math100gltextbook.pdf

Math 100G/L

Introduction to

Algebra and

Finance

BYU-Idaho

MESSAGE FROM THE FIRST PRESIDENCY

Dear Brothers and Sisters:

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

We encourage you wherever you may live in the world to prepare for adversity by looking to the condition of your finances. We urge you to be modest in your expenditures; discipline yourselves in your purchases to avoid debt. Pay off debt as quickly as you can, and free yourselves from this bondage. Save a little money 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 your hearts.

May the Lord bless you in your family financial effort.

The First Presidency

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

Table of Contents

Chapter 1 Arithmetic....1 Section 1.1...2 Addition and Multiplication Facts from 1+1 to 15 15 Section 1.2..10 Rounding and Estimation; Life Plan Section 1.3..15 Add, Subtract, Multiply, Divide Decimals; Income and Expense Section 1.4..34 Add, Subtract, Multiply, Divide Fractions; Unit Conversions

Chapter 2 Calculators and Formulas49 Section 2.1..50 Exponents Introduction, Order of Operations, Calculator Usage Section 2.2..61 Variables and Formulas Section 2.3..76 Formulas and Spreadsheet Usage

Chapter 3 Algebra.....89 Section 3.1.90 Linear Equations and Applications Section 3.2108 Linear Equations with Fractions; Percent Applications Section 3.3121 Exponents Revisited; Loan Payment and Savings Equations

Chapter 4 Graphs and Charts.....137 Section 4.1138 Maps and Coordinate Graphs Section 4.2148 Graphing Lines and Finding Slope Section 4.3162 Using Slope and Writing Equations of Lines

Chapter 1: ARITHMETIC

Overview Arithmetic 1.1 Facts 1.2 Rounding and Estimation 1.3 Decimals 1.4 Fractions

1

Section 1.1

2

Section 1.1 Facts 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&Ms, coconuts, gallons of water, money etc. From the beginning I am going to assume you know how to add in your head up to 15+15. If you dont, please make up some flash cards and get those in your brain. It is similar to learning the alphabet before learning to read. We need the addition facts to be available for instant recall.

Soon after addition was learned, I bet someone told you that there was a shortcut when you had to add some numbers over and over. For example: 3+3+3+3+3+3+3 = 21

7 If you notice, there are seven 3s.

3, seven times, turns out to be 21, so we write it as 73 = 21.

One of the best coincidences of the world is that 7, three times, is also 21. 37 = 21

Such a switching works for any numbers we pick: 45 = 20 and 54 = 20

313 = 39 and 133 = 39

Since we will be using the multiplication facts almost as much as we will be using the addition facts, you need to also memorize the multiplication facts up to 1515. Learn them well, and you will be able to catch on to everything else quite nicely.

2

Section 1.1 Exercises Part A 1. Make flash cards up to 15+15 and 1515. 2. Memorize the addition and multiplication facts up to 15+15 and 1515. 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.

Assignment 1.1a

3

Addition/Subtraction 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_________

Assignment 1.1 a

4

Multiplication Monster Name __________________ 1213= 56= 510= 129= 59= 811= 511= 144=

66= 712= 158= 1010= 107= 611= 612= 613=

77= 147= 79= 913= 614= 155= 1111= 75=

124= 1012= 810= 138= 55= 813= 512= 78=

99= 515= 911= 912= 156= 135= 915= 815=

67= 139= 812= 1013= 1014= 1015 713= 1113=

57= 1112= 149= 1114= 1115= 89= 106= 87=

1212= 610= 1214= 88= 127= 128= 1414= 126=

97= 1314= 105= 714= 69= 137= 136= 910=

68= 1415= 1410= 1215= 148= 814= 146= 1011=

85= 1511= 1510= 159= 98= 710= 914= 1315=

711= 514= 615= 157= 513= 715= 58= 76=

1313= 86= 95= 96= 154= 1515= 134= 145=

Time_________

Assignment 1.1a

5

Section 1.1 Exercises Part B Addition/Subtraction Monster 2

9 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 =

Assignment 1.1b Time_________

6

Multiplication Monster 2 96= 124= 510= 615= 155= 811= 129= 144=

66= 97= 158= 1010= 107= 611= 137= 58=

77= 712= 1510= 913= 614= 1213= 75= 1315=

511= 1012= 810= 157= 147= 813= 512= 78=

99= 515= 911= 912= 613= 55= 915= 815=

67= 1115= 812= 135= 1014= 1015= 713= 1113=

57= 1112= 1111= 1114= 138= 89= 106= 59=

1212= 149= 1214= 88= 127= 1013= 1414= 126=

1515= 1314= 105= 714= 128= 68= 136= 910=

56= 1415= 610= 1215= 148= 814= 146= 1011=

85= 1511= 139= 159= 69= 710= 914= 76=

711= 514= 156= 612= 1410= 715= 98= 79=

1313= 86= 95= 513= 154= 87= 134= 145=

Assignment 1.1b

Time_________

7

Section 1.1 Exercises Part C

Addition/Subtraction 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 =

Assignment 1.1 c

Time_________

8

Multiplication Monster Name __________________ 1213= 56= 510= 129= 59= 811= 511= 144=

66= 712= 158= 1010= 107= 611= 612= 613=

77= 147= 79= 913= 614= 155= 1111= 75=

124= 1012= 810= 138= 55= 813= 512= 78=

99= 515= 911= 912= 156= 135= 915= 815=

67= 139= 812= 1013= 1014= 1015 713= 1113=

57= 1112= 149= 1114= 1115= 89= 106= 87=

1212= 610= 1214= 88= 127= 128= 1414= 126=

97= 1314= 105= 714= 69= 137= 136= 910=

68= 1415= 1410= 1215= 148= 814= 146= 1011=

85= 1511= 1510= 159= 98= 710= 914= 1315=

711= 514= 615= 157= 513= 715= 58= 76=

1313= 86= 95= 96= 154= 1515= 134= 145=

Assignment 1.1 c

Time_________

9

Section 1.2Rounding and Estimation

Section 1.2

Now, you know that some arithmetic problems may get long and tedious, so you can understand why some folks choose to estimate and round numbers. Rounding is the quickest, so we will tackle that first. In rounding, we decide to not keep the exact number that

someone gave us. For example:

