Math 100GLTextBook

8/19/2019 Math 100GLTextBook

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Math 100G/L Introduction to

Algebraand

Finance

BYU-Idaho


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MESSAGE FROM THEFIRST PRESIDENCY

Dear Brothers and Sisters:

Latter-day Saints have been counseled for many years to prepare foradversity by having a little money set aside. Doing so adds immeasurably tosecurity and well-being. Every family has a responsibility to provide for its ownneeds to the extent possible.

We encourage you wherever you may live in the world to prepare foradversity by looking to the condition of your finances. We urge you to be modestin your expenditures; discipline yourselves in your purchases to avoid debt. Payoff debt as quickly as you can, and free yourselves from this bondage. Save a littlemoney regularly to gradually build a financial reserve.

If you have paid your debts and have a financial reserve, even though it be

small, you and your family will feel more secure and enjoy greater peace in yourhearts.

May the Lord bless you in your family financial effort.

The First Presidency

(From the pamphlet ALL IS SAFELY GATHERED IN: FAMILY FINANCES published bythe Church.)


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Table of Contents

Chapter 1 Arithmetic ……….…………………………………………………………...4Section 1.1………………………………………………………………………………...5

Addition and Multiplication Facts from 1+1 to 15 × 15 Section 1.2……………………………………………………………………………..…13Rounding and Estimation; Life Plan

Section 1.3………………………………………………………………………………..18Add, Subtract, Multiply, Divide Decimals; Income and Expense

Section 1.4……………………………………………………………………………..…37Add, Subtract, Multiply, Divide Fractions; Unit Conversions

Chapter 2 Calculators and Formulas ……………………………………………52Section 2.1…………………………………………………………………………..……53

Exponents Introduction, Order of Operations, Calculator Usage Section 2.2……………………………………………………..…………………………64Variables and Formulas

Section 2.3……………………………………………………..…………………………81Formulas and Spreadsheet Usage

Chapter 3 Algebra .………………....……………………………………………………94Section 3.1……………………………………………………………………………….95

Linear Equations and Applications Section 3.2………………………………………………………………………………113

Linear Equations with Fractions; Percent Applications Section 3.3………………………………………………………………………………126Exponents Revisited; Loan Payment and Savings Equations

Chapter 4 Graphs and Charts …………………………………..………………...142Section 4.1………………………………………………………………………………143

Maps and Coordinate GraphsSection 4.2………………………………………………………………………………153

Graphing Lines and Finding Slope Section 4.3………………………………………………………………………………168

Using Slope and Writing Equations of Lines


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Chapter 1 :ARITHMETIC

Overview rithmetic

1.1Facts1.2Rounding and Estimation1.3Decimals1.4Fractions


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Chapter 1

Everyone has to start somewhere, and that start, for you, is right here.When you first started learning math, you probably learned the names for

numbers, and then you started to add: 3apples + 7apples equals how many apples? Well 10, of

course.

My guess is that you caught on to what you were doing and can now add M&M’s,coconuts, gallons of water, money etc. From the beginning I am going to assume you know howto add in your head up to 15+15. If you don’t, please make up some flash cards and get those inyour brain. It is similar to learning the alphabet before learning to read. We need the additionfacts to be available for instant recall.

Soon after addition was learned, I bet someone told you that there was a shortcut whenyou had to add some numbers over and over. For example:

3+3+3+3+3+3+3 = 21

7If you notice, there are seven 3’s.

3, seven times, turns out to be 21, so we write it as 7×3 = 21.

One of the best coincidences of the world is that 7, three times, is also 21.3×7 = 21

Such a switching works for any numbers we pick:4×5 = 20 and 5×4 = 20

3×13 = 39 and 13×3 = 39

Since we will be using the multiplication facts almost as much as we will be using the additionfacts, you need to also memorize the multiplication facts up to 15×15. Learn them well, and youwill be able to catch on to everything else quite nicely.

Section 1.1Facts


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Exercises 1.1

Section 1.1 Exercises Part A1. Make flash cards up to 15+15 and 15×15.2. Memorize the addition and multiplication facts up to 15+15 and 15×15.3. Fill out the Addition/Subtraction Monster. Time yourself. Write the time it takes on the

paper. Correct the Addition/Subtraction Monster using your flashcards.4. Fill out the Multiplication Monster. Time yourself. Write the time on the paper. Correct

the Addition/Subtraction Monster using your flashcards.


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Exercises 1.1

Addition/Subtraction Monster Name __________________

1 1 5 6 5 1 1 − 5 8 11

6 6 7 1 15 8 1 1 1 7 6 11

7 7 14 7 7 1 6 14 15 5

1 − 4 1 1 8 1 1 − 8 5 5 8 1

5 15 11 1 15 − 6 1 − 5

6 7 1 − 8 1 1 1 1 14 1 15

5 7 11 1 14 − 11 14 11 15 8

1 1 6 1 1 14 8 8 1 − 7 1 − 8

− 7 1 14 1 − 5 7 14 6 1 − 7

6 8 14 15 14 − 1 1 15 14 − 8 8 14

8 − 5 15− 11 15 − 1 15 − − 8 7 1

7 11 5 14 6 15 15 − 7 5 1 7 15

1 1 8− 6 − 5 − 6 15 − 4 15 15

Time_________


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Exercises 1.1

Multiplication Monster Name __________________ 12×13= 5×6= 5×10= 12×9= 5×9= 8×11= 5×11= 14×4=

6×6= 7×12= 15×8= 10×10= 10×7= 6×11= 6×12= 6×13=

7×7= 14×7= 7×9= 9×13= 6×14= 15×5= 11×11= 7×5=

12×4= 10×12= 8×10= 13×8= 5×5= 8×13= 5×12= 7×8=

9×9= 5×15= 9×11= 9×12= 15×6= 13×5= 9×15= 8×15=

6×7= 13×9= 8×12= 10×13= 10×14= 10×15 7×13= 11×13=

5×7= 11×12= 14×9= 11×14= 11×15= 8×9= 10×6= 8×7=

12×12= 6×10= 12×14= 8×8= 12×7= 12×8= 14×14= 12×6=

9×7= 13×14= 10×5= 7×14= 6×9= 13×7= 13×6= 9×10=

6×8= 14×15= 14×10= 12×15= 14×8= 8×14= 14×6= 10×11=

8×5= 15×11= 15×10= 15×9= 9×8= 7×10= 9×14= 13×15=

7×11= 5×14= 6×15= 15×7= 5×13= 7×15= 5×8= 7×6=

13×13= 8×6= 9×5= 9×6= 15×4= 15×15= 13×4= 14×5=

Time_________


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Exercises 1.1

Section 1.1 Exercises Part BAddition/Subtraction Monster 2

− 6 1 − 4 5 1 6 15 15− 5 8 11 1

6 6 − 7 15− 8 1 1 1 − 7 6 11 1

7 7 7 1 15− 1 1 6 14 1 1

5 11 1 1 8 1 15− 7 14− 7 8 1

5 15 11 1 6 1 5 5

6 7 11 15 8 1 1 − 5 1 14 1 15

5 7 11 1 11 11 11 14 1 − 8 8

1 1 14 − 1 14 8 8 1 − 7 1 1

15 15 1 14 1 − 5 7 14 1 − 8 6 8

5 6 14 15 6 1 1 15 14− 8 8 14

8− 5 15 − 11 1 − 15− 6 7 1

7 11 5 14 15− 6 6 1 14− 1 7 15

1 1 8 − 6 − 5 5 1 15− 4 8− 7 1

Time_________


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Exercises 1.1

Multiplication Monster 29×6= 12×4= 5×10= 6×15= 15×5= 8×11= 12×9= 14×4=

6×6= 9×7= 15×8= 10×10= 10×7= 6×11= 13×7= 5×8=

7×7= 7×12= 15×10= 9×13= 6×14= 12×13= 7×5= 13×15=

5×11= 10×12= 8×10= 15×7= 14×7= 8×13= 5×12= 7×8=

9×9= 5×15= 9×11= 9×12= 6×13= 5×5= 9×15= 8×15=

6×7= 11×15= 8×12= 13×5= 10×14= 10×15= 7×13= 11×13=

5×7= 11×12= 11×11= 11×14= 13×8= 8×9= 10×6= 5×9=

12×12= 14×9= 12×14= 8×8= 12×7= 10×13= 14×14= 12×6=

15×15= 13×14= 10×5= 7×14= 12×8= 6×8= 13×6= 9×10=

5×6= 14×15= 6×10= 12×15= 14×8= 8×14= 14×6= 10×11=

8×5= 15×11= 13×9= 15×9= 6×9= 7×10= 9×14= 7×6=

7×11= 5×14= 15×6= 6×12= 14×10= 7×15= 9×8= 7×9=

13×13= 8×6= 9×5= 5×13= 15×4= 8×7= 13×4= 14×5=

Time_________


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Exercises 1.1

Section 1.1 Exercises Part C

Addition/Subtraction Monster Name __________________

1 1 5 6 5 1 1 − 5 8 11

6 6 7 1 15 − 8 1 1 1 − 7 6 11

7 7 14− 7 7 1 6 14 15 − 5

1 − 4 1 1 8 1 1 − 8 5 5 8 1

5 15 11 1 15 − 6 1 − 5

6 7 1 − 8 1 1 1 1 14 1 15

5 7 11 1 14 − 11 14 11 15 8

1 1 6 1 1 14 8 8 1 − 7 1 − 8

− 7 1 14 1 − 5 7 14 6 1 − 7

6 8 14 15 14 − 1 1 15 14 − 8 8 14

8 − 5 15− 11 15 − 1 15 − − 8 7 1

7 11 5 14 6 15 15 − 7 5 1 7 15

1 1 8− 6 − 5 − 6 15 − 4 15 15

Time_________


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Exercises 1.1

Multiplication Monster Name __________________ 12×13= 5×6= 5×10= 12×9= 5×9= 8×11= 5×11= 14×4=

6×6= 7×12= 15×8= 10×10= 10×7= 6×11= 6×12= 6×13=

7×7= 14×7= 7×9= 9×13= 6×14= 15×5= 11×11= 7×5=

12×4= 10×12= 8×10= 13×8= 5×5= 8×13= 5×12= 7×8=

9×9= 5×15= 9×11= 9×12= 15×6= 13×5= 9×15= 8×15=

6×7= 13×9= 8×12= 10×13= 10×14= 10×15 7×13= 11×13=

5×7= 11×12= 14×9= 11×14= 11×15= 8×9= 10×6= 8×7=

12×12= 6×10= 12×14= 8×8= 12×7= 12×8= 14×14= 12×6=

9×7= 13×14= 10×5= 7×14= 6×9= 13×7= 13×6= 9×10=

6×8= 14×15= 14×10= 12×15= 14×8= 8×14= 14×6= 10×11=

8×5= 15×11= 15×10= 15×9= 9×8= 7×10= 9×14= 13×15=

7×11= 5×14= 6×15= 15×7= 5×13= 7×15= 5×8= 7×6=

13×13= 8×6= 9×5= 9×6= 15×4= 15×15= 13×4= 14×5=

Time_________


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Section 1.2

Now, you know that some arithmetic problems may get long andtedious, so you can understand why some folks choose to estimate andround numbers. Rounding is the quickest, so we will tackle that first.

