do you have left for the rest of the year?

Answer: Key words – how much (money do you have) left

$57,000 - $5,600 (used first month) = $51,400 left

6. In a given month, your pay checks vary each payday. How muchdid you earn all together if your checks were $115, $126, $125, and$124?

Answer: Key words – all together

115 + 126 + 125 + 124 = $490

LESSON 6


7. Your department uses 120 file folders per week. You are told to buysupplies and to get enough for 2 months. How many file foldersshould you buy? (Assume 4 weeks equals 1 month.)

Answer: Define your problem – How many weeks are you buyingfor? In 2 months there are approximately 8 weeks. So,the problem is how many file folders do you buy for 8weeks?

120 (per week) × 8 (weeks) = 960 file folders

8. You take four prospective buyers out to lunch and everyone or-ders the sirloin steak for $8.99. What is the cost of lunch? (As-sume tax is included.)

Answer: Define your problem – Four buyers plus yourself means5 people ordered steak. The problem is how much did itcost to buy an $8.99 steak for all 5 people.

Decide on a plan – No key words are obvious, so restatethe question. How much did lunch cost?

Implied key words – how much (of equal amounts)

Carry out the plan – $8.99 × 5 = $44.95 cost for lunch

Examine the outcome – It is reasonable to expect topay $45 (rounded) to buy a steak lunch for 5 people.

9. A woman earns $135 a week. What are her total earnings for 14weeks?

Answer: Key words – total (of equal numbers, $135 each week)

$135 (per week) × 14 (weeks) = $1,890 total earnings

LESSON 6


10. A car dealership is advertising a 1994 Dodge Spirit for no moneydown and $225 per month for 5 years. What is the cost of this carbased upon this information?

Answer: Define your problem – How many months in 5 years?

12 (months in a year) × 5 (years) = 60 months in 5years

You want to know the total cost of a car with 60 monthsof payments at $225.

$225 (per month) × 60 (months) = $13,500 cost of the car

11. You work at an electronics store. One day you sold 6 VCRs costing$249 each. What was the total amount of your sales?

Answer: Key words – total amount (equal price for each VCR)

$249 (cost of each VCR) × 6 (VCRs sold)= $1,494 total amount of sales

12. Last year your recycling center took in 12,700 lb of glass. The glasswas sold to a local bottle manufacturer for $.15 per lb. How muchmoney did the recycling center receive for the glass?

Answer: Key words – how much (of equal amounts)

12,700 (lb of glass) × .15 (for each lb)= $1,905 from recycling

LESSON 6


13. A shipping clerk mailed 15 cartons to each of 740 customers. Whatwas the total number of cartons mailed?

Key words – total number (of equal amounts)

740 (customers) × 15 (cartons to each) = 11,100 cartonsmailed

14. A textile worker is paid $7.50 per hour overtime. One week he putsin 8 hours overtime. How much overtime pay does he earn?

Answer: Key words – how much (of equal amounts)

$7.50 (per hour pay) × 8 (hours) = $60.00 overtime pay

15. A tree nursery received a contract with the city for planting treesin the three city parks. In all, 720 trees are to be planted, with eachpark receiving an equal number of trees. How many trees will beplanted in each park?

Answer: Key words – Don’t be fooled by “how many.” Earlier theproblem stated “In all” there are 720 trees, so we do nothave an addition or multiplication problem. Rememberif the total is given, the operation is often subtraction ordivision. We want to know how many trees in each,which implies division.

720 ÷ 3 = 240 trees in each park

If we had subtracted, that would mean we had 717 treesfor each park. This does not make sense when we onlyhave a total of 720 trees. Our answer of 240 trees makesmore sense.

LESSON 6


16. A box contains 6 rolls of tape and sells for $1.86. What is the costof one roll of tape?

Answer: Implied key words – one roll of tape (similar to each rollof tape)

$1.86 ÷ 6 = $0.31 per each roll of tape

17. You have been told to order 500 legal pads for your office. They aresold in packs of 15. How many packs do you need to order?

Answer: You are given the total number of legal pads, 500. Thepacks are divided into groups of 15, so you need todivide.

500 ÷ 15 = 33.3 pads needed

Since you cannot buy part of a pack of legal pads (.3),you must round up to the next whole number. In orderto have enough legal pads (500), we have to purchase34 packs which will actually give us 510 legal pads. Ifwe bought 33 packs, we would only have 495 legal pads.

34 × 15 = 51033 × 15 = 495

18. A man purchases a piece of lumber that is 192 inches long. Howmany 16 inch long pieces can be cut from it? (Assume there is nowaste from cutting.)

Answer: Implied key words – equally divided (he is dividing theboard into equal length pieces)

Another clue is the given information of a total (192)

192 ÷ 16 = 12 pieces of wood

LESSON 6


19. A vial contains 150 cc of penicillin. How many 5 cc injections canbe administered from the vial?

Answers: Implied key words – divided equally (how many equalinjections from the vial)

150 ÷ 5 = 30 injections

20. You are volunteering at a local Habitat for Humanity house. Thepaint can you are to use indicates a gallon of paint covers 300 sq ft.How many gallons of paint will you need to cover 1,100 sq ft?

Answer: You might draw a sketch to help determine a plan:

You need to divide the area that needs painted by 300since one can covers 300 sq ft.

1,100 ÷ 300 = 3.7

Again, you cannot buy .7 cans of paint, so you mustround up to the nearest whole number which is4 gallons of paint.