Rounding

If I have $528.37 in the bank, I might easily say that I have about $500. I have just rounded to the nearest hundred. On the other hand, I might be a little more specific and say that I have about (still not exact) $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

Bill

ion

s

Hu

ndr

ed M

illio

ns

Ten

M

illio

ns

Mill

ion

s

Hu

ndr

ed Th

ou

san

ds

Ten

Th

ou

san

ds

Tho

usa

nds

Hu

ndr

eds

Ten

s

On

es

Ten

ths

Hu

ndr

edth

s

Tho

usa

ndt

hs

Ten

Th

ou

san

dths

Hu

ndr

ed Th

ou

san

dths

Mill

ion

ths

Example: Round to the nearest hundredth: 538.4691 This number is right between 538.46 and 538.47 Which one is nearest? The 9 tells us that we are closer to 538.47

2nd Example: Round to the nearest thousand: 783,299.4321 This 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

10

LAST EXAMPLE

Round $4,278.23 to the nearest hundred 00 Decide if our number is closer to the nearest

hundred above the number or below the number $4,300.$4,278.23 $4,200.00

$4,278.23 $4,300.00 Change our number to the one it is closer to Answer: $4,300.00

Estimation

Section 1.2

Estimation 1. Round to the highest value. 2. Do the easy problem.

Once rounding is understood, it can be used as a great tool to make sure that we have not missed 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 our answer makes sense.

LAST EXAMPLE Multiply by rounding: 986.7 4.9

986.7 1,000 Round the numbers 4.9 5

1,000 5 = 5,000 Multiply the rounded numbers together 986.7 4.9 5,000 Our answer for 986.7 4.9 will be about 5,000

11

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 60,000 2. 2,892.6 10. About 300,000 3. 40,000 11. About 8,000 4. 190 12. About 100 5. 3,250.1 13. About 2,400 6. 2,900 14. About 16,000 7. 39,450 15. Discuss it together 8. 200

Assignment 1.2a

12

Section 1.2 Exercises Part B

1. 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 189.59 to the nearest ten. 5. Round 3,250.647 to the nearest tenth. 6. Round 2,892.56385 to the nearest thousandth. 7. Round 34,454 to the nearest thousand. 8. Round 189,364,529.83 to the nearest million. 9. Describe what possible problems students could have with rounding.


10. 51 3250.07 11. 438.9 2,892.07 12. 32 789

13. 569.456 6.1987 14. 58 391 15. 54,200 12

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

17. As a group, estimate a monthly budget for a family with a few children living in your area. Please include estimates of costs for housing, transportation, food, utilities, and clothing.

18. Enter the budget into a spreadsheet document.

Answers: 1. 7,250 10. About 150,000 2. 2,862.84 11. About 1,200,000 3. 540,000 12. About 24,000 4. 190 13. About 100 5. 3,250.6 14. About 24,000 6. 2,892.564 15. About 5,000 7. 34,000 16. Make sure they are all there. 8. 189,000,000 17. Should look neat. 9. d vs. dth, lack of 1th, any others 18. Complete when everyone can do it.

Assignment 1.2b

13


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 expenses and income will be at that time..

16. Create your own spreadsheet document to record your one month estimated expenses and income. 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 current income and expenses.

Answers: 1. 7,254.1 10. About 360 2. 2,860 11. About 240,000 3. 538,000 12. About 100 4. 140 13. About 24,000 5. 3,250.65 14. About 6,000 6. 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.

14

Section 1.3 Decimals

Section 1.3

DEFINITIONS & BASICS

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

Example: If someone asks you 5 sheep + 2 sheep =

you would be able to tell them 7 sheep.

What if they asked you 5 sheep + 2 penguins =

We really cant add them together, because they arent like things.

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

3) Negative The negative sign means opposite direction.

Example: 5.3 is just 5.3 in the opposite direction

5.3 0 5.3

Example : is just in the opposite direction.

Example: 7 5 = 12, because they are both headed in that direction

4) Decimal Deci is a prefix meaning 10. Since every place value is either 10 times larger 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 decimals 2. Add in columns 3. Carry by 10s

15

EXAMPLE

Add. 3561.5 + 274.38 3561.5 + 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 8 3 8 3 5. 8 8

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

Subtraction of Decimals

1. Biggest on top 2. Line up decimals; subtract in columns. 3. Borrow by 10s 4. Strongest wins.

EXAMPLE

Subtract. 283.5 3,476.91 - 3476.91 283.5 1.Biggest on top

- 3 4 7 6. 9 1 2 8 3. 5 3. 4 1

2. Line up decimals; subtract in columns

3 - 3 4 17 6. 9 1 2 8 3. 5 3 1 9 3. 4 1

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

3 - 3 4 17 6. 9 1 2 8 3. 5 - 3 1 9 3. 4 1

3. Biggest one wins.

Section 1.3

16

Multiplication of Decimals

EXAMPLES

29,742 538 237,936 892,260 +14,871,000 16,001,196

Next: 2 2 1 29,742 30 892,260

Last: 4 3 2 1 29,742 500 14,871,000

3. Add the pieces together.

Multiplication of Decimals 1. Multiply each place value 2. Carry by 10s 3. Add 4. Right size. 1. Add up zeros or decimals 2. Negatives

Start: 7 5 31 29,742 8 237,936

Section 1.3

17

Final example with decimals:

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

-70139.278

Division of Decimals

-7414.3 9.46 444858 2965720 +66728700 -70139278

Next: 1 1 1 74143 40 2965720

Last: 3 1 3 2 74143 900 66728700

3. Add the pieces together.

4. Right size. Total number of decimal places = 3. Answer is negative.

Start: 2 21 74143 6 444858

Division of Decimals 1. Set up. 2. Divide into first. 3. Multiply. 4. Subtract. 5. Drop down. 6. Write answer.

1. Move decimals 2. Add zeros

1. Remainder 2. Decimal

Section 1.3

18

EXAMPLES 5

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 58

Step 4.subtract.

53 4298

-40 29

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

Step 2: 8 goes into 29 about 3 times.

53 4298

-40 29 -24 5

Step 3: Multiply 38

Step 4: subtract.