In rounding, we decide to not keep the exact number that someonegave us. For example:

Rounding

If I have $528.37 in the bank, I might easily say that I have about $500. I have justrounded to the nearest hundred.

On the other hand, I might be a little more specific and say that I have about (still notexact) $530. I have just rounded to the nearest ten.Here are the places:Just to make sure you are clear on it, here is a big example:

6,731,239,465.726409

Example:Round to the nearest hundredth:

538.4691This number is right between 538.46 and 538.47

Which one is nearest? The 9 tells us that we are closer to538.47

2nd Example:Round to the nearest thousand:

783,299.4321This number is right between 783,000 and 784,000

Which one is nearest? The 2 in the hundreds tells us that we are closer to :783,000

Section 1.2Rounding andEstimation

B i l l i o n s

H u n

d r e d

M i l l i o n s

T e n

M i l l i o n s

M i l l i o n s

H u n

d r e d

T h o u s a n d s

T e n

T h o u s a n

d s

T h o u s a n

d s

H u n

d r e d s

T e n s

O n e s

T e n

t h s

H u n

d r e d

t h s

T h o u s a n

d t h s

T e n

T h o u s a n

d t h s

H u n

d r e d

T h o u s a n d

t h s

M i l l i o n

t h s


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Section 1.2

LAST EXAMPLE

Round $4,278.23 to the nearest hundred

Answer: $4,300.00

Estimation

Once rounding is understood, it can be used as a great tool to make sure that we have notmissed something major in our computations. If we have a problem like:

3,427,000× 87.3

We could see about where the answer is if we estimate first:Round each number to the greatest value you can

3,000,000× 90

Voila! Our answer will be about 270,000,000

We should note that the real answer is:299,177,100

but the estimation will let us know that we are in the right ball park. It ensures that ouranswer makes sense.

LAST EXAMPLEMultiply by rounding: 86.7 4. 86.7 ≈ 1 4. ≈ 5

Round the numbers

1 5 5 Multiply the rounded numbers together86.7 4. ≈ 5 Our answer for 86.7 4. will be about 5,000

$4,300.00

$4,278.23 $4,200.00

Decide if our number is closer to the nearest

hundred above the number or below the number

$4 78. ≈ $4 . Change our number to the one it is closer to

Estimation1. Round to the highest value.

2.Do the easy problem.


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Exercises 1.2A

Section 1.2 Exercises Part A

1. Round 3,254.07 to the nearest ten.2. Round 2,892.56 to the nearest tenth.3. Round 39,454 to the nearest ten thousand.4. Round 189 to the nearest ten.5. Round 3,250.07 to the nearest tenth.6. Round 2,892.56 to the nearest hundred.7. Round 39, 454 to the nearest ten.8. Round 189 to the nearest hundred.

Estimate the following.

9. 21 × 3250.07 10. 138.9 × 2892 11. 42 × 189

12. 369.456 3.987 13. 58 × 39 14. 351 × 44

Preparation:15. Find the monthly income for 5 different jobs and be ready to share them with your group.

Answers:1. 3,250 9. About 60,0002. 2,892.6 10. About 300,0003. 40,000 11. About 8,0004. 190 12. About 1005. 3,250.1 13. About 2,4006. 2,900 14. About 16,0007. 39,450 15. Discuss it together8. 200


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Exercises 1.2B

Section 1.2 Exercises Part B1. Round 7,254.07 to the nearest ten.2. Round 2,862.843 to the nearest hundredth.3. Round 538,484 to the nearest ten thousand.4. Round 2,892.56385 to the nearest thousandth.5. Round 189,364,529.83 to the nearest million.6. Describe what possible problems students could have with rounding.

Estimate.

9. Estimate the number of heartbeats in a lifetime:(70 beats in a minute, 60 minutes each hour, 24 hours each day, 365 days each year, 80 years)

10. Estimate the number of hairs on your head:(500 hairs covered by your thumb, maybe 120 thumbprints to cover your head)

11. Estimate the daily revenue of a local market or grocery store.(How many people enter each hour? How much do they spend? How long is it open?)

12. Estimate the amount of water needed for the members of your ward for a month.(4 liters per person per day, 30 days per month, number of members in your ward?)

13. Working with your group, find the yearly income for 10 of the jobs brought in by groupmembers.

14. Estimate the lifetime earning of one of the jobs from #14. (40 years of working)

15. Estimate monthly expenses for a family with a few children living in your area. Pleaseinclude estimates of costs for housing, transportation, food, utilities, and clothing.

16. Enter the estimates for income and expenses into a spreadsheet document.Answers:1. 7,250 9. About 2,500,000,000 (give or take a few)

2. 2,862.84 10. About 50,000 to 60,0003. 540,000 11. Completely depends on your numbers4. 2,892.564 12. Probably between 20,000L and 30,000L5. 189,000,000 13. Make sure they are all there.6. d vs. dth, lack of 1 th, any others 14. Depends on the job you selected7. About 24,000 15. Should look neat.8. About 1,200,000 16. Complete when everyone can do it.

7. 58 × 391 8. 438.9 × 2,892.07

Assignment 1.2


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Exercises 1.2C


1. Round 7,254.07 to the nearest tenth.2. Round 2,862.843 to the nearest ten.3. Round 538,484 to the nearest thousand.4. Round 139.79 to the nearest ten.5. Round 3,250.647 to the nearest hundredth.6. Round 2,892.56385 to the nearest thousand.7. Round 34,454 to the nearest thousand.8. Round 189,364,529.83 to the nearest ten million.


9. 41 × 7250.07 10. 43 × 9.07 11. 82 × 2,890

12. 639.456 6.1987 13. 58 × 391.04 14. 56,200 12

Begin “Life Plan” Portfolio Project.15. Imagine your life five years from now. Estimate one month of what you think your expensesand income will be at that time.

16. Create your own spreadsheet document to record your one month estimated expenses andincome. Remember, you are forecasting five years into the future and recording a one month estimate of your anticipated income and expenses into a spreadsheet.

Prepare for “Budget and Expenses” Portfolio Project.17. Report to your group that you have started keeping track of your income and expenses.

18. Receive reports from your group members that they have started tracking their currentincome and expenses.

Answers:1. 7,254.1 10. About 3602. 2,860 11. About 240,0003. 538,000 12. About 1004. 140 13. About 24,000

5. 3,250.65 14. About 6,0006. 3,000 15. Include any expenses you can think of.7. 34,000 16. Save it as “Life Plan”. You will submit it

to your teacher in this lesson.8. 190,000,000 17. Start your record, then report to your

progress to your group by email, phone,letter, carrier pigeon…

9. About 280,000 18. Complete when everyone has done it.


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Section 1.3

DEFINITIONS & BASICS

1) Like things – In addition and subtraction we must only deal with like things.

Example : If someone asks you5 sheep + 2 sheep =

you would be able to tell them 7 sheep.

What if they asked you 5 sheep + 2 penguins =

We really can’t add them together, because they aren’t like things.

2) We do not need like things for multiplication and division.

3) Negative – The negative sign means “opposite direction.”

Example: −5. is just 5.3 in the opposite direction

−5. 0 5.

Example : − is just in the opposite direction.Example: −7 5 −1, because they are both headed in that direction

4) Decimal – Deci is a prefix meaning 10. Since every place value is either 10 timeslarger or smaller than the place next to it, we call each place a decimal place.

5) Place Values – Every place on the left or right of the decimal holds a certain value

Arithmetic of Decimals, Positives and Negatives

LAWS & PROCESSES

Addition of Decimals

1. Line up decimals2. Add in columns3. Carry by 10’s

Section 1.3Decimals


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Section 1.3

EXAMPLE

Add. 3561.5 + 274.383561.5

+ 274.38 1. Line up decimals

3 5 6 1. 5+ 2 7 4. 3 8

5. 8 8

2. Add in columns

1

3 5 6 1. 5+ 2 7 4. 3 83 8 3 5. 8 8

3. Carry by 10’s. Carry the 1 and leave the 3.

Subtraction of Decimals

1. Biggest on top2. Line up decimals; subtract in columns.3. Borrow by 10’s4. Strongest wins.

EXAMPLE

Subtract. 283.5 – 3,476.91- 3476.91

283.5 1.Biggest on top

- 3 4 7 6. 9 12 8 3. 5

3. 4 1

2. Line up decimals; subtract in columns

3

- 3 4 17 6. 9 12 8 3. 5

3 1 9 3. 4 1

3. Borrow by 10’s. Carry the 1 and leave the 3.

3

- 3 4 17 6. 9 12 8 3. 5

- 3 1 9 3. 4 1

4. Strongest one wins .


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Section 1.3

Multiplication of Decimals

EXAMPLES

29,742×538

237,936892,26 0

+14,871,0 00 16,001,196

Next:2 2 1

29,742× 30 892,26 0

Last:4 3 2 1

29,742× 500 14,871,0 00

3. Add the piecestogether.

Multiplication of Decimals 1. Multiply each place value2. Carry by 10’s3. Add4. Right size. 1. Add up zeros or decimals2. Negatives

Start:7 5 31

29,742× 8237,936


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Section 1.3

Final example with decimals:

The only thing left is to count the number of decimal places. Wehave one in the first number and two in the second. Final answer:

-70139.278

Division of Decimals

-7414.3×9.46

444858296572 0

+667287 00

-70139278

Next:1 1 1

74143× 40 296572 0

Last:3 132

74143×900

667287 00

3. Add the pieces together .

4. Right size. Total number ofdecimal places = 3. Answer isnegative.

Start:2 21

74143× 6444858

Division of Decimals 1. Set up.