LESSON 6


21. You work at a shoe manufacturing plant. You have an order for 78pairs of shoes that need to be boxed for shipment. If each boxholds 4 pairs of shoes, how many boxes will you need to fill theorder?

Answer: Implied key words – divided equally (how many boxesif each box holds 4)

Given a total of 78 pairs of shoes.

78 ÷ 4 = 19.5

Round up to 20 boxes needed.

22. There are 24 Mars bars in a case. How many cases would you needto hold 4,032 Mars bars?

Answer: Given a total of 4,032 Mars bars.

4,032 (total) ÷ 24 (divided equally per case)= 168 cases needed

23. A 12-foot board of lumber costs $1.92. What is the cost of onefoot?

Answer: Implied key words – one foot (per foot which meanstotal cost must be divided equally into 12 parts)

Given the total cost of the board.

$1.92 ÷ 12 = $.16 or 16¢ per foot

24. A new copier can produce 600 copies of a document in 5 minutes.How many copies does it make per minute?

Answer: Key words – how many per (minute)

600 ÷ 5 = 120 copies per minute

LESSON 6


LESSON 6

25. Your office uses 200 pencils per month. You are told to requisitionenough pencils for the next month. If pencils come in boxes of 25,how many boxes do you need to requisition?

Answer: No key words are obvious, but it is given in the problemthat a total of 200 pencils are used each month. Sinceyou are given the total, division is implied but so issubtraction. The problem restated indicates 25 pencilsare in each box. This problem takes some thought.Drawing a sketch may be helpful:

200 (pencils) ÷ 25 (per box) = 8 boxes

26. While selling Girl Scout Cookies, each of the 17 Girl Scouts sold51 cases of cookies. How many cases of Girl Scout Cookies didthe troop sell?

Answer: Key words – how many (cases) in all (did the troop sell)

Each girl sold the same or equal amounts (51)

17 × 51 = 867 cases of cookies

27. A sofa normally sells for $225. A customer can save $43 by payingfor the sofa in cash. What is the cash price of the sofa?

Answer: Key word – save ( means less or decrease in price)

$225 (price) - $43 (savings for cash purchase)= $182 price of sofa if a cash purchase


28. During a fund raiser, 37 employees donated $7.25 each. How muchmoney was raised from the employees?

Answer: Key words – how much (equal amounts of $7.25 given)

37 (people) × $7.25 (given by each person)= $268.25 donated

29. Your company purchased 7 laser printers for $8,721.86. If eachprinter costs the same amount, how much did each printer cost?

Answer: Key words – how much (did) each

Total amount is given $8,721.86Total amount must be divided equally into 7 parts tofind cost per unit.

$8,721.86 ÷ 7 = $1,245.98 for each printer

30. A drill usually costs $29.95. This week it is on sale for $21.86. Whatis the difference in price?

Answer: Key word – difference

$29.95 (original price) - $21.86 (sale price)= $8.09 difference or savings

LESSON 6


LESSON 7

ADDITION AND SUBTRACTION OFSIGNED NUMBERS

I hope you did well on the word problems.Application of math is what this course is all about.So, if you had trouble go back and work some problemsagain. Repetition is one way you will learn to recognizekey words. The ACT™ WorkKeys® AppliedMathematics assessment contains problems similar tothe word problems you encounter in this course.Remember, practice makes perfect.

Improving workplace skillsimproves the paycheck!


Now, we will begin to look at signed numbers.

This is a number line:

The numbers on the right of zero are positive, andthe numbers on the left are negative. Zero (0) does nothave a sign; it is neutral. Notice that the positivenumbers do not have a sign. A positive number can bewritten with or without a sign (for example, 5 or +5).The farther to the right you move, the larger thenumber. The farther to the left you move, the smallerthe number.

If you think about it, you already know how toadd positive numbers:

4 + 5 = 9

You have just added two positive numbers.Sometimes, though, the signs get a little confusing. Forexample, you might have a problem that looks like this:

+4 + (+5) =

LESSON 7


Now, that’s exactly what we did in the previousexample, but it looks a little strange. When you see aproblem like that, concentrate on finding two signsthat are together:

Once you have located this, check to see if the signsare the same or different.

If the two signs are the same, change the sign to a“plus.” If they are different, change the sign to a“minus.” Now your problems look like this:

Notice that the signs in the middle have all beenchanged to reflect the previous rule.

LESSON 7


We still haven’t added or subtracted yet. Place thenumbers “up and down.”

Now, if the signs of both numbers are the same, youshould add the numbers and carry the sign down.

If the signs are different, subtract and keep the signof the larger number.

Same signs:

Different signs:

LESSON 7


It sounds a little complicated, but it just takespractice. These rules are for anyone who does not havea calculator. I hope you do, then signed numbers willbe much easier to learn. Your calculator will add andsubtract signed numbers, but you must know how toenter the information.

So, let’s take a look at our calculators. You shouldhave a button or key that looks like this if yourcalculator will handle signed numbers:

(-) or +/-

- is not the same as the +/- . If you do not

have the (-) or +/- keys, you will have to use the

signed number rules or invest in a calculator thatcomputes signed numbers.

LESSON 7

Run out and buy aninexpensive calculator if

you need one.