8 doesnt go into 5 (remainder)

Which means that 429 8 = 53 R 5 or in other words 429 8 = 53 85

Example: 5875 22

2 587522

44

Step 2: 22 goes into 58 about 2 times. Step 3: Multiply 222 = 44

2 587522

-44 147

Step 4: Subtract.

Step 5: Bring down the next column

27 587522

-44 147 154

22 goes into 147 about ???? times. Lets estimate. 2 goes into 14 about 7 times try that. Multiply 227 = 154 Oops, a little too big

Section 1.3

19

26 587522

-44 147 -132 155

Since 7 was a little too big, try 6. Multiply 622 = 132

Subtract.

Bring down the next column.

267 587522

-44 147 -132 155 -154 1

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

Multiply 227 = 154. It worked.

Subtract. Remainder 1

5875 22 = 267 R 1 or 221267

An example resulting in a decimal:

Write 94

as a decimal:

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

.4 0000.49

-36 4

Step 2: Divide into first. 9 goes into 40 about 4 times. Step 3. Multiply 49 = 36

Step 4. Subtract. .44

0000.49 -36 40 -36 4

Step 5. Bring down the next column. Repeat steps 2-4 Step 2: 9 goes into 40 about 4 times. Step 3: Multiply 49 = 36

Step 4: Subtract.

.444 0000.49

-36 40 -36 40 -36 4

Step 5. Bring down the next column. Repeat steps 2-4 Step 2: 9 goes into 40 about 4 times. Step 3: Multiply 49 = 36

Step 4: Subtract.

This could go on forever!

Thus 94

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

The bar signifies numbers or patterns that repeat.

Repeating decimal

Section 1.3

20

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

4.358005.

3584005

Step 1. Set it up and move the decimals 2961.3

00.296031

7 3584005

35

Step 2. Divide into first

Step 3. Multiply down

9 00.296031

279 7

3584005

-35 08

Step 4. Subtract

Step 5. Bring down

9 00.296031

-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 -155 150

716 3584005

-35 08 - 5 34 -30 40

Repeat steps 2-5 as necessary Step 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 necessary Step 2: Divide into first

Step 3: Multiply down

Step 4: Subtract

Step 5: Bring down

95.48 000.296031

-279 170 -155 150 -124 260 - 248 120

Section 1.3

21

71680 3584005

-35 08 - 5 34 -30 40 -40 00 - 0 0

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

95.483 000.296031

-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 means opposite direction, when we switch direction twice, we are headed back the way we started.

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

- False in Addition and Subtraction With addition and subtraction negatives and positives work against each other in a sort of tug o war. Whichever one is stronger will win.

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

Section 1.3

22

Example: Falling is negative and rising is positive. An airplane rises 307 feet and then 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 a fall 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 the sign 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

Section 1.3

23

What is

as a percent?

5 32 = .15625 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 percent 5

32= 15.652%

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

we are turning this into a decimal 124%=1.24

Solving Of with Percents

The most important thing that you should know about percents is that they never stand alone. 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% of your 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

. 25 64 = 16 Multiply the two numbers together 25% of 64 is 16

What is 13% of $25? 13%=.13


. 13 25 = 3.25 Multiply the two numbers together 13% of $25 is $3.25

What is 30% of 90 feet? 30%=.30


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

In math terms the word of means multiply.

Section 1.3

24

Section 1.3 Exercises Part A Add. 1. 36,451

+ 2,197 2. 143.29

+ .923 3. 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:$32.50 Discount:$1.79 Final Price:

16. Temp:67 F Change:18 warmer Final:

17. Altitude: 7,380 ft Fall: 3,200 ft Final:

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

19. Temp: 17 C Change: 28 colder Final:

20. Altitude:300 m Rise:7,250 m Final:

Change into a decimal.

21. 52 22. 41 23. 83

24. 91 25. 87 26. 61

Assignment 1.3a

25

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. 2019 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: 2,300 Percent men: 40% Men:

41. Students: 4 Number of Bs: 3 Percent of Bs:

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.

Insurance

9%

Car

14%

House

47%

Fun

10%

Food

20%

Expenses

Assignment 1.3a

26

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 C 20. 7550 m 21. .4 22. .25 23. .375 24. .1 25. .875 26. .16 27. 7333 or 33.428571 or 33 R3 28. 27 29. 11653 or 53.54 or 53 R6 30. 1407.5

Assignment 1.3a

27

Section 1.3 Exercises Part B Add. 1. 36,851

+ 3,197 2. 153.29

+ .922 3. 8,434,916.7

+ 54.3527

Subtract.

4. 9 - (-3) = 5. -18 32 = 6. -14 (-19) =

7. -18 + 6 = 8. 15 47 = 9. -24 8 =

10. 754 -57

11. 29.84 -64.643

12. 4,786 -5,919

13. 2.35 -13.946

14. 23,754 - 4,151

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

16. Temp:67 F Change:28 warmer Final:

17. Altitude: 4,380 ft Fall: 2,230 ft Final:



20. Altitude:300 m Rise:2,250 m Final:


21. 54 22. 92 23. 85

24. 81 25. 65 26. 101

Assignment 1.3b

28

Divide.

27. 4347 28. 1356 29. 78912

30. 347.5604. 31. 4536. 32. 12.1251.3



36. Food 37. Car 38. Fun


Tax rate: 6% Tax:



Begin Budget and Expenses Portfolio Project 42. Make sure all members of the group have seen the pattern of budget and expense reports found 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 reporting to your group and receiving reports when all have created a spreadsheet titled, Budget and Expenses.

Insurance

9%

Car

14%

House

47%

Fun

10%

Food

20%

Expenses

Assignment 1.3b

29

Answers: 1. 40,048 31. 755 2. 154.212 32. 40.361 3. 8,434,971.0527 33. 58.3% 4. 12 34. 85% 5. -50 35. 50% 6. 5 36. $260 7. -12 37. $182 8. -32 38. $130 9. -32 39. $4.63 10. 697 40. 1896 men 11. -34.803 41. 91.67% 12. -1,133 42. Submit it to your teacher

later in this lesson. 13. -11.596 14. 19,603 15. $26.71 16. 95 F 17. 2150 ft 18. $35.68 19. -21 C 20. 2550m 21. .8 22. .2 23. .625 24. .125 25. .83 26. .1 27. 62 28. 22.5 29. 65.75 30. 1408.675

Assignment 1.3b

30


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

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

+ 3,137 8. 756.29

+ .522 9. 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



18. Altitude:300 m Fall:2,250 m Final:


19. 201 20. 94 21. 32

Assignment 1.3c

31

Divide.