2. Divide into first.3. Multiply.4. Subtract.5. Drop down.6. Write answer.

1. Move decimals2. Add zeros

1. Remainder2. Decimal


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Section 1.3

EXAMPLES5

4298 Step 1. No decimals to set up. Go to Step 2.Step 2.We know that 8 goes into 42 about 5

times.5

4298

-40

Step 3. Multiply 5×8

Step 4. subtract .

53 4298

-4029

Step 5. Bring down the 9 to continue on.Repeat steps 2-5

Step 2: 8 goes into 29 about 3 times.

53 4298

-4029

-245

Step 3: Multiply 3×8

Step 4: subtract.

8 doesn’t go into 5 (remainder)

Which means that 429 ÷ 8 = 53 R 5or in other words 429 ÷ 8 = 53 8

5

Example:5875 ÷ 22

2587522

44

Step 2: 22 goes into 58 about 2 times.Step 3: Multiply 2×22 = 44

2587522

-44147

Step 4: Subtract.

Step 5: Bring down the next column

27 587522

-44147154

22 goes into 147 about ????times.Let’s estimate.2 goes into 14 about 7 times – try that.Multiply 22×7 = 154 Oops, a little too big


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Section 1.3

26 587522

-44147

-132 155

Since 7 was a little too big, try 6.Multiply 6×22 = 132

Subtract.

Bring down the next column.267

587522

-44147

-132155

-154 1

22 goes into 155 about ?????times.Estimate.2 goes into 15 about 7 times. Try 7

Multiply 22×7 = 154 . It worked.

Subtract.Remainder 1

5875 ÷ 22 = 267 R 1 or 221267

An example resulting in a decimal :

Write94

as a decimal:

0000.49 Step 1: Set it up. Write a few zeros, just to besafe.

.4 0000.49

-36 4

Step 2: Divide into first.9 goes into 40 about 4 times.Step 3. Multiply 4×9 = 36

Step 4 . Subtract..44 0000.49

-3640

-36 4

Step 5. Bring down the next column.Repeat steps 2-4Step 2: 9 goes into 40 about 4 times.Step 3: Multiply 4×9 = 36

Step 4: Subtract.

.444 0000.49

-3640

-3640

-36 4

Step 5. Bring down the next column.Repeat steps 2-4Step 2: 9 goes into 40 about 4 times.Step 3: Multiply 4×9 = 36

Step 4: Subtract.

This could go on forever!

Thus94

= .44444. . . which we simply write by .4

The bar signifies numbers or patterns that repeat.

Repeating decimal


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Section 1.3

Two final examples:358.4 -(.005) 296 3.1

4.358005.

3584005

Step 1. Set it up and move the decimals2961.3

00.296031 7

3584005

35

Step 2. Divide into first

Step 3. Multiply down

900.296031

279

73584005

-35

08

Step 4. Subtract

Step 5. Bring down

900.296031

-279

170

71

3584005 -35

08- 5

34

Repeat steps 2-5 as necessary

Step 2: Divide into first Step 3: Multiply down Step 4: Subtract Step 5. Bring down

95.

00.296031 -279

170-155

150716

3584005

-3508

- 5

34-30 40

Repeat steps 2-5 as necessaryStep 2: Divide into first Step 3: Multiply down Step 4: Subtract Step 5. Bring down

95.4 00.296031

-279

170-155

150-124 26

7168 3584005

-35

08- 5

34-30

40-40

00

Repeat steps 2-5 as necessaryStep 2: Divide into first

Step 3: Multiply down

Step 4: Subtract

Step 5: Bring down

95.48000.296031

-279

170-155

150-124

260-248

120


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Section 1.3

71680 3584005

-35

08- 5

34-30

40-40

00- 0

0

Repeat steps 2-5 as necessaryStep 2: Divide into first Step 3: Multiply down Step 4: Subtract

95.483000.296031

-279

170-155

150-124

260-248

120-93 27

-71,680 Step 6: Write answer 95.483 . . .

COMMON MISTAKES

Two negatives make a positive

- True in Multiplication and Division – Since a negative sign simply meansopposite direction, when we switch direction twice, we are headed back the way westarted.

Example: -(-5) = 5Example: -(-2)(-1)(-3)(-5) = - - - - -30 = -30Example: -(-40 -8) = -(- -5) = -5

- False in Addition and Subtraction – With addition and subtraction negativesand positives work against each other in a sort of tug ‘o war. Whichever one is strongerwill win.

Example: Debt is negative and income is positive. If there is more debt thanincome, then the net result is debt. If we are $77 in debt and get income of $66then we have a net debt of $11

-77 + 66 = -11

On the other hand if we have $77 dollars of income and $66 of debt, then the netis a positive $11

77 – 66 = 11

One negative in the original problem gives

a negative answer .

The decimal obviously keeps going.

Round after a couple of decimal places.


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Section 1.3

Example: Falling is negative and rising is positive. An airplane rises 307 feet andthen falls 23 feet, then the result is a rise of 284 feet:

307 – 23 = 284

If, however, the airplane falls 307 feet and then rises 23 feet, then the result is afall of 284 feet:

-307 + 23 = -284

Other examples: Discount is negative and markup or sales tax is positive.Warmer is positive and colder is negative. Whichever is greater will give you thesign of the net result.

1) Percent: Percent can be broken up into two words: “ per ” and “ cent ” meaning per hundred,or in other words, hundredths.

Example:100

7= .07 = 7%

10031

= .31 = 31%10053

= .53 = 53%

Notice the shortcut from decimal to percents : move the decimal right two places.

LAWS & PROCESSES

Converting Percents

EXAMPLES

Convert .25 to a percent.25= 25% Move the decimal two places to the right because

we are turning this into a percent.25=25%

Percents 1. If fraction, solve for decimals.2. Move decimal 2 places.3. “OF” means times.

1. Right for decimal to %2. Left for % to decimal


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Section 1.3

What is as a percent?

5 .156 5 Turn the fraction into a decimal by dividing.15625=15.625% Move the decimal two places to the right because

we are turning this into a percent5 15.65 %

Convert 124% to decimals124%=1.24 Move the decimal two places to the left because

we are turning this into a decimal124%=1.24

Solving “Of” with Percents

The most important thing that you should know about percents is that they never standalone . If I were to call out that I owned 35%, the immediate response is, “35% of what?”

Percents always are a percent of something. For example, sales tax is about 6% or 7% ofyour purchase. Since this is so common, we need to know how to calculate this.

If you buy $25 worth of food and the sales tax is 7%, then the actual tax is 7% of $25..07×$25 = $1.75

EXAMPLES

What is 25% of 64?25%=.25 Turn the percent into a decimal

. 5 64 16 Multiply the two numbers together25% of 64 is 16

What is 13% of $25?13%=.13 Turn the percent into a decimal

.1 5 . 5 Multiply the two numbers together

13% of $25 is $3.25

What is 30% of 90 feet?30%=.30 Turn the percent into a decimal

. 7 Multiply the two numbers together 30% of 90 feet is 27 feet

In math termsthe word “of”means multiply.


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28

Exercises 1.3A

Section 1.3 Exercises Part AAdd.1. 36,451

+ 2,1972. 143.29

+ .9233. 5,834,906.2

+ 54.3227

Subtract.

4. 7- (-2) = 5. -7 – 2 = 6. -13 –(-10) =

7. -18 + 5 = 8. 10 – 57 = 9. -14 – 8 =

10. 234-57

11. 19.275-74.63

12. 4,386-5,119

13. 2.35-17.986

14. 2,984- 151

15. Cost:$32.50Discount:$1.79Final Price:

16. Temp:67° FChange:18° warmerFinal:

17. Altitude: 7,380 ftFall: 3,200 ftFinal:

18. Cost:$32.50Tax:$2.08Final Price:

19. Temp: 17° CChange: 28° colderFinal:

20. Altitude:300 mRise:7,250 mFinal:

Change into a decimal.

21.52 22. 4

1 23. 83

24.91 25. 8

7 26. 61


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29

Exercises 1.3A

Divide.Example: See examples in section 1.3

27. 2347 28. 1355 29. 58911

30. 3.5604. 31. 428. 32. 2.1511.2

Change into a percent.33.

129 34. 20

19 35. 4515

Using the chart, find out how much money was spent if the total budget was $1600.

36. Insurance 37. House 38. Fun

Find the following:39. Price: $30.00

Tax rate: 6%

Tax:

40. Attendees: 2,300Percent men: 40%

Men:

41. Students: 4Number of B’s: 3

Percent of B’s:

Preparation .42. Go to providentliving.org and read the “One for the Money” and “All is Safely Gathered In”pamphlets. Be ready to share thoughts and notes with your group.

%

%

%

%

%


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30

Exercises 1.3A

Answers:1. 38,648 31. 52.5

2. 144.213 32. 72

3. 5,834,960.5227 33. 75%

4. 9 34. 95%5. -9 35. 33.3%

6. -3 36. $144

7. -13 37. $752

8. -47 38. $160

9. -22 39. $1.80

10. 177 40. 920 men

11. -55.355 41. 75%

12. -733 42. Discuss it together.