This is your negative key +/- . You may have to

press it before the number or after the number. Itdepends on the brand and model of your calculator.Play with your calculator for a minute or two to findout. Try to get -5 on the display. Press 5, (+/-) or(+/-),5. See which way will display -5 on your screen.Now, you can key this problem into your calculator:

5 - (-3) =

Press:

5 - +/- 3 =

or

5 - 3 +/- =

You should get “8” on your screen.

-5 + -2 =

Press:

+/- 5 + +/- 2 =

or

5 +/- + 2 +/- =

You should get “-7” on your screen.

Try +7 - +2 =

7 - 2 =

You should get “5” on your screen.

LESSON 7


Practice using the negative key on your calculatorin the following exercise.

After you finish, work the practical problemscontaining signed numbers. Remember to use your keywords. The answers are provided following the exercise.

LESSON 7

Let’s dive into wordproblems!


EXERCISE – SIGNED NUMBERS ADDITION/SUBTRACTION

Instructions:Complete the following problems using signed numbers.

1. 7 - (-3) =_________ 2. +8 + (-2) =_________

3. -3 + (-2) =_________ 4. 0 + 4 =_________

5. +2 + (+4) =_________ 6. -5 - 8 =_________

7. 8 - (+2) =_________ 8. -4 - 8 =_________

9. 17 - (+9) =_________ 10. -18 + (+2) =_________

LESSON 7


LESSON 7

Pop Quiz: Solve the following problem:

In preparation for the basketball game, your assignment in the concession standis to fill drink carriers which hold 40 drinks. If you expect to sell 2,520 drinksthrough vendors who sell in the stands, how many carriers will you have to fill?


ANSWERS TO EXERCISE

1. 7 - (-3) = 2. +8 + (-2) =

Answer: 37 +/-- = Answer: 28 + =+/-

or or37 +/-- = 28 + =+/-

7 + 3 = 10 8 - 2 = 6

3. -3 + (-2) = 4. 0 + 4 =

Answer: 23 +/-+/- + = Answer: 4+ =0

or23 +/-+/- + = 0 + 4 = 4

-3 - 2 = -5 Don’t hesitate touse your mindinstead of yourcalculator.

5. +2 + (+4) = 6. -5 - 8 =

Answer: 2 4+ = Answer: 5 8+/- - =

or2 + 4 = 6 5 8+/- - =

-5 - 8 = -13

LESSON 7


7. 8 - (+2) = 8. -4 - 8 =

Answer: 28 - = Answer: 4 8+/- - =

or8 - 2 = 6 4 8+/- - =

-4 - 8 = -12

9. 17 - (+9) = 10. -18 + (+2) =

Answer: 17 9- = Answer: 18 2+ =+/-

or17 - 9 = 8 18 2+ =+/-

-18 + 2 = -16

LESSON 7


EXERCISE – APPLICATION OF SIGNED NUMBERS

Instructions: Solve the following problems using your calculator and your skills we havebeen developing.

1. One year the highest temperature in Darbyville was 119 degrees whilethe lowest was 18 degrees below zero. What is the difference betweenthose temperatures?

2. In November, your company had a loss of $2,400. Due to an aggressivesales campaign, your profits were $4,350 for the month of December.How much more did the company earn in December than inNovember?

LESSON 7


3. The floor of Death Valley is 282 feet below sea level and close byOwens Telescope Peak is 11,045 feet above sea level. How many feetwould you change in altitude if you went from the bottom of DeathValley to the top of the peak?

4. A quarterback lost 15 yards in one play and then gained 8 yards onthe next play. What is the net result of the two plays?

5. In a company, 3 employees quit in January and 4 more quit inFebruary. No new employees were hired. This represents what changein the total number of employees?

LESSON 7


6. One morning the temperature was -15° F. By noon it increased 7°.What was the temperature at noon?

7. While scuba diving you noticed that you were 30 feet deep. You wentdown another 5 feet. How deep were you then?

LESSON 7


ANSWERS TO EXERCISE

1. One year the highest temperature in Darbyville was 119 degrees whilethe lowest was 18 degrees below zero. What is the difference betweenthose temperatures?

Answer: Key word – difference

119 - (-18) = 137° difference in high and low temperatures

2. In November, your company had a loss of $2,400. Due to an aggressivesales campaign, your profits were $4,350 for the month of December.How much more did the company earn in December than inNovember?

Answer: Key words – how much more4,350 - (-2,400) = $6,750

3. The floor of Death Valley is 282 feet below sea level and close byOwens Telescope Peak is 11,045 feet above sea level. How many feetwould you change in altitude if you went from the bottom of DeathValley to the top of the peak?

Answer: Key word – change11,045 - (-282) =11,327 feet from the valley to the peak

4. A quarterback lost 15 yards in one play and then gained 8 yards onthe next play. What is the net result of the two plays?

Answer: -15 + 8 = -7 yards or 7 yards lost

LESSON 7


5. In a company, 3 employees quit in January and 4 more quit inFebruary. No new employees were hired. This represents what changein the total number of employees?

Answer: Key words – total number

-3 + -4 = -7

The total number of employees decreased by 7.