22. 4348 23. 1856 24. 68914

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



31. Insurance 32. Car 33. Fun


Tax rate: 6% Tax:



Insurance

8%

Car

15%

Housing

37%

Fun

10%

Food

30%

Expenses

Assignment 1.3c

32

Answers: 1. Titled Budget and Expenses and save

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

31. $108.32

2. 54,000 32. $203.10 3. 386,000,000 33. $135.40 4. 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. -1950m 19. .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%

Assignment 1.3c

33


1) Numerator the top of a fraction 2) Denominator the bottom of the fraction 3) 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 and subtraction fractions that have large denominators is to crack them open and see what they are made of. Scientists get to use a scalpel or microscope. Math guys use prime factorization.

Addition of Fractions

1. Common Denominator 2. Add numerators 3. Carry by denominator

EXAMPLE

Add

+

+

Step 1. The least common multiple of 4 and 2 is a 4, so we replace the

with an equivalent fraction, which is

.

3

4

+ 2

4

= 5

Step 2. Now that the denominators are the same, add the numerators.

1. Observation 2. Multiply the denominators 3. Prime factorization

Section 1.4 Fractions

Section 1.4

34

Step 3. Carry the denominator across.

3

41

25

4

Changing from mixed numbers to improper fractions:

5

5

Changing them back again:

43 8 53 5

Subtraction of Fractions

1. Biggest on top 2. Common Denominator; Subtract numerators 3. Borrow by denominator 4. Strongest wins

EXAMPLE

Do this:

3

- 3

5

9

3

is bigger, so put it on top.

- 3

5

9

The common denominator is 9,

so change the

to a

.

- 2

5

9

- 2

Subtract the numerators. Borrow by denominator as needed.

5

9 3

1

3 2

7

9

1. Observation 2. Multiply the denominators 3. Prime factorization

Section 1.4

35

Multiplication of Fractions

EXAMPLES

5

6

1

3

For multiplication dont worry about getting common denominators

%

=

?

Multiply the numerators straight across

%

=

Multiply the denominators straight across

5

6

1

3=

5

18

Multiplication of Fractions 1. No common denominators 2. Multiply Numerators 3. Multiply Denominators

Section 1.4

36

Division of Fractions

EXAMPLES

Divide 3 $

$

$+

$

$

Turn the fractions into improper fractions

25

7

3

2

Keep the first fraction the same Change the division sign to a multiplication sign Flip the second fractions numerator and denominator

$

=

$

Multiply straight across the numerator and denominator

34

7

2

3=

75

14

Divide

1

2

5

1 4

4+

3

4

2

5

7

4

Turn the fractions into improper fractions

2

5

4

7

KEEP the first fraction the same Change the division sign to a multiplication sign Flip the second fractions numerator and denominator

$=

Multiply straight across the numerator and denominator

1

=

Section 1.4

Division of Fractions 1. Improper Fractions 2. Keep it, change it, flip it. 3. Multiply.

37

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

10

6321

55

Now, we can do this the normal way or we can try to notice if there is anything that we will 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 a much 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 much more than that. It opens the door to a much larger world. Here is an example. If we travelled 180 miles 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 can actually find how many miles we can drive for one dollar:

. = 4.7 miles per dollar.

Another example: Carpet is on sale for 15 dollars per square yard. How much is that in dollars per square foot (9 ft2 per yd2)? 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 yd2 will cancel out, leaving us with dollars per ft2:

New and improved slick method:

=

and we try to see if any factors will cancel ahead of time 25 37

=

337 511

Section 1.4

38

1/**.2,

31'

31'

# 45'

Then cancel the yd2:

1/**.2,

31'

31'

# 45' =

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:

6 1/**.2,

4++5

4//5

7 )089+, =

1/**.2,

)089+, =

$.156 or 15.6 cents per inch.

Here are a few numbers that will help you with the conversions: 12 in = 1 foot 16 oz = 1 pound 60 seconds = 1 minute 1000watts = 1 kilowatt

1 yd = 3 ft 60 minutes = 1 hour 1 yd2 = 9 ft2

And also some exchange rates with the American dollar as they were sometime in 2010: 1 Mexican Peso = $0.08 1 Euro = $1.30 1 British Pound = $1.50 1 Brazilian Real = $0.55

1.666 3 00.5 -3 2 0 -18 20 -18

.1562 32 00.5 -3 2 180 -160 200 -192 80

Section 1.4

39

Section 1.4 Exercises Part A Find 4 different names for each fraction:

1. 73 2. 32 3. 117 4. 94

Simplify each fraction.

5. 5236 6. 3627 7. 5616

8. 1210 9. 4515 10. 280120

Create each fraction with a denominator of 36. 11. 61 12. 95 13. 1210

Add or Subtract. Simplify.

14. =+ 3252 15. =+ 8541 16. = 253307

17. =+ 12731 18. =+ 6543 413 19. = 51107 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.

Assignment 1.4a

40

20. = 76149 63 21. =+ 3272 94 22. = 4385 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. 92 29. - 107 30. 87

31. - 6

5

32. 13 33. 4213 34. 37

Divide.

35. = 3152 36. = 8341 37. = 8365

38. = 12783 39. = 6143 72 40. = 3275 35

41. = 109547 42. = 3287 9 43. = 83612

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 per dollar do you get?

Example: 85

58

Example: = 5

4832

= 45

832 Multiply by reciprocal

= 45

819

Change to improper fraction

= 45

819

3295

or 32312 Multiply straight across.

Assignment 1.4a

41

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.

12

27. 47 or 431 28. 29 or 214 29. 710 or 731 30. 78

Assignment 1.4a

42

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

1. 32 2. 127 3. 4840

Add or Subtract. Simplify.

4. =+ 7252 5. =+ 9743 6. = 87125

7. = 9732 163 8. =+ 6575 67 9. = 5385 92

Fill out the table.

Mixed Improper 10. 952 11. 746 12. 835 13. 1157

Find the multiplicative inverse or reciprocal of each number.