13. -15.636

14. 2833

15. $30.71

16. 85° F

17. 4180 ft

18. $34.58

19. -11° C20. 7550 m

21. .4

22. .25

23. .375

24. .125. .875

26. .16

27. 7333 or 33.428571 or 33 R328. 27

29. 11653 or 53.54 or 53 R630. 1407.5


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31

Exercises 1.3B

Section 1.3 Exercises Part BAdd.1. 153.29

+7.922

Subtract.

2. 9 - (-3) = 3. -18 – 32 = 4. -14 –(-19) =

5. 23,754- 4,151

6. 29.84-64.643

7. 4,786-5,919

8. Cost:$32.50Discount:$5.79Final Price:

9. Temp:67° FChange:28° warmerFinal:

10. Altitude: 4,380 mFall: 2,230 mFinal:


11.54 12. 9

2 13. 85

Divide.

14. 4347 15. 4536. 16. 78912

Change into a percent.

17. 127

18. 2017

19. 3015


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32

Exercises 1.3B


20. Food 21. Car 22. Fun

Find the following:23. If the price of a bicycle is $35.20, and it goes on sale for 20% off. How much money wastaken off the price?

24. In 2010, President Thomas S. Monson said that 83% of the members of the church livedwithin 200 miles of a temple. At the end of 2009, there were almost 14,000,000 members. Howmany LDS church members lived within that limit?

25. In 2014, President Thomas S. Monson said that 85% of the members of the church livedwithin 200 miles of a temple. At the end of 2013, there were just over 15,000,000 members. Howmany church members lived within that limit?

26. Discuss “One For the Money” by Elder Marvin J. Ashton. What principles are important foryour life?

Begin “Budget and Expenses” Portfolio Project27. Make sure all members of the group have seen the pattern of budget and expense reportsfound in “All is Safely Gather In” and “One for the Money.” Begin a monthly budget and record

of your expenses that will continue through the remainder of the semester. Commit to reportingto your group and receiving reports when all have created a spreadsheet titled, “Budget andExpenses.”

%

%

%

%

%


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33

Exercises 1.3B

Answers:1. 161.212

2. 12

3. -50

4. 55. 19,603

6. -34.803

7. -11.596

8. $26.71

9. 95° F

10. 2150 m

11. .8

12. .2

13. .625

14. 62

15. 755

16. 65.75

17. 58.3%

18. 85%

19. 50%20. $260

21. $182

22. $130

23. $7.04

24. 11,620,00025. 12,750,000

26. Discuss it together.

27. Submit it to your teacher later inthis lesson.


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34

Exercises 1.3C


Begin “Budget and Expenses” Portfolio Project.1. Continue to record all expenses and income for the remainder of the course in a spreadsheetdocument.

Round the following.2. Round 54,454 to the nearest thousand.3. Round 385,764,524.83 to the nearest million.


4. 71 × 3250.07 5. 538.9 × 2,892.07 6. 82 × .00000789

Add.7. 46,821

+ 3,1378. 756.29

+ .5229. 8,434.7

+54.3527

Subtract.

10. 115 - (-3) = 11. -19 – 320 = 12. -18 –(-151) =

13. 7.54

-57

14. 298.4

-64.643

15. 3,784

-5,919

16. Cost:$44.50Tax:$3.18Final Price:

17. Temp: 48° CChange: 29° colderFinal:

18. Altitude:300 mFall:2,250 mFinal:


19. 201 20. 9

4 21. 32


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35

Exercises 1.3C

Divide.

22. 4348 23. 1856 24. 68914

25. 347.5602. 26. 5536. 27. 12.17531.


4037 29. 50

38 30. 2527


31. Insurance 32. Car 33. Fun


Tax rate: 6%Tax:

35. Attendees: 2,413Percent men: 39%Men:

36. Students: 15Number of B’s: 11Percent of B’s:

%

%

%

%

%


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36

Exercises 1.3C

Answers:1. Titled “Budget and Expenses” and save

document on your computer. You will turn it into your teacher in this lesson.

31. $108.32

2. 54,000 32. $203.10

3. 386,000,000 33. $135.404. About 210,000 34. $4.52

5. About 1,500,000 35. 941 men

6. About .00064 36. 73.3%

7. 49,958

8. 756.812

9. 8489.0527

10. 118

11. -339

12. 133

13. -49.46

14. 233.757

15. -2135

16. $47.68

17. 19° C

18. -1950m19. .05

20. .4

21. .6

22. 54.25

23. 30.83

24. 49.214…25. 2817.35

26. 921.6

27. 564.903…

28. 92.5%

29. 76%

30. 108%


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37

Section 1.4


1) Numerator – the top of a fraction2) Denominator – the bottom of the fraction3) Simplify – Fractions are simplified when the numerator and denominator have no factors in

common.4) One – any number over itself = 1.5) Common Denominators – Addition and subtraction require like things. In the case of

fractions, “like things” means common denominators.6) Prime Factorization – Breaking a number into smaller and smaller factors until it cannot be

broken down further.

LAWS & PROCESSES

Prime Factorization – One of the ways to get the Least Common Denominator for adding andsubtraction fractions that have large denominators is to crack them open and see what they aremade of. Scientists get to use a scalpel or microscope. Math guys use prime factorization.

Addition of Fractions

1. Common Denominator

2. Add numerators3. Carry by denominator

EXAMPLE

Add Step 1. The least common multiple of 4 and 2 is a 4, so wereplace the with an equivalent fraction, which is .

Step 2. Now that the denominators are the same, add thenumerators . Step 3. Carry the denominator across.

1. Observation2. Multiply the denominators3. Prime factorization

Section 1.4Fractions


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Section 1.4

Changing from mixed numbers to improper fractions:

Changing them back again:

Subtraction of Fractions

1. Biggest on top2. Common Denominator; Subtract numerators

3. Borrow by denominator4. Strongest wins

EXAMPLE

Do this:

3 is bigger, so put it on top.

- 3

The common denominator is 9,

so change the to a .

- 2

- 2

Subtract the numerators. Borrow by denominator asneeded.

1. Observation2. Multiply the denominators3. Prime factorization


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39

Section 1.4

Multiplication of Fractions

EXAMPLES

For multiplication don’t worry about gettingcommon denominators Multiply the numerators straight across

Multiply the denominators straight across

Multiplication of Fractions 1. No common denominators

2. Multiply Numerators3. Multiply Denominators


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Section 1.4

Division of Fractions

EXAMPLESDivide

Turn the fractions into improper fractions

Keep the first fraction the sameChange the division sign to a multiplicationsignFlip the second fraction’s numerator anddenominator Multiply straight across the numerator anddenominator

Divide

Turn the fractions into improper fractions

KEEP the first fraction the same

Change the division sign to a multiplicationsignFlip the second fraction’s numerator anddenominator Multiply straight across the numerator anddenominator

Division of Fractions 1. Improper Fractions

2. Keep it, change it, flip it.3. Multiply.


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Section 1.4

Now that you have had a little time to multiply fractions together and simplify them, youmay have noticed one of the slickest tricks that we can do with fractions, and that is that we canactually do the simplification before we multiply them. Take for example:0

Now, we can do this the normal way or we can try to notice if there is anything that wewill be simplifying out later . . . and do that simplification before we multiply:

Normal method:

and now we try to simplify which probably took quite a while to get.So,

What I was hoping to show is that the same answer was obtained and the same cancelling

was done, but if you are able to see it before you multiply, then you will be able to simplify in amuch simpler way. Here is another example:

the 4 and the 8 can simplify before we multiply:

This may seem like just a convenient way to make the problem go a bit quicker, but it does muchmore than that. It opens the door to a much larger world. Here is an example. If we travelled 180miles on 12 gallons of gas, then we calculate the mileage by = 15 miles per gallon.Carrying that example just a bit further, what if gas were $3.2 per gallon? We canactually find how many miles we can drive for one dollar:

.

= 4.7 miles per dollar.

New and improved slick method:

and we try to see if any factors will cancelahead of time

2×5 3×7

3×3×7 5×11


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Section 1.4

Another example:Carpet is on sale for 15 dollars per square yard. How much is that in dollars per square

foot (9 ft 2 per yd 2)?Now, knowing that we will be able to cancel anything on the top with anything that is the

same on the bottom we write the multiplication so the yd 2 will cancel out, leaving us with dollars

per ft2

: Then cancel the yd 2: = dollars per square foot= $1.67 per square foot.

One more example:

A rope costs $15 for 8 feet. How much does is cost per inch?We want to get rid of feet and get inches, so we write the multiplication: = =

$.156 or 15.6 cents per inch.

Here are a few numbers that will help you with the conversions:12 in = 1 foot16 oz = 1 pound60 seconds = 1 minute1000watts = 1 kilowatt

1 yd = 3 ft60 minutes = 1 hour1 yd2 = 9 ft 2

And also some exchange rates with the American dollar as they were sometime in 2010:1 Mexican Peso = $0.08

1 Euro = $1.301 British Pound = $1.501 Brazilian Real = $0.55

1.6663 00.5

-32 0

-1820

-18

.156232 00.5

-3 2180

-160200

-19280


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43

Exercises 1.4A

Section 1.4 Exercises Part AFind 4 different names for each fraction:

1.73 2. 3

2 3. 117 4. 9

4

Simplify each fraction.

5.5236 6. 36

27 7. 5616

8.1210 9. 45

15 10. 280120

Create each fraction with a denominator of 36.11.

61 12. 9

5 13. 1210

Add or Subtract. Simplify.

14. =+32

52 15. =+ 8

541 16. =− 25

3307

17. =+127

31 18. =+ 6

543 413 19. =− 5

1107 39

Example:

113

...000,11000,3

,11030

,5515

,4412

,339

,226

,113

Example:

1413

146

147

73

21

=+

=+

Example:

41

83 135 −

- 4113

835

- 8213

835

- 81012

835

- 877

Swap to subtract.Answer is negative

Common denominator Borrow from the 13 .