6. One morning the temperature was -15° F. By noon it increased 7°.What was the temperature at noon?

Answer: Keyword – increased

-15 + 7 = -8° F

by noon it was -8° F

LESSON 7


7. While scuba diving you noticed that you were 30 feet deep. You wentdown another 5 feet. How deep were you then?

Answer: Key words – deep and down (indicates negative numbersas opposed to above and up)-30 - 5 = -35 (or 35 feet deep)

LESSON 7


CONVERSION INVOLVING WHOLENUMBERS, FRACTIONS, DECIMALS, ANDPERCENTS

Lesson 8 will deal with conversions involving wholenumbers, fractions, percents, and decimals. Rememberwhole numbers have an implied decimal at the end(on the right side) of the number.

LESSON 8

Pop Quiz: If the giveninformation in a problemincludes a total amount,what 2 operations areyour “likely” choices?


42 and 42.0 represent the same number. If we arereferring to money, we would write: $42.00 or $42(the decimal is implied).

First, we will convert whole numbers and decimalsto percents. When converting whole numbers anddecimals to percents, always move the decimal twoplaces to the right.

Examples: 0.45 = 45%

0.003 = .3%

1.2 = 1.20 = 120%

Notice if the decimal includes a whole number (likethe last example 1.2), the percentage will be greaterthan 100%.

When converting percents to decimals, alwaysmove the decimal two places to the left.

Examples: 45% = .45

35.2% = .352

LESSON 8


Now how are you going to remember when tomove which way?

Think about your math problem. If you arechanging a decimal to percent or percent to a decimalwrite D P, always D first since alphabetically D comesbefore P. (This is an association with something youalready know.) If you are given a decimal to change toa percent, put your pencil on D (for decimal) and fromD to P you must move right (always two places). Areyou given a percent to change to a decimal? If so, putyour pencil on P (for percent) and from P to D youmust move left (always 2 places).

Many calculators have percentage keys which willmake these conversions for you. If you have thisfunction, use it. If not, remember the D P, D P trickand let’s practice a few problems together.

LESSON 8


Change 20% to a decimal.

You might think why would I ever want to do that?Well, you cannot do math operations withpercentages. You must first convert percentages todecimals. So, if you are told your work hours mustbe cut by 20% because of budget cuts, you wouldfirst change 20% to a decimal and then calculatehow many hours you are expected to work.

20% (Hint: the decimal is implied after the zero(0) and using D P we are starting with a P,percent, so move left to make a decimal.)

20% = 20% = .20 or .2

Now, if your boss really told you to reduce yourhours by 20%, you would multiply .2 times thenumber of hours you regularly work. This answeris how many hours your regular hours must be cut.If you work 40 hours a week, then:

20% of 40 =.2 × 40 =8 hours

To calculate how many hours you will be workingsubtract the 20% from your regular work hours.

40 (regular hours) - 8 (20%) = 32 hours per weekfor new schedule.

LESSON 8


I hope you can see how important it is for you toknow how to use percentages and the conversionprocess. Many workplace problems involve percents.


52% = .52 (D P)

Change .15 to a percent.

.15 = 15% (D P)


2% = .02 (D P)

Change 1.25 to a percent.

1.25 = 125% (D P)

Not only do we need to convert decimals topercents and percents to decimals, but problem solvingsometimes requires the conversion of fractions.

LESSON 8


To convert fractions to decimals, divide the bottomnumber into the top number.

Examples:

1

81 8 125= ÷ = .

1

41 4 25= ÷ = .

2

32 3 666667 67= ÷ = =. . (rounded to

hundredths)

If you wanted to convert these fractions to percents,you would simply move the decimal to the right afterdividing.

Let’s review this process again. First, change thefraction to a decimal. Second, remember D P movesthe decimal right two places. So, move the decimal andadd the % sign.

Examples:

1

8125 12 5= =. . %

1

425 25= =. %

2

367 67= =. %

Now, let’s reverse the order and start with a percent.Sometimes word problems require this process. First, Ichange the percent to a decimal. I will drop the percentsign, move the decimal two places to the left (D P).Then I will convert to a fraction by placing the decimalnumber without the decimal point over the appropriateplace value. All of these examples indicate 2 decimalplaces which is hundredths, so we place the decimalnumber (without the actual decimal point) over 100.We then reduce the fraction.

LESSON 8


Examples:

45 45

45

100

9

20% .= = =

50 50

50

100

1

2% .= = =

Some calculators even have a key that will reducefractions. It looks like:

ab/ or ab c/

Key in:

14 5 00ab c/ =

and on your screen you will see:

920

or 9 20 or 9 20

LESSON 8


If the percentage has a decimal with it, first changethe percent to a decimal. You are starting with a percentso go to the decimal in the percent and move two placesto the left. 45.2% = .452 (D P moves left). Fromthere, you must change the decimal to a fraction. Youmust count the places past the decimal. In this case,there are 3 places past the decimal. This tells you howmany 0s (zeros) to put on the bottom of the fraction.

Now reduce the fraction.

Don’t forget your calculator might reduce thefraction.

which is 452 ÷ 1000 =

LESSON 8

124 5 =0 0 0ab c/

(if you divide top and bottom by 2) = (need to divide by 2 again) =4521000

226500

113250

113250

4521000

.452

3 places 3 zeros

=


.375

375

1000

75

200

3

8= = =

Let’s practice some problems of each kind.

Change 37.5% to a decimal:

D P moves left. You are starting with a percent(37.5%) so go first to the decimal in the percentand move left.

37.5% = .375 is the decimal.