14. 53 15. 943 16. - 125 17. 7

Divide.

18. = 3572 19. = 7643 20. = 9461

21. = 103322 22. = 2185 4 23. - = 75732


24. 52 25. 41 26. 83

27. 91 28. 87 29. 61

Assignment 1.4b

43

Change into a fraction and simplify.

30. .5 31. .7 32. .45

33. .52 34. .75 35. .6

Convert the following units. Example: Dog food cost $7.00 for 20 pounds. How many ounces per dollar?

Solution:

=

=45.71 ounces per dollar

36. Cereal cost $4.50 for 2 pounds. How much did it cost per ounce? 37. Fishing line costs $.02 per foot. How much would 200 yards cost? 38. 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? 39. 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? 40. How many Pesos are equal to 5 Euros? (1 Mexican Peso = $0.08, 1 Euro = $1.30) 41. How many Reais (plural for Real) are equal to 7 Pounds? (1 Brazilian Real = $0.55, 1 British Pound = $1.50) 42. Create a visual chart for all arithmetic of decimals. Use plenty of examples. 43. Create a visual chart for all arithmetic of fractions including Unit Conversions.

Example .12

.12 = 12 (100th) = 10012 = 253 simplify

Assignment 1.4b

44

Answers: 1. 2416 31. 107 2. 2414 32. 209 3. 2420 33. 2513 4. 3524 34. 43 5. 36191 or

%

35. 53 6. 2411 36. $0.14 per ounce 7. 9113 37. $12.00 8. 422314 38. 5.38 miles per dollar 9. 40396 39. $0.20 per hour 10. 923 40. 81.25 Pesos 11. 746 41. 19.09 Reals 12. 834 42. Part of Portfolio 13. 1125 43. Part of Portfolio 14. 35 15. 319 16. 512 17. 71 18. 356 19. 87 20. 83 21. 988 22. 365 23. - 523 24. .4 25. .25 26. .375 27. .1 28. .875 29. .16 30. 21

Assignment 1.4b

45

Section 1.4 Exercises Part C Exam 1 Review Exercises

Estimate the product (round to the greatest value, then multiply). 1. 2,589,00059.34 2. .005608.07816 3. 3.8472,564

Add. 4. 36,841

+ 249.7 5. 723.3

+ 39.7 6. 1413149 516 + =

Subtract.

7. Temp: -35.5 F Change: 13.4 warmer Final:

8. -8 (-11) = 9. = 7674 113

Multiply. 10. Cost: $35.20

Quantity: 17 Total:

11. 369(-23) = 12. = 121154

Add or Subtract. Simplify. 13. =+ 9523 14. =+ 1451211 15. = 65185

16. = 9761 615 17. =+ 81109 135 18. = 14294 912

Fill out the table.

Mixed Improper 19. 753 20. 659

Divide. 21.

18598

22. = 3298 4 23. ( ) = 54437 Change into a decimal.

24. 125 25. 97 26. 72

Change into a fraction and simplify.

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

Assignment 1.4c

46

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 per kilowatt-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?



40. Car 41 House 42 Food


Tax rate: 7% Tax: Final Price:

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

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

46. Round to the nearest ten: 583.872

Insurance

9%

Car

14%

House

47%

Fun

10%

Food

20%

Expenses

Assignment 1.4c

47

Answers: 1. About 180,000,000 31. 31260 or 260.3 2. About .00048 32. 432815 or 15.65116 3. About 12,000 33. 94.62 4. 37,090.7 34. 1,406,000 5. 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

Assignment 1.4c

48

Chapter 2: CALCULATORS and

FORMULAS

Overview 2.1 Exponents and Calculator Usage 2.2 Variables and Formulas 2.3 More 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.

49

While we are on multiplication, did you know that there is some short hand? Remember when we started multiplication we did: 6+6+6+6+6+6+6+6+6 = 54 but we did it a bit shorter

9 96 = 54

There is a way to write multiplication in shorthand if you do the same thing over and over again: 2222222 = 128

7 For the shorthand we write 27 = 128.

That little 7 means the number of times that we multiply 2 by itself and is called and exponent; sometimes we call it a power. Here are a couple more examples: 53= 125 72 = 49 24 = 16

Pretty slick. You wont have to memorize them . . . yet, but you should be familiar enough with them to be able to recognize them.

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

104= 10,000 108 = 100,000,000 103 = 1,000

EXAMPLE

Evaluate 74

7 = 7 7 7 7 49 7 7 343 7 2401 Answer: 2401

Set up the bases, and then multiply each couple in turn.

Section 2.1 Exponents

Section 2.1

50

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 and then multiply by 4 to get 20 and then subtract 5 to get 15.

Unfortunately, that doesnt jive with what we have learned about what multiplication is. Remember that multiplication is a shorthand way of writing repeated addition. Technically we have: 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 multiplication as a group, before we can involve it in other computations. Multiplication is done before addition and subtraction.

Here is another one: 4 32 7 2 + 4 Now remember that exponents are shorthand for a bunch of multiplication that is hidden, so we need to take care of that even before we do multiplication: 4 32 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 Exponents 2nd 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 the difference between these:

52542236322632 2

=

=

=

( )

1601622232422182

26322

2

=

=

=

=

( )

182362361

2632 2

=

=

=

( )( )( )

1282256216

21822632

2

2

2

=

=

=

=

Section 2.1

51

Section 2.1 Exercises Part A Calculator Usage Assignment

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

Estimate the product (round to the greatest value; then multiply). 1. 75,80049.34 2. .004208.06916 3. 4.4477,164

Add. 4. 37,291

+ 348.23 5. 5.871

+ 39.7 6.

235

239 517 + =

Subtract. 7. Temp: 85.3 F

Change: 130.4 colder Final:

8. -5 3 = 9. = 118114 1523


Quantity: 27 Total:

11. 44129 = 12. - = 11

1652

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

Add or Subtract. Simplify. 16. =+ 9443 17. =+ 10785 18. = 97158

19. = 9481 714 20. =+ 81109 195 21. = 16385 54

Fill out the table.


Divide.

24. 187

1211

25. = 2165 4 26. = 83857


27. 117 28. 53 29. 92

Assignment 2.1a

52

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.

Evaluate 38.