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44

Exercises 1.4A

20. =−76

149 63 21. =+ 3

272 94 22. =− 4

385 912

Fill out the table.Mixed Improper

23.987−

24.513

25.843

26.451

Find the multiplicative inverse or reciprocal of each number.

27.74 28. 9

2 29. - 107 30. 8

7

31. - 65 32. 13 33. 42

13 34. 37

Divide.

35. =÷31

52 36. =÷ 8

341 37. =÷ 8

365

38. =÷127

83 39. =÷ 6

143 72 40. =÷ 3

275 35

41. =÷109

547 42. =÷ 3

287 9 43. =÷ 8

3612

Preparation .44. If you drive 280 miles on 12 gallons of gas, how many miles per gallon do you get? 45. If you drive 280 miles on 12 gallons of gas, and gas is $3.20 per gallon, how many miles perdollar do you get?

Example:

85

58

Example:=÷

54

832

=×4

5

8

32 Multiply by reciprocal

=×45

819 Change to improper fraction

=×45

819

3295 or 32

312 Multiply straight across.


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45

Exercises 1.4A

Answers:1. ...,,,, 49212812219146 others 31. 56− or 511− 2. ...,,,, 181215109664 others 32. 131 3. ...,,,, 5535442833212214 others 33. 1342 or 1333

4. ...,,,, 632836162712188 others 34. 73 5. 139 35. 56 or 511 6. 43 36. 32 7. 72 37. 920 or 922 8. 65 38. 149 9. 31 39. 8633 10. 73 40. 77120 or 77431

11. 366 41. 326 or 328 12. 3620 42. 23221 13. 3630 43. 952 or 975 14. 1511 or 1516 44. Discuss it together.

15. 87 45. Discuss it together.

16. 15017 17. 1211 18. 12718

19. 216 20. 1433− 21. 212013 22. 872 23. 971− 24. 516 25. 835 26. 27. 47 or 431 28. 29 or 214 29. 710− or 731− 30. 78


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46

Exercises 1.4B

Section 1.4 Exercises Part BCreate each fraction with a denominator of 24.

1.32 2. 12

7 3. 4840

Add or Subtract. Simplify.

4. =+72

52 5. =+ 6

575 67 6. =− 5

385 92


7.952−

8. 1157

Find the multiplicative inverse or reciprocal of each number.

9.53 10. 9

43 11. - 125 12. 7

Divide.

13. =÷35

72 14. =÷ 2

185 4 15. - =÷ 7

5732


16.91 17. 8

7 18. 61

Change into a fraction and simplify.

19. .5 20. .7 21. .45

22. .52 23. .75 24. .6

Example.12

.12 = 12 (100 th) = 10012 = 25

3 simplify


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47

Exercises 1.4B

Convert the following units.Example: Flour costs $7.00 for 20 pounds. How many ounces per dollar?

Solution:

45.71 ounces per dollar

25. If a heart beats an average of 70 beats per minute, how many beats per day is that?

26. Cereal costs $4.50 for 2 pounds. How much does it cost per ounce?

27. Fishing line costs $.02 per foot. How much would 200 yards cost?

28. I was able to drive 250 miles on 15 gallons of gas. If gas costs $3.10 per gallon, how many

miles can I drive per dollar?29. If my sprinkler sends out 5 gallons per minute, and if water costs $0.65 per 1000 gallons,

how much does watering my lawn cost per hour?

30. How many Pesos are equal to 5 Euros? (1 Mexican Peso = $0.08, 1 Euro = $1.30)

31. How many Reais (plural for Real) are equal to 7 Pounds? (1 Brazilian Real = $0.55, 1 British

Pound = $1.50)

Scripture Connections

32. Convert the fraction in Mosiah 11:3, which King Noah required of his people, to a percent

tax rate.

33. In Alma 11:5-18, the Nephite money system is given. Use verses 8-9 to find how many

senines of gold make a shum.

34.Create a visual chart for all arithmetic of decimals. Use plenty of examples.

35. Create a visual chart for all arithmetic of fractions including Unit Conversions.


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48

Exercises 1.4B

Answers:1. 2416 31. 19.09 Reals

2. 2414 32. 20%

3. 2420 33. 4 senines per shum

4. 3524 34. Part of Portfolio5. 422314 35. Part of Portfolio

6. 40396− 7. 923− 8. 1125 9. 35 10. 319

11. 512− 12. 71 13. 356 14. 365 15. - 523 16. .1

17. .875

18. .16

19. 21 20. 107 21. 209 22. 2513 23. 43 24. 53 25. 100,800

26. $0.14 per ounce

27. $12.00

28. 5.38 miles per dollar

29. $0.20 per hour

30. 81.25 Pesos


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49

Exercises 1.4C

Section 1.4 Exercises Part CExam 1 ReviewExercises

Estimate the product (round to the greatest value, then multiply).1. 2,589,000×59.34 2. .005608×.07816 3. 3.847×2,564

Add.4. 36,841

+ 249.75. 723.3

+ 39.76.

1413

149 516 + =

Subtract.

7. Temp: -35.5° FChange: 13.4° warmerFinal:

8. -8 – (-11) = 9. =−76

74 113

Multiply.

10. Cost: $35.20Quantity: 17Total:

11. 369×(-23) = 12. =× 121154

Add or Subtract. Simplify. 13. =+

95

23 14. =+ 14

51211 15. =− 6

5185

16. =−97

61 615 17. =+ 8

1109 135 18. =− 14

294 912


19.753−

20.6

59

Divide.21.

18598

22. =÷

32

98 4 23. ( )=−÷ 54437


24. 125 25. 97 26. 72

Change into a fraction and simplify.

27. .3 28. .055 29. .375


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50

Exercises 1.4C

Divide.

30. 4857 31. 7813 32. 67343

33.31.475.

34.4.5620004.

35. A dishwasher uses about 1400 watts of power. If the power company charges 9 cents perkilowatt-hour, how much does it cost to run a dishwasher for 16 hours in the month?

36. I bought 8 yards of rope for $9.84. How much did it cost per foot?


2524 38. 40

36 39. 5017


40. Car 41 House 42 Food

Find the following:43. Price: $45.20Tax rate: 7%Tax:Final Price:

44. Attendees: 239Percent men: 29%Men:

45. Price: $15.30Discount: 30%Amount of discount:Final Price:

46. Round to the nearest ten: 583.872

%

%

%

%

%


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51

Exercises 1.4C

Answers:1. About 180,000,000 31. 31260 or 260.32. About .00048 32. 432815 or 15.65116…3. About 12,000 33. 94.62

4. 37,090.7 34. 1,406,0005. 763 35. $2.02

6. 7422 36. $0.41 per foot

7. -22.1° F 37. 96%

8. 3 38. 90%

9. 7511 39. 34%

10. $598.40 40. $448

11. -8,487 41. $1504

12. 1511 42. $640

13. 1812 43. $3.16, $48.36

14. 84231 44. 69 men

15. 95− 45. $4.59, $10.71

16. 1878 46. 580

17. 40119 18. 63193

19. 726− 20. 659 21. 513 or 516 22. 214 23. - 16119 or - 16155 24. .416

25. .7

26. .285714

27. 103 28. 20011 29. 83 30. 7269 or 69.285714


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52

Section 2.1

Chapter 2 :CALCULATORS andFORMULAS

Overview 2.1Exponents and Calculator Usage2.2Variables and Formulas

2.3More Variables and Formulas - Excel

Note to student: Beginning with this Chapter, unless specifically requested,answers need not be in a specific form; equivalent answers are acceptable.For example, exercise 2.2A, #1 has 6 as the answer; -6.5, − , -650%,or any other equivalent answer is acceptable.


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53

Section 2.1

While we are on multiplication, did you know that there is some short hand? Rememberwhen we started multiplication we did:

6+6+6+6+6+6+6+6+6 = 54 but we did it a bit shorter

99×6 = 54

There is a way to write multiplication in shorthand if you do the same thing over and over again:2×2×2×2×2×2×2 = 128

7For the shorthand we write 2 7 = 128.

That little 7 means the number of times that we multiply 2 by itself and is calledand exponent; sometimes we call it a power . Here are a couple more examples:

53= 125 7 2 = 49 2 4 = 16

Pretty slick. You won’t have to memorize them . . . yet, but you should be familiar enough withthem to be able to recognize them.

Some of the easiest to calculate are the powers of 10. Try these:

104= 10,000 10 8 = 100,000,000 10 3 = 1,000

EXAMPLE

Evaluate 7 4

7 7 7 7 7 49 × 7 × 7

343 × 72401

Answer: 2401

Set up the bases, and then multiply each couple inturn.

Section 2.1Exponents


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54

Section 2.1

Order of Operations The last small note to finalize all your abilities in arithmetic is to make sure you know

what you need to do when you have multiple operations going on at the same time. For example,

2 + 3 × 4 – 5

If you were to read that from left to right you would first add the 2 and the 3 to get 5 andthen multiply by 4 to get 20 and then subtract 5 to get 15.

Unfortunately, that doesn’t jive with what we have learned about what multiplication is.Remember that multiplication is a shorthand way of writing repeated addition. Technically wehave:

2 + 3 × 4 – 5 =2 + 4 + 4 + 4 – 5 = 9.

Ahh, now there is the right answer. It looks like we need to take care of the multiplicationas a group, before we can involve it in other computations. Multiplication is done beforeaddition and subtraction .

Here is another one:4 × 3 2 – 7 × 2 + 4

Now remember that exponents are shorthand for a bunch of multiplication that is hidden, so weneed to take care of that even before we do multiplication:

4 × 3 2 – 7 × 2 + 4 = Take care of exponents 4 × 9 – 7 × 2 + 4 = Take care of multiplication

36 – 14 + 4 = Add/Sub left to right. 22 + 4 = 26.