Now complete the change of 37.5% to afraction (3 decimal places means three zeros):

Now, look at the table in the following exercise.We have learned that we can convert percents, decimals,and fractions from one form to the other. You will needto become comfortable with these processes becauseapplication or word problems frequently require youto do so before you can solve the problems.

LESSON 8


EXERCISE – PERCENT, DECIMAL, AND FRACTION CONVERSION

Instructions: Complete the table by filling in the missing values. Use the given informationin each row to calculate the other 2 forms of that number. Use your calculatoras needed.

LESSON 8


ANSWERS TO EXERCISE

LESSON 8


The next table contains some common conversions. You may want to memorize thesebecause they are used frequently. Many people assume you know these commonconversions.

LESSON 8

You should try to memorizethis information.


EXERCISE – APPLICATION OF PERCENTS, DECIMALS, AND FRACTIONS

Instructions: Solve each problem using the 4 steps, described in Lesson 2, looking for keywords, and using the conversion process as needed.

1. Two-fifths of the people in your office have worked for the companyfor more than 10 years. What percent is this?

2. An order for computer disks to be shipped to a customer is 70%ready. What fraction of the order is ready?

LESSON 8


3. Last year, 58 of the trash picked up beside state roads originated

from fast food restaurants. Express this as a decimal and as apercent.

4. An engine manufacturer discovered that .08 of a certain productionrun was defective. What fraction of the run does this represent?

5. The time needed by an employee to do a particular task is .30 of anhour. What fraction of an hour is needed?

LESSON 8


6. At Barker Printing Company, 38% of the employees are female.What fraction of the employees are female?

7. In a shipment of 40 stoves, 2 are defective. What percent isdefective?

LESSON 8


ANSWERS TO EXERCISE

1. Two-fifths of the people in your office have worked for the companyfor more than 10 years. What percent is this?

Answer: Define the problem – What percent (10 years is notrelevant to this question)

25

2 5 .40= ÷ = = 40%

2. An order for computer disks to be shipped to a customer is 70%ready. What fraction of the order is ready?

Answer: 70% .7070

100710

= = =

3. Last year, 58 of the trash picked up beside state roads originated

from fast food restaurants. Express this as a decimal and as apercent.

Answer: 58

= .625 = 62.5% (Remember to convert fractions

divide the bottom number into the top number)

4. An engine manufacturer discovered that .08 of a certain productionrun was defective. What fraction of the run does this represent?

Answer: .088

1002

25= =

LESSON 8


5. The time needed by an employee to do a particular task is .30 of anhour. What fraction of an hour is needed?

Answer: .3030

1003

10= =

6. At Barker Printing Company, 38% of the employees are female.What fraction of the employees are female?

Answer: 38%38

1001950

= =

7. In a shipment of 40 stoves, 2 are defective. What percent isdefective?

Answer:2

402 40 .05= ÷ = =5%

LESSON 8


Well, you have now completed this level of AppliedMathematics. Congratulations!! I hope you did not findit too difficult. Now, if you feel confident enough,complete the posttest. If you still feel doubtful, go backand review the information in Level 3. Take the Posttestuntil you make a good score. Personally, I think 95%is pretty good, but why not go for 100%? Good luck...I know you can do it.

Answers for the Posttest questions are provided atthe end of the workbook... but don’t peek! If you peek,your score will not be accurate and it will not reflectwhether or not you have learned the information inthis course thoroughly!!

LESSON 9

No fair peeking on thetest.


EXERCISE - POSTTEST

Instructions: Solve the following word problems using your new skills. Remember toexamine your answers to make sure they make sense. Round decimals to thenearest hundredth.

1. In 1997, Smith Brothers, Inc., sold 123,690 washers and 95,125dryers. What was the total number of appliances sold that year?

2. Last week, you worked 8 hours more than your usual 35 hours.What was the total number of hours you worked?

POSTTEST


3. A bank needs part-time tellers. The pay is $7.50 per hour and part-time employees may work a maximum of 20 hours per week. Whatis the most a part-time employee can earn per week?

4. Your department manufactures thermostats. In one week theyaverage making 2,150, but 25 thermostats are usually founddefective and are eliminated. How many thermostats, on an average,does your department contribute to inventory per week?

5. A single mother is entitled to a welfare grant of $633 per month. Ifshe works, however, part of her earnings must be applied to thisamount. In Sally Lewis’s case, $69 must be deducted. How muchmoney does Sally receive from the welfare grant?

POSTTEST


6. To calculate the tax charged on an item, you multiply the originalprice by the rate. If the tax rate is 9.2% and a ladder costs $59.95,how much tax is due?

7. When Larry’s wife was hospitalized, his co-workers wanted to showtheir support by donating some money. John gave $100, Chuckcontributed $225, Ellen gave $170, and Casey put in $55. How muchmoney did they collect?

POSTTEST


8. Tony is paid $7.25 an hour and time and a half for overtime hours.Overtime begins after 40 hours of work in one week. Last week heworked 42.5 hours. What were his total earnings?

9. To receive a $125 rebate, Teresa must place an order beforeJanuary 1. If she purchases a copier for $1,475 by the deadline,how much is her net cost?

10. It takes Howard 5 minutes to press and cut one needle. How manyneedles can he produce per hour?

POSTTEST


11. A checking account contained $6,274.54. After a $385.79 checkwas drawn, what was left in the account?

12. A produce plant processes 5,424 pounds of beans each day. Theplant packages the beans in 4-pound bags. How many bags dothey package each day?