5 3 + 8 2 39. (5 3) + 8 2 40. 5 (4 + 8) 2

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



45. Fun 46. Insurance 47. Food



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

50. Students: 30 Number of As: 24 Percent of As:

Insurance

9%

Car

16%

House

45%

Fun

13%

Food

17%

Expenses

Assignment 2.1a

53

Answers: 1. About 4,000,000 31. 2511 2. About .00028 32. 85 3. About 28,000 33. 49 4. 37,639.23 34. 6113 or 13.16 5. 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 second 12. - 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 Assignment 2.1a

54

Section 2.1 Exercises Part B Add. 1. 57,831

+ 348.23 2. 4.83

+ 39.7 3. 115119 814 + =

Subtract. 4. Temp: -85.3 F

Change: 130.4 colder Final:

5. -5 53 = 6. = 218214 1523


Quantity: 527 Total:

8. - = 14

1552

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

12. (2.38)2 = 13. (1.07)27 = 14. (1.12)12 = 15. If I place 2 cents on the first square of a chess board, 4 cents on the second square, and keep doubling the amount on each square, how much money will be on the 30th square?

Fill out the table.


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)



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: 250 Number of As: 147 Percent of As:

Assignment 2.1b

55

30. For a savings account that begins with $100 and has a 5% interest rate, fill out the following table: Time Beginning Balance Interest earned Ending Balance 1st year 100 .05 100 = 5 105 2nd year 105 .05 105 = 5.25 110.25 3 110.25 .05 110.25 =5.51 115.76 4 115.76 5 6 7 8 9 10 11 12

31. For a savings account that begins with $100 and has a 6% interest rate, fill out the following table: Time Beginning Balance Ending Balance 1st year 100 100 1.06 = 106 2nd year 106 106 1.06 = 112.36 3 112.36 112.36 1.06 = 119.10 4 119.10 5 6 7 8 9 10 11 12

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

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


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

Assignment 2.1b

56

1. 58,179.23 31. 12 year end balance - $201.22 ($201.23 also acceptable)

2. 44.53 32. 1 adds in the beginning balance and .05 adds in the 5%

3. 23

33. $225.22 4. -215.7 F 34. $443.04 5. -58 35. #34 can be done by 100 (1.07)22 6.

7

7. $20,236.80 8.

-

9. 243 10. 1,369 11. 195.112 12. 5.6644 13. 6.214 14. 3.896 15. $10,737,418.24 16.

17. - 28

18. 2.19 cents per ounce 19. 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 27. $33.64; $514.14 28. 97 kids 29. 58.8% 30. 12 year end balance - $179.59

($179.60 also acceptable)

Assignment 2.1b

57

Section 2.1 Exercises Part C 1. Find three different places to save your money. Report the interest rates to your group, and receive their reports.

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

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

Fill out the table.


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


Change into a percent. 14.

15.

16. ,

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%




Assignment 2.1c

58

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

Time Beginning Balance Ending Balance 1st year 350 350 1.05 = 367.50 2nd year 367.50 3 4 5 6 7 8 9 10 11 12


24. For a savings account that begins with $100 and has a 6% interest rate and to which you are able to add $25 per year, fill out the following table and place it on Sheet 2 of your Life Plan spreadsheet: Time Beginning Balance Ending Balance 1st year 100 100 1.06 + 25 = 131 2nd year 131 131 1.06 + 25 = 163.86 3 163.86 163.86 1.06 + 25 = 4 5 6 7 8 9 10 11 12

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

Assignment 2.1c

59

1. Complete when all reports are done.

2. 1024 3. 7569 4. 143.489 5. 28.944 6. 4.29 7. 3.88 8.

9. 12

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. $241.08 20. $5.63; $86.03 21. (135.8) 136 kids 22. $628.55 23. $1329.12 24. $622.97 25. $1,165.98

Assignment 2.1c

60

Variables and Formulas


1) Variables: These symbols, being letters, actually represent numbers, but the numbers can change 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 numbers on 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 have completed a walk of 78 ft. I bet we could come up with the pattern for how we would do this all of the time. Well, first of all, we just pick general terms for the sides of the rectangle: 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 can change from time to time. This pattern that we have created to describe all cases is called a formula.

Section 2.2

Section 2.2 Variables and Formulas

61

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 how to make them up on your own. I will show you on a couple of them.

Distance, rate If 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) = distance or in other words:

rt = d where r is the rate t is the time d is the distance

Percentage If 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 = rP Where T is tax r is rate of tax P is the purchase amount.

Interest This 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 end of three years would be given by the formula: A = 500(1.09)3 = $647.51

Section 2.2

62

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 rate Y is the number of years that it is invested.

Temperature Conversion Most 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 Fahrenheit C is the degree in Celsius

Money If 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 + .10d where V is the Total Value of money q is the number of quarters d is the number of dimes

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

l

w Rectangle

P = 2l + 2w

A = lw

P is the perimeter

l is the length

w is the width

A is the Area

Section 2.2

63

b a 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 leg

d is a leg

A is the Area

h is the height

h b

Triangle

P = s1+s2+s3

A = 21 bh

P is the perimeter

s is a side

A is the Area

b is the base

h is the height

b

c

a Triangle

a + b + c = 180 a is one angle

b is another angle

c is another angle

Section 2.2

64

H

w l

Rectangular Solid

SA = 2lw+2wh+2lh

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 = 2pir

A = pir2

C is the Circumference or Perimeter

pi is a number, about 3.14159 . . . it has a button on your calculator

r is the radius of the circle

A is the area inside the circle.

r

h

Cylinder

LSA = 2pirh

SA =2pirh+2pir2

V = pir2h

LSA is Lateral Surface Area or area just on the sides



h is the height

SA is total surface area

V is Volume

Section 2.2

65

h l

r

Cone

LSA = pirl

SA = pir2+ pirl

V = 31pir2h

LSA is Lateral Surface Area or the area just on the sides



h is the height l is the slant height

SA is total surface area

r

Sphere

SA = 4pir2

V = 34pir3

SA is the surface area


r is the radius

V is the Volume

Section 2.2

66

Section 2.2 Exercises Part A Add or Subtract. Simplify.

1. = 8387 136 2. =+ 43125 1877 3. = 15265 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 power company charges 12 cents per kilowatt-hour?


