Math 100GLText Book PDF

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Introduction to Algebra and Finance...

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Math 100G/L Introduction to Algebra and Finance BYU-Idaho

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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.)

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Table of Contents Chapter 1 Arithmetic……….…………………………………………………………...4 Section 1.1………………………………………………………………………………...5 Addition and Multiplication Facts from 1+1 to 15 × 15

Section 1.2……………………………………………………………………………..…13 Rounding and Estimation; Life Plan

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

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

Chapter 2 Calculators and Formulas……………………………………………52 Section 2.1…………………………………………………………………………..……53 Exponents Introduction, Order of Operations, Calculator Usage

Section 2.2……………………………………………………..…………………………64 Variables and Formulas

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

Chapter 3 Algebra.………………....……………………………………………………94 Section 3.1……………………………………………………………………………….95 Linear Equations and Applications

Section 3.2………………………………………………………………………………113 Linear Equations with Fractions; Percent Applications

Section 3.3………………………………………………………………………………126 Exponents Revisited; Loan Payment and Savings Equations

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

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

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Section 1.1

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 Facts 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 how to add in your head up to 15+15. If you don’t, 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 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 addition facts, you need to also memorize the multiplication facts up to 15×15. Learn them well, and you will be able to catch on to everything else quite nicely.

Chapter 1

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Section 1.1 Exercises Part A 1. 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.

Exercises 1.1

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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_________

Exercises 1.1

8

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_________

Exercises 1.1

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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 =

Time_________ Exercises 1.1

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Multiplication 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=

Time_________

Exercises 1.1

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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 =

Time_________ Exercises 1.1

12

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_________

Exercises 1.1

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Section 1.2 Rounding and Estimation

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

Tenths Hundredths Thousandths Ten Thousandths Hundred Thousandths Millionths

Hundreds Tens Ones

Hundred Thousands Ten Thousands Thousands

Hundred Millions Ten Millions Millions

Billions

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 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

Section 1.2

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LAST EXAMPLE Round $4,278.23 to the nearest hundred $4,300.00 $4,278.23 $4,200.00 $4,278.23 ≈ $4,300.00

Decide if our number is closer to the nearest hundred above the number or below the number Change our number to the one it is closer to Answer: $4,300.00

Estimation 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...