13. Wecandoit, Inc. reported a loss of $17,225 in March, but in Aprilshowed a profit of $32,500. How much more did Wecandoit, Inc.make in April than in March?

POSTTEST


14. Your department employed 35 laborers in January 1996, lost 12employees in July, and regained 3 in October. How many totallaborers are employed in October?

15. The temperature on Monday morning was -2°F. By noon it hadwarmed up to 5°F. How many degrees did the temperature change?

POSTTEST


16. Any Company showed a profit of $12,250 dollars for the first quarter,a loss of $2,575 for the second quarter, another loss in the thirdquarter of $5,100, and a slight profit of $875 in the last quarter.What profit/loss did Any Company have for the total year?

17. One out of every 25 workers at Dean Manufacturing claimedWorker’s Compensation this year. What percent of the workers doesthis indicate have had accidents?

POSTTEST


18. A manufacturer of engineered metal structures, claims that a newsystem helped them reduce man-hours by 50 hours per unit perweek. If each unit averages 200 man-hours a week, by what percentdid they reduce the number of hours per unit?

19. A company initially gave assessments to 45 applicants and filled27 positions. What percentage of these 45 applicants were hired?

20. A manufacturer of engines and clutches, increased employmentfrom 125 in 1991 to 750 in 1997. What percentage was this increase?

POSTTEST


ANSWERS TO EXERCISE

1. In 1997, Smith Brothers, Inc., sold 123,690 washers and 95,125dryers. What was the total number of appliances sold that year?

Answer: 218,815

Assuming washers and dryers are the only appliancessold, 218,815 appliances were sold in 1997.

Key word-total 123,690 + 95,125 = 218,815.

2. Last week, you worked 8 hours more than your usual 35 hours.What was the total number of hours you worked?

Answer: 43 hours

Key word-total 8 + 35 = 43

3. A bank needs part-time tellers. The pay is $7.50 per hour and part-time employees may work a maximum of 20 hours per week. Whatis the most a part-time employee can earn per week?

Answer: $150.00

Key words (implied) – how much money can he/she make(equal amounts per hour)

$7.50 x 20 = $150

POSTTEST


4. Your department manufactures thermostats. In one week theyaverage making 2,150, but 25 thermostats are usually founddefective and are eliminated. How many thermostats, on an average,does your department contribute to inventory per week?

Answer: 2,125 thermostats per week

Key words – how many (implied) left or remain from theword eliminated

2,150 - 25 = 2,125

5. A single mother is entitled to a welfare grant of $633 per month. Ifshe works, however, part of her earnings must be applied to thisamount. In Sally Lewis’s case, $69 must be deducted. How muchmoney does Sally receive from the welfare grant?

Answer: $564 a month

Key words – how much money... deducted

$633 - $69 = $564

6. To calculate the tax charged on an item, you multiply the originalprice by the rate. If the tax rate is 9.2% and a ladder costs $59.95,how much tax is due?

Answer: $5.52 tax due

Remember you cannot use math operations with %.Change 9.2% to a decimal (D P decimal moves left).092

$59.95 × .092 = 5.5154 rounded to $5.52 (monetary unitsmust be rounded to 2 decimal places)

POSTTEST


7. When Larry’s wife was hospitalized, his co-workers wanted to showtheir support by donating some money. John gave $100, Chuckcontributed $225, Ellen gave $170, and Casey put in $55. How muchmoney did they collect?

Answer: $550

Key words-how much (not equal amounts)

100 + 225 + 170 + 55 = $550

8. Tony is paid $7.25 an hour and time and a half for overtime hours.Overtime begins after 40 hours of work in one week. Last week heworked 42.5 hours. What were his total earnings?

Answer: $317.20

Key word – total (equal amounts) but at 2 different rates

Base Rate – $7.25

Overtime Rate – $7.25 × 112

= $10.88

$7.25 × 40 = $290.00$10.88 × 2.5 = $27.20$290.00 + 27.20 = $317.20 total earnings

POSTTEST


9. To receive a $125 rebate, Teresa must place an order before January1. If she purchases a copier for $1,475 by the deadline, how muchis her net cost?

Answer: $1,350

Key word – rebate (money back from original price)

$1,475 - $125 = $1,350

10. It takes Howard 5 minutes to press and cut one needle. How manyneedles can he produce per hour?

Answer: 12 needles

Key words – how many... per hour

One hour equals 60 minutes

60 (minutes) ÷ 5 (minutes for each needle) = 12

11. A checking account contained $6,274.54. After a $385.79 checkwas drawn, what was left in the account?

Answer: $5,888.75

Key words – what was left

$6,274.54 - $385.79 = $5,888.75

POSTTEST


12. A produce plant produces 5,424 pounds of beans each day. Theplant packages the beans in 4-pound bags. How many bags dothey package each day?

Answer: 1,356 bags

Key words – how many divided equally into 4 pound bags

5,424 ÷ 4 = 1,356

13. Wecandoit, Inc. reported a loss of $17,225 in March, but in Aprilshowed a profit of $32,500. How much more did Wecandoit, Inc.make in April than in March?

Answer: $49,725

Key words – how much more, loss, profit$32,500 - $-17,225 = $49,725

<——————|———————0—————————|———>-17,225 32,500

How much more-indicates a difference which means theoperation needed is subtraction. There are 49,725 unitsbetween -17,225 and 32,500. If you set your problem up-17,225 - +32,500 and calculated $-49,725, step 4 ofproblem solving should help you find your mistake.Examine your outcome. Did the company’s earningsincrease or decrease in April?