Tax rate: 5% Tax: Total Price:

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

11. Birds: 140 Black : 47 Percent 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

19 k-12

20. 15

9 5

13 r

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

21. 3t - 7 22. 2(n+9) 23. a283 + m2

Assignment 2.2a

67

24. 12 a3 25. m 12 26. 2n 3a + 5t

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

27. r = 7 t = 15 d =

28. r = 55 t = 7.2 d =

29. r = 45 t = 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 for quarters (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 = 9 d = 12 V =

34. p = 19 d = 17 V =

35. n = 37 q = 23 V =

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 is A=pir2

What is the area of a circle with radius 7?

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

Example: r = 3 t = 14 d =

Formula is found in section 2.3: rt = d 3(14) = d 42 = d

Assignment 2.2a

68

Answers: 1. 216 31. 83 2. 61195 32. 108 3. 10375 33. $3.45 4. 2.5876 34. $1.89 5. .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 + k 20. 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

Assignment 2.2a

69

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 time period.

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

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

6. P = 200 r = 8.9% Y = 7 A =

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

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

8. p = p d = q-13 V =

9. p = p q = q n = q+7 V =

Use the formula for Temperature Conversion to calculate the temperature in degrees Celsius.

10. F = 300 C =

11. F = -45 C =

12. F = 102 C =

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

13. r = 6 h = 11 V =

14. r = 5 l = 9 SA =

15. r = 3 l = 8 LSA =

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

16. b = 24 h = 5 A =

17. b = 15 h = 4 A =

18. Two angles are 37 and 81; what is the third?

Use the formulas for a trapezoid to calculate the missing value. 19. b = 7

B = 10 h = 7 A =

20. b = 9 B = 15 h = 3 A=

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

Assignment 2.2b

70

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

22. l = 6 w = 9 h = 7 SA =

23. l = 4 w = 15 h = 7 SA =

24. l = 6 w = 14 h = 2 V =

Simplify.

25. 8y + 5y 26. 4a 9 + 4a 27. 16r 5t + 3t + 12r 28. 7(x 5) +15x 29. 7t + 4(t + 12) 30. 8 6(7 4t) +4t 31. 8 12x2 + 5 + 3x2 32. 7x2 5x 9x2 + 13x 33. 13xy + 7x(6y 4)

As a group, discuss the following:

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

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

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

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

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

Assignment 2.2b

71

Answers: 1. 39 31. -9x2 + 13 2. 76 32. -2x2 + 8x 3. -87 33. 55xy 28x 4. $661.46 34. m3 cubic meters 5. $60,174.51 35. in2 square inches 6. $363.27 36. mm millimeters 7. $8.70 37. mi2 square miles 8. V = .01p + .1(q-13) 38. yd3 cubic yards 9. V = .01p + .3q + .35 10. 148.9 11. -42.8 12. 38.9 13. 132pi or 414.69 14. 70pi or 219.91 15. 24pi or 75.4 16. 60 17. 30 18. 62 19. 59.5 20. 36 21. 42 22. 318 23. 386 24. 168 25. 13y 26. 8a 9 27. 28r 2t 28. 22x 35 29. 11t + 48 30. 28t 34

Assignment 2.2b

72

Section 2.2 Exercises Part C Please label everything with the correct units.

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

1. 6t f3 2. +2f12 - 10a t 3. 2fr 31a + 15a

Use the formula for Interest.

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

5. P = 2,300 r = 6% Y = 8.7 A =

6. P = 1,300 r = 8.9% Y = 7 A =

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

7. q = t+5 d = m n = 13 V =

8. p = 15 d = 9 V =

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

Use the formula for Temperature Conversion to calculate the temperature in degrees Celsius.

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 in h = 12 in V =

14. r = 9 m h = 5 m SA =

15. r = 3 yd h = 8 yd LSA =

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

16. b = 6 ft h = 5 ft A =

17. b = 15 cm h = 4 cm A =

18. Two angles are 45 and 79; what is the third?

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

19. b = 9 km B = 11 km h = 7 km A =

20. b = 8 mm B = 15 mm h = 5 mm A=

21. b = 12 ft B = 25 ft a = 13 ft d = 17 ft P =

Assignment 2.2c

73

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) +4p 28. 8x2 34x3 + 9x2 + 10x3 29. 12x4 5x 4x4 + 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 power company 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)

Assignment 2.2c

74

Answers: 1. -121 31. $13.50 per yd2

2. 1538 or 1582 32. $1.50 3. -38 33. 48.75 Pesos 4. $22,854.03 34. 45 miles per hour 5. 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 in3 or 432pi in3 14. 791.68 m2 or 252pi m2 15. 150.8 yd2 or 48pi yd2 16. 15 ft2 17. 30 cm2 18. 56 19. 70 km2 20. 2115 or 57.5 mm2 21. 67 ft 22. -2y 23. 14a 11b 24. 56r 48t 25. 2x 3 26. 12m + 60t 27. 49p 21 28. -24x3+17x2 29. 8x4 + 8x 30. -32xy + 28xm

Assignment 2.2c

75

Section 2.3 More Formulas A 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 are now ready to take another step with a much more powerful calculator a computer. During this lesson, you are going to learn the basics of spreadsheets and how to make a computer do the calculations for you. During this discussion, we will use Microsoft Excel as the spreadsheet, but similar functions can be done in spreadsheets that are available at no cost such as OpenOffice Calc.

Microsoft Excel Basics

Microsoft Excel is spreadsheet software that allows you to perform calculations that help solve math 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. The main spreadsheet in Excel will appear. The spreadsheet is divided into cells each of which has a column 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 cell below 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 can enter data rapidly using the keypad.

Enter the = (equal) sign in the cell before you perform any calculation in Excel. This tells Excel 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 by formatting the cell.

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

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

Section 2.3

76

Lifelong Income Example Beginning Salary

You 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 years income at $31,200. These entries are illustrated

below:

Yearly Income Calculation Format In 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 for the 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 addresses in 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.

Section 2.3

77

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

Circle Example Pick 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 a circle is

=

So, in C2 we write =PI()*B2^2

pi 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, isnt it? You can change the radius to any number you would like and the area calculation will automatically update.