Now division can always be written as multiplication of the reciprocal, so make sure you

do division before addition and subtraction as well.Look at that. We have established an order which the operations always follow, and we

need to know it if we are to get the answers that the problem is looking for:1st – Exponents2nd – Multiplication and Division (glues numbers together)3rd – Addition and Subtraction (left to right)

Parentheses can change everything. We put parentheses when we intend on grouping (or gluing)numbers together manually. Though they all have the same numbers and operations, see thedifference between these:

52542236322632 2

−=−

=÷×−

=÷×−

( )

1601622232422182

26322

2

−=−

=÷−

=÷−

=÷×−

( )

182362361

2632 2

−=÷−

=÷×−

=÷×−

( )( )( )

1282256216

2182

2632

2

2

2

=÷

=÷−

=÷−

=÷×−


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55

Exercises 2.1A

Section 2.1 Exercises Part ACalculator Usage Assignment

On this assignment, you should use your calculator . Become familiar with it. It isnow your friend!

Estimate the product (round to the greatest value; then multiply).1. 75,800×49.34 2. .004208×.06916 3. 4.447×7,164

Add.4. 37,291

+ 348.235. 5.871

+ 39.76.

235

239 517 + =

Subtract.7. Temp: 85.3° F

Change: 130.4° colderFinal:

8. -5 –3 = 9. =−118

114 1523

Multiply.10. Cost: $38.40

Quantity: 27Total:

11. 441×29 = 12. - =× 1116

52

Find.13. 37= 14. 272= 15. 117=

Add or Subtract. Simplify. 16. =+

94

43 17. =+ 10

785 18. =− 9

7158

19. =−94

81 714 20. =+ 8

1109 195 21. =− 16

385 54


22.1147

23.25−

Divide.24.

187

1211

25. =÷

21

65 4 26. =÷ 8

3857


27.117 28. 5

3 29. 92


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56

Exercises 2.1A

Change into a fraction and simplify.30. .07 31. .44 32. .625

Divide.

33. 3437 34. 796 35. 627357

36. 731.45. 37. 4.967004.

Evaluate38. 5 − 8 39. 5− 8 40. 5 − 4 8

41. Change 60 miles per hour into feet per second. (5280 feet = 1 mile)

Change into a percent.42. 30

28 43. 5741 44. 10037


45. Fun 46. Insurance 47. Food


Tax rate: 7%Tax:Final Price:

49. Attendees: 48Percent kids: 25%Kids:

50. Students: 30Number of A’s: 24Percent of A’s:

%

%

%

%

%


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57

Exercises 2.1A

Answers:1. About 4,000,000 31. 2511 2. About .00028 32. 85

3. About 28,000 33. 494. 37,639.23 34. 6113 or 13.165. 45.571 35. 110.0526…

6. 231422 36. 9.462

7. -45.1° F 37. 241,850

8. -8 38. 0

9. 1177 39. 20

10. $1,036.80 40. -7

11. 12,789 41. 88 feet per second12. - 5532 42. 93.3%

13. 2187 43. 71.9%

14. 729 44. 37%

15. 19,487,171 45. $316.81

16. 3671 46. $219.33

17. 40131 47. $414.29

18. 4511−

48.$26.64, $407.14

19. 72496 49. 12 kids

20. 40125 50. 80%

21. 169− 22. 1181 23. 212− 24. 1452 or 1433 25. 275

26. 3120 or 361 27. .63

28. .6

29. .2

30. 1007


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58

Exercises 2.1B

Section 2.1 Exercises Part BAdd.1. 57,831

+ 348.232. 4.83

+ 39.73. 11

5119 814 + =

Subtract.4. Temp: -85.3° F

Change: 130.4° colderFinal:

5. -5 –53 = 6. =− 218

214 1523

Multiply.7. Cost: $38.40

Quantity: 527Total:

8. - =× 1415

52

Find.9. 35 = 10. 372 = 11. (5.8)3 =

12. (2.38) 2 = 13. (1.07) 27 =

14. In a family history chart, there are 2 parents in the first generation of ancestors, 4grandparents in the second generation, 8 people in the third, how many direct ancestors are in the14 th generation of ancestors?

15. If I place 2 cents on the first square of a chess board, 4 cents on the second square, and keepdoubling the amount on each square, how much money will be on the 30 th square?


16.325

17.2

57−

18. A product costs $7 for 20 pounds. How much is that in cents per ounce?19. Change 17 Euros into pesos. (1 Mexican Peso = $0.08, 1 Euro = $1.30)20. Change 60 miles per hour into feet per second. (5280 feet = 1 mile)


3524 22. 64

72 23. 200014

Using the percentages, find out how much money was spent if the total budget was $2437.24. Fun: 12.3% 25. Insurance: 7.9% 26. Food: 38%




29. Students: 250Number of A’s: 147Percent of A’s:


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59

Exercises 2.1B

30. For a savings account that begins with $100 and has a 5% interest rate, fill out the followingtable:

Time Beginning Balance Interest earned Ending Balance1st year 100 .05 × 100 = 5 105

2nd

year 105 .05 × 105 = 5.25 110.253 110.25 .05 × 110.25 =5.51 115.764 115.7656789101112

31. For a savings account that begins with $100 and has a 6% interest rate, fill out the followingtable:

Time Beginning Balance Ending Balance1st year 100 100 × 1.06 = 1062nd year 106 106 × 1.06 = 112.363 112.36 112.36 × 1.06 = 119.104 119.1056789101112

32. Discuss in your group why multiplying by .05 and then adding to the balance is the same asmultiplying the balance by 1.05.

33. If a savings account started at $100 and earned 7% per year, how much would be in theaccount at the end of 12 years?

34.If a savings account started at $100 and earned 7% per year, how much would be in theaccount at the end of 22 years?

35.How can exponents be used to find the balance after many years?


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60

Exercises 2.1B

Answers:1. 58,179.23 27. $33.64; $514.14

2. 44.53 28. 97 kids

3. 29. 58.8%

4. -215.7° F 30. 12 year end balance - $179.59($179.60 also acceptable)

5. -58 31. 12 year end balance - $201.22($201.23 also acceptable)

6. 7 32. 1 adds in the beginning balance and.05 adds in the 5%

7. $20,236.80 33. $225.22

8. - 34. $443.04

9. 243 35. #34 can be done by 100 × (1.07) 22

10. 1,369

11. 195.112

12. 5.6644

13. 6.214

14. 16,384

15. $10,737,418.24

16. 17. - 8 18. 2.19 cents per ounce19. 276.25 Pesos

20. 88 feet per second

21. 68.6%

22. 112.5%

23. 0.7%

24. $299.75

25. $192.52

26. $926.06


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61

Exercises 2.1C

Section 2.1 Exercises Part C1. Find three different places to save your money. Report the interest rates to your group, andreceive their reports.

Find.

2. 45= 3. 872= 4. (2.7)5=

5. (5.38) 2 6. (1.06) 25 7. (1.11) 13


8.525

9. 337−

10. If I place 1 cent on the first square of a chess board, 2 cents on the second square, and keepdoubling the amount on each square, how much money will be on the 20 th square?

11. A product sells for $2.50 per square foot. How much is that per square yard?

12. Change 400 Pesos into Pounds. (1 Mexican Peso = $0.08, 1 British Pound = $1.50)

13. Change 50 miles per hour into feet per second. (5280 feet = 1 mile)

Change into a percent.14. 8

57

15. 74

1 6

16.

15

Using the percentages, find out how much money was spent if the total budget was $287.

17. Fun – 17.3% 18. Insurance – 6% 19. Food – 84%





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62

Exercises 2.1C

22. For a savings account that begins with $350 and has a 5% interest rate, fill out the followingtable and place the entries in the “Life Plan” spreadsheet on Sheet 2:

Time Beginning Balance Ending Balance1st year 350 350 × 1.05 = 367.50

2nd

year 367.503456789101112

23.If a savings account started at $300 and earned 7% per year, how much would be in theaccount at the end of 22 years?

24. For a savings account that begins with $100 and has a 6% interest rate and to which you areable to add $25 per year, fill out the following table and place it on Sheet 2 of your Life Planspreadsheet:

Time Beginning Balance Ending Balance1st year 100 100 × 1.06 + 25 = 1312nd year 131 131 × 1.06 + 25 = 163.863 163.86 163.86 × 1.06 + 25 =456789101112

25. If a savings account started at $200 and earned 7% per year, how much would be in theaccount at the end of 12 years if you are able to add $40 per year?


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63

Exercises 2.1C

1. Complete when all reports aredone.

2. 1024

3. 7569

4. 143.4895. 28.944

6. 4.29

7. 3.88

8. 9. −1 10. $5,242.88

11. $22.50 per square yard

12. 21.33 pounds

13. 73.3 feet per second

14. 66.7%

15. 54.4%

16. .02%

17. $49.65

18. $17.22

19. $241.0820. $5.63; $86.03

21. (135.8) 136 kids

22. $628.55

23. $1329.12

24. $622.97

25. $1,165.98


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64

Section 2.2

Variables and Formulas


1) Variables: These symbols, being letters, actually represent numbers, but the numbers canchange from time to time, or vary. Thus they are called variables.

Example: Tell me how far you would be walking around this rectangle.24 ft

15 ft 15ft

24 ft

It appears that to get all the way around it, we simply add up the numberson each side until we get all the way around.

24+15+24+15 = 78.

So if you walked around a 24ft X 15ft rectangle, you would havecompleted a walk of 78 ft. I bet we could come up with the pattern forhow we would do this all of the time.

Well, first of all, we just pick general terms for the sides of therectangle:

length

width width

length

Then we get something like this:

Distance around the rectangle = length + width + length + width

Let's try and use some abbreviations. First, “ perimeter ” means“around measure”. Substitute it in:

Perimeter = length + width + length + width

Let's go a bit more with just using the first letters of the words:P = l + w + l + w

Notice now how each letter stands for a number that we could use. The number canchange from time to time. This pattern that we have created to describe all cases is called aformula .

Section 2.2Variables andFormulas


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65

Section 2.2

2) Formula: These are patterns in the form of equations and variables, often with numbers,which solve for something we want to know, like the perimeter equation before, or like:

Area of a rectangle: A = B × H

Volume of a Sphere: Pythagorean Theorem: Through the same process we can come up with many formulas to use. Though it has all

been made up before, there is much to gain from knowing where a formula comes from and howto make them up on your own. I will show you on a couple of them.