When moving from -17,250 to 32,500 you move in apositive direction. Think about the problem. The companyincreased their profits in April indicating a gain (a positiveanswer).

POSTTEST


14. Your department employed 35 laborers in January 1996, lost 12employees in July, and regained 3 in October. How many totallaborers are employed in October?

Answer: 26 laborers

Key word – total, lost, regained

July: 35 - 12 = 23October: 23 + 3 = 26

15. The temperature on Monday morning was -2°F. By noon it hadwarmed up to 5°F. How many degrees did the temperature change?

Answer: 7°

Key word – change

5 - (-2) = 7

16. Any Company showed a profit of $12,250 dollars for the first quarter,a loss of $2,575 for the second quarter, another loss in the thirdquarter of $5,100, and a slight profit of $875 in the last quarter.What profit/loss did Any Company have for the total year?

Answer: $5,450 profit

Key words – total, profit, loss

+12,250 + (-2,575) + (-5,100) + 875 = $5,450

POSTTEST


17. One out of every 25 workers at Dean Manufacturing claimedWorker’s Compensation this year. What percent of the workers doesthis indicate have had accidents?

Answer: 4% of the workers

one out of 25 = 125

Change the fraction to a decimal ...

1 ÷ 25 = .04

... then, change the decimal to a percent.

.04 (D P) 4%

18. A manufacturer of engineered metal structures, claims that a newsystem helped them reduce man-hours by 50 hours per unit perweek. If each unit averages 200 man-hours a week, by what percentdid they reduce the number of hours per unit?

Answer: 25%

50 number of hours reduced200 total hours per week

.25 25%= =

POSTTEST


19. A company initially gave assessments to 45 applicants and filled27 positions. What percentage of these 45 applicants were hired?

Answer: 60%

27 number of applicantshired

45 total number of applicants.6=

.6 change decimal to percent 60%

20. A manufacturer of engines and clutches, increased employmentfrom 125 in 1991 to 750 in 1997. What percentage was this increase?

Answer: 600%

750 employees in 1997125 employees in 1991

6 600%= =

POSTTEST


Calculate your score counting the number of questions you answered correctly. Dividethe number of your correct answers by 20. Change the decimal answer to a percent bymoving the decimal two places to the right.

CALCULATING YOUR SCORE


Well, how did you do on the Posttest? If you scored95% or higher, you have a reasonable chance to passLevel 3 of the ACT WorkKeys® Applied Mathematicsassessment. Remember the basic steps for solvingmathematics problems. Take your time and think abouteach question, and you will do fine. But, you may wantto complete Level 4 with me before you take theassessment. Hope to see you there.

Now don’t be discouraged if you scored below 95%.There is a lot of information to remember. You can doit! And, your enhanced work skills will pay off in thelong run.

Take time to review the Workplace Problem SolvingGlossary and Test-Taking Tips provided at the end ofthis workbook. Good luck improving your work skillsand attaining your goals!

SUMMARY

You should be proud ofyour progress.


WORKPLACE PROBLEM SOLVING GLOSSARY

The following is a partial list of words that has been compiled for you to review beforetaking the ACT WorkKeys® Applied Mathematics assessment. The assessment consists ofapproximately 30 application (word) problems that focus on realistic workplace situations.It is important that you are familiar with common workplace vocabulary so that youmay interpret and determine how to solve the problems.

Annual - per year

Asset - anything of value

Budget - estimate of income and expenses

Capital - money, equipment, or property used in a business by a person or corporation

Capital gain (loss) - difference between what a capital asset costs and what it sells for

Commission - an agent’s fee; payment based on a percentage of sales

Contract - a binding agreement

Convert - to change to another form

Deductions - subtractions

Denominate number - numbers with units i.e., 5 feet, 10 seconds, 2 pounds

Depreciation - lessening in value

Difference - answer to a subtraction

Discount - reduction from a regular price

Dividend - money a corporation pays to its stockholders

Expense - cost

REFERENCE


Fare - price of transportation

Fee - a fixed payment based on a particular job

Fiscal year - 12-month period a corporation uses for bookkeeping purposes

Gross pay - amount of money earned

Gross profit - gross pay less immediate cost of production; difference in sales price ofitem or service and expenses attributed directly to it

Interest - payment for use of money; fee charged for lending money

Interest rate - rate percent per unit of time i.e., 7% per year

Liquid asset - current cash or items easily converted to cash

Markup - price increase

Measure - a unit specified by a scale, such as an inch

Net pay - take-home pay; amount of money received after deductions

Net profit (income) - actual profit made on a sale, transaction, etc., after deducting allcosts from gross receipts

Overtime - payment for work done in addition to regular hours

Per - for each

Percent off - fraction of the original price that is saved when an item is bought on sale

Product - answer to a multiplication problem

Profit - income after all expenses are paid

Proportion - an equation of 2 ratios that are equal

REFERENCE


Quotient - answer to a division problem

Rate - a ratio or comparison of 2 different kinds of measures

Ratio - a comparison of 2 numbers expressed as a fraction, in colon form, or with theword “to”

Regular price - price of an item not on sale or not discounted

Return rate - percentage of interest or dividends earned on money that is invested

Revenue - amount of money a company took in ( interest, sales, services, rents, etc.)