Now, the power of Excel doesnt stop just there. We can see the areas of a whole bunch of radii at the same time. List out several numbers in the cells beneath the 7 in B2. Now, if you copy the formula from C3 and paste it in C4, C5, C6, etc. you will notice that we can make a whole table of areas. If you label the columns, then others that see your spreadsheet will be able to tell what 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)

Circle Radius Area

2 12.56637

4 50.26548

6 113.0973

8 201.0619

10 314.1593

12 452.3893

Section 2.3

78

Copy and paste the formula into the cells next to the list of temperatures. See if it looks something like this:

Fahrenheit Celsius

-40 -40.0

-20 -28.9

0 -17.8

15 -9.4

32 0.0

38 3.3

45 7.2

72 22.2

100 37.8

150 65.6

212 100.0

Section 2.3

79

Section 2.3 Exercises Part A 1. Using the formula for a rectangle and a calculator, fill out the following table: length width Perimeter Area 5 7 14 3 7.2 18.34 13 2.5 15 17 16 33 281 541.5

2. If the unit for length and width in #1 is inch, what are the units for Perimeter and Area?

3. If the unit for length and width in #1 is centimeter, what are the units for Perimeter and Area?

4. Using the formula for a rectangle and a spreadsheet (Create a new file called Formula Practice), fill out the table in #1 using the formula abilities of the spreadsheet.

5. Using the formula for a circle and a calculator, fill out the following table: radius Circumference Area 3 12 5.1 17 4 38 114

6. If the unit for radius in #5 is feet, what are the units for Circumference and Area?

7. If the unit for radius in #5 is kilometer, what are the units for Circumference and Area?

8. Using the formula for a circle and a spreadsheet, fill out the table in #5 using the formula abilities of the spreadsheet.

9. Using the formula for a cone and a calculator, fill out the following table: radius height slant height LSA SA Volume 3 4 5 5 12 13 15 8 17 24 7 25 6 8 10

Assignment 2.3a

80

10. If the unit for radius, height and slant height in #9 is inch, what are the units for Lateral Surface Area, Surface Area, and Volume?

11. If the unit for radius, height and slant height in #9 is centimeter, what are the units for Lateral Surface Area, Surface Area, and Volume?

12. Using the formula for a cone and a spreadsheet, fill out the table in #9 using the formula abilities of the spreadsheet.

13. Open your, Budget and Expense spreadsheet. Make sure that all budgets and expenses are updated. Using the sum formula, create cells that are the totals of your expenses and incomes. This spreadsheet will be submitted in your portfolio.

Assignment 2.3a

81

Answers: 1. length width Perimeter Area 5 7 24 35 14 3 34 42 7.2 18.34 51.08 132.048 13 2.5 31 32.5 15 17 64 255 16 33 98 528 281 541.5 1645 152,161.5

5. radius Circumference Area 3 18.85 28.27 12 75.40 452.39 5.1 32.04 81.71 17 106.81 907.92 4 25.13 50.27 38 238.76 4,536.46 114 716.28 40,828.14

9. radius height slant height LSA SA Volume 3 4 5 47.12 75.40 37.70 5 12 13 204.20 282.74 314.16 15 8 17 801.11 1507.96 1884.96 24 7 25 1884.96 3694.51 4222.30 6 8 10 188.50 301.59 301.59

2. P in; A in2 3. P cm; A cm2 4. On Spreadsheet

6. C ft; A ft2 7. C km; A km2 8. On Spreadsheet

10. LSA in2; SA in2; V in3 11. LSA cm2; SA cm2; V cm3 12. On Spreadsheet 13. In Portfolio

Assignment 2.3a

82

Section 2.3 Exercises Part B 1. Using the formula for a cylinder and a calculator, fill out the following table: radius height Surface Area Volume 5 7 14 3 7.2 18.34 13 2.5 15 17 16 33 281 541.5

2. If the unit for length and width in #1 is inch, what are the units for Surface Area and Volume?

3. If the unit for length and width in #1 is centimeter, what are the units for Surface Area and Volume?

4. Using the formula for a cylinder and a spreadsheet, fill out the table in #1 using the formula abilities of the spreadsheet.

5. Using the formula for a Sphere and a calculator, fill out the following table: radius Surface Area Volume 3 12 5.1 17 4 38 114

6. If the unit for radius in #5 is feet, what are the units for Surface Area and Volume?

7. If the unit for radius in #5 is kilometer, what are the units for Surface Area and Volume?

8. Using the formula for a sphere and a spreadsheet, fill out the table in #5 using the formula abilities of the spreadsheet.

83

9. Using a spreadsheet fill out the table for a savings account that has a beginning balance of $150 and grows at 7% with an additional $25 added at the end of each year: year Beginning Balance Ending Balance 1 150 150 1.07 + 25 = 185.5 2 185.5 185 1.07 + 25 =

.

.

.

use your calculator to make sure that the spreadsheet is calculating it correctly.

15

10. As a group, select a typical job that one of you anticipates having in the next five years. Then open a spreadsheet document and go through the lifelong income example in this section. How much money do you expect to earn over your lifetime?

Assignment 2.3b

84

Answers: 1. radius height Surface Area Volume 5 7 376.99 549.78 14 3 1,495.40 1,847.26 7.2 18.34 1,155.40 2,986.86 13 2.5 1,266.06 1,327.32 15 17 3,015.93 12,016.59 16 33 4,926.02 26,540.17 281 541.5 1,452,185.50 134,326,275.61

5. radius Surface Area Volume 3 113.10 113.10 12 1,809.56 7,238.23 5.1 326.85 555.65 17 3,631.68 20,579.53 4 201.06 268.08 38 18,145.84 229,847.30 114 163,312.55 6,205,877.00

2. SA in2; V in3 3. SA cm2; V cm3 4. On Spreadsheet

6. SA ft2; V ft3 7. SA km2; V km3 8. On Spreadsheet 9. At the end of 15 years you should

have $1,042.08

10. Complete when everyone can do it on their own.

Assignment 2.3b

85

Section 2.3 Exercises Part C Chapter 2 Exam Review

Find the following: 1. )5(83673 + 2. mv 92 3. )47(4)73(6 2 +

Find the perimeter of the following shapes:

4. 12

11

math100gltextbook.pdf

Documents