Distance, rateIf you were traveling at 40mph for 2 hours, how far would you have traveled? Well, most

of you would be able to say 80 mi. How did you come up with that? Multiplication:(40)(2) = 80

(rate of speed) ⋅ (time) = distanceor in other words:

rt = d where r is the rate

t is the timed is the distance

PercentageIf you bought something for $5.50 and there was an 8% sales tax, you would need to find

8% of $5.50 to find out how much tax you were being charged..44 = .08(5.50)

Amount of Tax = (interest rate) ⋅ (Purchase amount)or in other words:

T = rPWhere T is tax

r is rate of taxP is the purchase amount.

InterestThis formula is a summary of what we did in the last section with interest. If you invested

a principal amount of $500 at 9% interest for three years, the amount in your account at the endof three years would be given by the formula:

A = 500(1.09) 3 = $647.51


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66

Section 2.2

A = P(1 + r) Y where A is the Amount in your account at the end

P is the principal amount (starting amount)r is the interest rateY is the number of years that it is invested.

Temperature ConversionMost of us know that there is a difference between Celsius and Fahrenheit degrees, but

not everyone knows how to get from one to the other. The relationship is given by:

C =95 (F – 32)

where F is the degrees in FahrenheitC is the degree in Celsius

MoneyIf you have a pile of quarters and dimes, each quarter is worth 25¢ (or $.25) and each

dime is worth 10¢ ($.10), then the value of the pile of coins would be:

V = .25q + .10dwhere V is the Total Value of money

q is the number of quartersd is the number of dimes

3) Common Geometric Formulas : Now that you understand the idea, these are some basicgeometric formulas that you need to know:

l

wRectangle

P = 2 l + 2w

A = lw

P is the perimeter

l is the length

w is the width

A is the Area


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67

Section 2.2

ba

h

Parallelogram

P = 2a + 2b

A = bh

P is the perimeter

a is a side length

b is the other side length

A is the Area

h is the height

b

a h d

B

Trapezoid

P = b+a+B+d

A =21 h(B+b)

P is perimeter

b is the shorter base

B is the longer base

a is a legd is a leg

A is the Area

h is the height

hbTriangle

P = s 1+s2+s3

A =21 bh

P is the perimeter

s is a sideA is the Area

b is the base

h is the height

b

c

aTriangle

a + b + c = 180°

a is one angle

b is another angle

c is another angle


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68

Section 2.2

H

w

l

Rectangular Solid

SA =2 lw+2wh+2 lh

V = lwh

SA is the Surface Area

l is the length

w is the width

h is the height

V is volume

r

Circle

C = 2 π r

A = π r2

C is the Circumference orPerimeter

π is a number, about3.14159 . . . it has a button

on your calculatorr is the radius of the circle

A is the area inside thecircle.

r

h

Cylinder

LSA = 2 π rh

SA =2 π rh+2π r2

V = π r2h

LSA is Lateral SurfaceArea or area just on thesides

π is a number, about

3.14159 . . . it has a buttonon your calculator

r is the radius of the circle

h is the height

SA is total surface area

V is Volume


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69

Section 2.2

h l

r

Cone

LSA = π rl

SA = π r2+ π rl

V =31 π r2h

LSA is Lateral SurfaceArea or the area just on thesides

π is a number, about

3.14159 . . . it has a buttonon your calculator

r is the radius of the circle

h is the heightl is the slant height

SA is total surface area

r

Sphere

SA = 4 π r2

V =34 π r3

SA is the surface area

π is a number, about3.14159 . . . it has a buttonon your calculator

r is the radius

V is the Volume


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70

Exercises 2.2A

Section 2.2 Exercises Part AAdd or Subtract. Simplify.

1. =−83

87 136 2. =+ 4

3125 1877 3. =− 15

265 9721

Divide.4. 574.97.3 5. 7.2546000 6. 65.37008.

7.If a wood floor costs $4.50 per square foot, how much is that per square yard?

8. How much does it cost to run a 700 watt microwave for 17 hours if the powercompany charges 12 cents per kilowatt-hour?


Tax rate: 5%Tax:Total Price:

10. Price: $2,736.00Percent off: 35%Amount saved:Final Price:

11. Birds: 140Black : 47Percent of black birds:

Evaluate the following:12. )9(834 −⋅ 13. pd ⋅⋅⋅ 75 14. )45(2)93(5 3 +⋅−−

15. 45(7.8) 16. 273 ⋅⋅⋅ m 17 2(32)+5(4)+8 ⋅m

Find the perimeter of the following shapes:

18.17

11 19

t+3 8

19.14

19k-12

20. 15

95

13r

Evaluate the following when m = 3, n = 7, t = 15, and a = 4.

21. 3t - 7 22. 2(n+9) 23.a283 ⋅ + m2


71/186

71

Exercise 2.2A

24. 12 – a 3 25. m – 12 26. 2n – 3a + 5t

Use the formula for distance, rate and time to calculate the distance.

27. r = 7t = 15d =

28. r = 55t = 7.2d =

29. r = 45t = 3

12 d =

Use the formula for angles in a triangle to calculate the measure of the remaining angle.

30. a = 73°b = 24°c =

31. a = 38°b =c = 59°

32. a =b= 24°c= 48°

Use the formulas for Money totals (you may have to make up your own) when q stands forquarters (1 quarter = $0.25), d for dimes (1 dime = $0.10), n for nickels (1 nickel = $0.05)and p for pennies (1 penny = $0.01).

33. q = 9d = 12V =

34. p = 19d = 17V =

35. n = 37q = 23V =

Use the formulas for Temperature Conversion.

36. F = 75°C =

37. F = 15°C =

38. F = -23°C =

Preparation:

39. If the formula for area of a circle isA=π r2

What is the area of a circle with radius 7?

40. Where did π come from? (Try finding out using dictionaries or the internet)

Example:r = 3t = 14d =

Formula is found in section 2.3: rt = d3(14) = d42 = d


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72

Exercises 2.2A

Answers:1. 216− 31. 83°

2. 61195 32. 108°

3. 10375− 33. $3.45

4. 2.5876 34. $1.895. .04245 35. $7.60

6. 4,706.25 36. 23.9° C

7. $40.50 per square yard 37. -9.4° C

8. $1.43 38. -30.6° C

9. $1.97 and $41.45 39. Discuss together.

10. $957.60 and $1,778.40 40. Discuss together.

11. 33.6%

12. -60

13. 35dp

14. -102

15. 351

16. 42m

17. 38 + 8m or 8m + 38

18. 58 + t or t + 58

19. k + 21 or 21 + k20. 42 + r or r + 42

21. 38

22. 32

23. 30

24. -52

25. -9

26. 77

27. 105

28. 396

29. 105

30. 83°


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73

Section 2.2

Combining, Simplifying, and the Distributive Property

TO SIMPLIFY, ADD OR SUBTRACT ALL THINGS THAT ARE LIKE

Example : If someone asks you5 sheep + 2 sheep = ?

you would be able to tell them 7 sheep.

What if they asked you 5 sheep + 2 penguins = ?We really can’t add them together, because they aren’t like things.

It works the same way with variables. Just think of “sheep” and “penguins” in thisexample as variables. In fact, let’s say s stands for sheep, and p stands for penguins. We can re-write these two equations using variables:

5 sheep + 2 sheep = 7 sheep5s + 2s = 7s

5 sheep + 2 penguins = 5s + 2p

So adding and subtracting like terms works the same way with variables as it does withsheep, penguins, fractions with common denominators, and other quantities with like terms.

Distributive Property:Looking at how the problem 2 · 3412 is done by hand, we can see that the 2 “jumps” in

and multiplies each piece of the 3412:

Multiplication can be done by multiplying one small piece at a time, like this:

7(13) = 7(10 + 3) = 70 + 21 = 91

This ability of numbers to “jump in” is called the Distributive Property and works with allnumbers. So, it must work with variables as well. This is how we can distribute numbers and getrid of parentheses:

7(x + 3) = 7x + 21

3412× 26824


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74

Section 2.2

Simplify 3x + 9x – 7y

3x + 9x – 7y12x – 7y Combine like terms

Answer: 12x – 7y

Now putting them both together:

Simplify 3(2a – 4b) + 5(2b)

3(2a – 4b) + 5(2b)6a – 12b + 10b

6a – 2b

Distributive property and multiplication

Combine like termsAnswer: 6a – 2b

Getting the proper unitsWhen using the geometry formulas, the proper units of measurement are as follows:

1-Dimensional 2-Dimensional 3-DimensionFinding length, width,height, radius, diameter,circumference, perimeter,or distance

Finding any kind of area Finding volume

Answers are in the form:mi, ft, km, yd, m, cm, in,mm

Answers are in the form:mi2, ft2, km2, yd2, m2,cm2, in2, mm2

Answers are in the form:mi3, ft3, km3, yd3, m3,cm3, in3, mm3

EXAMPLES


75/186

75

Exercises 2.2B

Section 2.2 Exercises Part B

Evaluate the following when p = 8, r = -7, t = 32 , and a = 3.

1. 12 + a3

2. 3r12-10a

3. 5r – 7p + 6t

Use the formula for Interest to calculate the amount in the account at the end of the timeperiod.

4. P = 520r = 6.2%Y = 4A =

5. P = 35,000r = 6%Y = 9.3A =

Use the formulas for Money totals (you may have to make up your own) when q stands forquarters, d for dimes, n for nickels and p for pennies.

6. q = 25d = 17n = 15V =

7. p = pd = q-13V =

8. p = pq = qn = q+7V =

Use the formula for Temperature Conversion to calculate the temperature in degreesCelsius.

9. F = 300°C =

10. F = -45°C =

Use the formulas for a cone to calculate the missing value.

11. r = 6h = 11V =

12. r = 5l = 9SA =

Use the formulas for a triangle to calculate the missing value.