Salary - a fixed rate of payment for services on a regular basis

Sale price - price of an item that has been discounted or marked down

Sum - answer to an addition problem

Yield - amount of interest or dividends an investment earns

REFERENCE


REFERENCE

EDWIN’S TEST–TAKING TIPS

Preparing for the test . . .

Complete appropriate levels of the WIN Instruction Solution self-study courses. Practiceproblems until you begin to feel comfortable working the word problems.

Get a good night’s rest the night before the test and eat a good breakfast on test day.Your body (specifically your mind) works better when you take good care of it.

You should take the following items with you when you take the assessment: (1)pencils; pens are not allowed to be used; it is a good idea to have more than one pencilsince the test is timed and you do not want to waste time sharpening a broken pencillead; and (2) your calculator; be sure your batteries are strong if you do not have asolar-powered calculator and that your calculator is working properly.

Allow adequate time to arrive at the test site. Being in a rush or arriving late will likelyupset your concentration when you actually take the test.

About the test . . .

The test is comprised of approximately 33 multiple-choice questions. All test questionsare in the form of word problems which are applicable to the workplace. You will notbe penalized for wrong answers, so it is better to guess than leave blanks. You willhave 45 minutes to complete the test.

The test administrator will provide a Formula Sheet exactly like the one provided inthis workbook. You will not be allowed to use scratch paper, but there is room in yourassessment booklet to work the problems.


REFERENCE

During the test . . .

Listen to instructions carefully and read the test booklet directions. Do not hesitateto ask the administrator questions if you do not understand what to do.

Pace yourself since this is a timed test. The administrator will let you know when youhave 5 minutes left and again when you have 1 minute remaining. Work as quickly aspossible, but be especially careful as you enter numbers into your calculator.

If a problem seems too difficult when you read it, skip over it (temporarily) and moveon to an easier problem. Be sure to put your answers in the right place. Sometimesskipping problems can cause you to get on the wrong line, so be careful. You mightwant to make a mark in the margin of the test, so that you will remember to go backto any skipped problems.

Since this is a multiple-choice test, you have an advantage answering problems thatare giving you trouble. Try to eliminate any unreasonable answers and make aneducated guess from the answers you have left.

If the administrator indicates you have one minute remaining and you have someunanswered questions, be sure to fill in an answer for every problem. Your guess isbetter than no answer at all!

If you answer all of the test questions before time is called, use the extra time to checkyour answers. It is easy to hit the wrong key on a calculator or place an answer on thewrong line when you are nervous. Look to see that you have not accidentally omittedany answers.


Dealing with math anxiety . . .

Being prepared is one of the best ways to reduce math or test anxiety. Study the list ofkey words for solving word problems. If your problem does not include any keywords, see if you can restate the problem using your key words. Feeling like you knowseveral ways to try to solve problems increases your confidence and reduces anxiety.

Do not think negatively about the test. The story about the “little engine that could”is true. You must, “think you can, think you can, think you can.” If you prepareyourself by preparing properly, there is no reason why you cannot be successful.

Do not expect yourself to know how to solve every problem. Do not expect to knowimmediately how to work word problems when you read them. Everyone has to readand reread problems when they are solving word problems. So, don’t get discouraged;be persistent.

Prior to the test, close your eyes, take several deep breaths, and think of a relaxingplace or a favorite activity. Visualize this setting for a minute or two before the test isadministered.

During the test if you find yourself tense and unable to think, try the followingrelaxation technique:

1. Put feet on floor.2. Grab under your chair with your hands. (hope there are no surprises!)3. Push down with your feet and up on your chair at the same time - hold for 5

seconds.4. Relax 5 seconds (especially try to relax your neck and shoulders).5. Repeat a couple of times as needed, but do not spend the entire 45 minutes of

test trying to relax!

Studying with a partner is another way to overcome math anxiety. Encouragementfrom each other helps to increase your confidence.

REFERENCE


REFERENCE

FORMULA SHEET(≈ indicates estimate, not equal)


POP QUIZ QUESTION ANSWER KEY

1. Page 37 – any of the following questions would be correct(answers do not need to be word for word as long asthe meaning is similar)

Step 1 – Define the Problem• What am I being asked to do or find?• What information have I been given?• Is there other information that I need to know or need to

find?• Will a sketch help?• Can I restate the problem in my own words?• Are there any key words?

Step 2 – Decide on a Plan• What operations do I need to perform and in what order?• On which numbers do I perform these operations?

Step 3 – Carry Out the Plan

Step 4 – Examine the Outcome• Is this a reasonable outcome?• Does the outcome make sense in the original problem?• If I estimated the answer would it be close to the result?• Does the outcome fall outside any limits in the problem? Is it

too large or too small?

2. Page 42 – subtraction

3. Page 50 – refer to page 17 to check your answers.

4. Page 83 – 2,520 ÷ 40 = 63 drink carriers

5. Page 92 – subtraction or division

REFERENCE

Worldwide Interactive Network, Inc.1000 Waterford Place Kingston, TN 37763

Toll-free 888.717.9461Fax 865.717.9461 www.w-win.com

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Math 3 (pt 1) - Weeblyedselplus.weebly.com/uploads/1/9/7/5/19755251/applied... · 2020-01-25 · Applied Mathematics • 3 Hi, my name is EdWIN. I will be your guide through Applied