13. b = 24h = 5A =

14. Two angles are 37°and 81°; what is thethird?

Use the formulas for a trapezoid to calculate the missing value.15. b = 7

B = 10h = 7A =

16. b = 7B = 15a = 12d = 8P =


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76

Exercises 2.2B

Use the formulas for a rectangular solid to calculate the missing information.

17. l = 6

w = 9h = 7SA =

18. l = 6

w = 14h = 2V =

Simplify.

19. 8y + 5y 20. 16r – 5t + 3t + 12r21. 7(x – 5) +15x 22. 8 – 6(7 – 4t) +4t23. 8 – 12x 2 + 5 + 3x 2 24. 13xy + 7x(6y – 4)

25. Use the shape formulas for circles, triangles, and/or rectangles to find the area of the floor ofthe room you are currently in.

As a group, discuss the following:

26. If the radius and height in #13 are in meters, what is the unit of the Volume?

27.If the bases and height in #19 are in inches, what is the unit of the Area?

28. If all the sides in #21 are measured in millimeters, what is the unit of the Perimeter?

29. If the radius and height in #15 are in miles, what is the unit of the Lateral Surface Area?

30. If all the sides in #24 are measured in yards, what is the unit of the Volume?


77/186

77

Exercises 2.2B

Answers:1. 39 22. 28t – 34

2. 76− 23. -9x2 + 13

3. -87 24. 55xy – 28x

4. $661.46 25. Check with the others to see if you did it right.5. $60,174.51 26. m3 – cubic meters

6. $8.70 27. in2 – square inches

7. V = .01p + .1(q-13) 28. mm – millimeters

8. V = .01p + .3q + .35 29. mi2 – square miles

9. 148.9° 30. yd3 – cubic yards

10. -42.8°

11. 132π or 414.69

12. 70π or 219.91

13. 60

14. 62°

15. 59.5

16. 42

17. 318

18. 168

19. 13y20. 28r – 2t

21. 22x – 35


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78

Exercises 2.2C

Section 2.2 Exercises Part CPlease label everything with the correct units.

Evaluate the following when f = 5, r = -7, t = 32 , and a = -2.

1. 6t – f 3

2. +2f 12-10a

t 3. 2fr – 31a + 15a

Use the formula for Interest.

4. P = $15,000r = 6.2%Y = 7A =

5. P = £ 2,300r = 6%Y = 8.7A =

6. P = € 1,300r = 8.9%Y = 7A =

Use the formulas for Money totals (you may have to make up your own) when q stands forquarters, d for dimes, n for nickels and p for pennies.

7. q = t+5d = mn = 13V =

8. p = 15d = 9V =

9. p = h+9q = 7n = x - 20V =

Use the formula for Temperature Conversion to calculate the temperature in degreesCelsius.

10. F = -20°C =

11. F = 59°C =

12. F = 32°C =

Use the formulas for a cylinder to calculate the missing value.

13. r = 6 inh = 12 inV =

14. r = 9 mh = 5 mSA =

15. r = 3 ydh = 8 ydLSA =

Use the formulas for a triangle to calculate the missing value.

16. b = 6 fth = 5 ftA =

17. b = 15 cmh = 4 cmA =

18. Two angles are 45°and 79°; what is thethird?

Use the formulas for a trapezoid to calculate the missing value.

19. b = 9 kmB = 11 kmh = 7 kmA =

20. b = 8 mmB = 15 mmh = 5 mmA=

21. b = 12 ftB = 25 fta = 13 ftd = 17 ftP =


79/186

79

Exercises 2.2C

Simplify.

22. 9y – 11y 23. 10a – 2b + 4a – 9b 24. 8(r – 7t) + 8(t +6r)

25. 2(x – 5) +7 26. 8m+ 4(m + 15t) 27. 9 – 5(6 – 9p) +4p28. 8x2 – 34x 3 + 9x2 + 10x 3 29. 12x4 – 5x – 4x 4 + 13x 30. 3xy – 7x(5y – 4m)

31. If tile costs $1.50 per square foot, how much is that per square yard?

32. How much does it cost to run an 800 watt microwave for 17 hours if the powercompany charges 11 cents per kilowatt-hour?

33. Change 3 Euros into Pesos. (1 Euro = $1.30, 1 Mexican Peso = $0.08)

34. Change 66 feet per second into miles per hour. (5280 feet = 1 mile)


80/186

80

Exercises 2.2C

Answers:1. -121 31. $13.50 per yd 2

2. 1538− or 1582− 32. $1.50

3. -38 33. 48.75 Pesos

4. $22,854.03 34. 45 miles per hour5. £ 3,818.47

6. € 2,361.23

7. .25t + .1m + 1.9

8. $1.05

9. .01h + .05x + .84

10. -28.9° C

11. 15° C

12. 0° C

13. 1,357.17 in 3or 432 π in3

14. 791.68 m 2 or 252 π m2

15. 150.8 yd 2 or 48 π yd2

16. 15 ft 2

17. 30 cm 2

18. 56°

19. 70 km2

20. 2115 or 57.5 mm 2 21. 67 ft

22. -2y

23. 14a – 11b

24. 56r – 48t

25. 2x – 3

26. 12m + 60t

27. 49p – 21

28. -24x3+17x 2

29. 8x4 + 8x

30. -32xy + 28xm


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Section 2.3

Section 2.3 – More FormulasA calculator is a beautiful thing. You have been able to use one for a short time now and

have probably enjoyed it considerably when compared to doing all of the math by hand. You arenow ready to take another step with a much more powerful calculator – a computer. During thislesson, you are going to learn the basics of spreadsheets and how to make a computer do thecalculations for you.

During this discussion, we will use Microsoft Excel as the spreadsheet, but similarfunctions can be done in spreadsheets that are available at no cost such as OpenOffice – Calc.

Microsoft Excel BasicsMicrosoft Excel is spreadsheet software that allows you to perform calculations that help solvemath problems in this course. You supply key figures and Excel automatically makes the

calculations for you.

Open Excel on your computer by clicking Start then Programs then Microsoft Excel . Themain spreadsheet in Excel will appear. The spreadsheet is divided into cells each of which has acolumn and row address. Excel identifies columns by alphabetical letters and rows by numbers.The first cell in the upper left corner is A1. The cell to the right of it is B1 and so forth. The cellbelow A1 is A2 and so forth. You enter numbers, formulas, or words into the cells.

Use the following guidelines as you enter data into Excel. It is easiest to enter numerical data in cells by using the number keypad on your keyboard.

Be sure the Num Lock key is pressed and the Num Lock light is on.

The number keypad also has four arithmetic functions you will need which are + (add), -(subtract), * (multiply), and / (divide). It also has the numbers and an enter key so you canenter data rapidly using the keypad.

Enter the = (equal) sign in the cell before you perform any calculation in Excel. This tellsExcel you want it to perform a calculation.

Use the following guidelines to format data in Excel.

Never enter dollar signs ($) or commas (,) when entering data in Excel. Enter these byformatting the cell.

Right click the cell or range of cells and select Format Cells. This opens a window thatallows you to set the format in number, general, currency, percent, etc. You can set thenumber of decimal points you want to use and you can set alignment, font, etc. in thiswindow. The cell format already has been set in most of the exhibits you will be using in thiscourse.

TIP: You can also format data in cells by clicking the cell or range of cells then clicking theappropriate symbol on the formatting tool bar.


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Lifelong Income Example – Beginning SalaryYou can estimate your lifelong income using Excel

To determine Lifelong Income do the following:1. Enter the beginning hourly rate you will earn in your first job after you graduate in cell E3,

for example $15.00.2. Enter the number of hours you will work in a year in cell E5 as follows: =40*52 where 40 is

the number of hours per week and 52 is the number of weeks in a year.3. Press enter. Excel automatically multiplies 40 hours per week times 52 weeks per year and

provides the result or 2080 working hours per year.4. To calculate your first year salary in cell E7, enter (a) the equal sign, (b) click cell E3 (rate

per hour) then enter * (multiplication sign) and (c) click cell E5 (hours per year).5. Press enter. Excel calculates your first year’s income at $31,200. These entries are illustrated

below:

Yearly Income Calculation – FormatIn Cell Enter Results

Rate Per Hour: E3 15 $15.00

Hours Per Year E5 =40*52 2080

Income - First Year of Employment (Beginning): E7 =E3*E5 $31,200.00

When you click on a cell that has a calculation set up, the formula for that cell appears in the

formula line (to the right of the = sign) at the top of the page. For example, the formula line forthe calculation performed in step 5 above would be: =E3*E5

Once your calculations are in place, Excel can save you time and effort if changes are required.If you were to change the beginning rate per hour to $10.00 and you have used the cell addressesin each of your formulas, Excel will recalculate all of the numbers and give you the new values.Try it. Enter “10” in E3 and watch what happens to the Income.


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To help get you used to formulas in Excel and how they work, we will use some of our familiarformulas from last week:

Circle ExamplePick a cell where you will enter the radius – say B2. Put “2” in B2 as a starting radius.

Then we write the formula for area in a cell next to it – C2. Remember the formula for area of acircle is So, in C2 we write

“=PI()*B2^2”

π variable for radius exponent in Excel

Then you will notice that the area 12.56637 pops up in C2.

Change the radius to “7” and you will be able to see that the area automatically changes. Nifty,isn’t it? You can change the radius to any number you would like and the area calculation willautomatically update.

Now, the power of Excel doesn’t stop just there. We can see the areas of a whole bunch of radiiat the same time. List out several numbers in the cells beneath the “7” in B2. Now, if you copythe formula from C3 and paste it in C4, C5, C6, etc. you will notice that we can make a wholetable of areas. If you label the columns, then others that see your spreadsheet will be able to tellwhat you did. It should look something like this:

Temperature Conversion Example Make a column of numbers that are temperatures in Fahrenheit starting with cell C10.

Then type in the formula that converts Fahrenheit to Celsius in D10:

“=5/9*(C10 – 32)”

. . . . . .

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