UNIT V STUDY GUIDE Percet Notatio Course Learig Outcomes for Uit V Upo completio of this uit, studets should be able to: 1. Write three kids of otatio for a percet. 2. Covert betwee percet otatio ad decimal otatio, ad covert betwee fractio otatio ad percet otatio. 3. Traslate percet problems to percet equatios ad solve percet problems usig percet equatios. 4. Traslate percet problems to proportio equatios ad use proportios to solve percet problems. 5. Solve applied problems ivolvig percet, percet of icrease, or percet of decrease. 6. Solve applied problems ivolvig sales tax ad percet, commissio ad percet, ad discout ad percet. 7. Solve applied problems ivolvig simple iterest ad compoud iterest.. Solve applied problems ivolvig iterest rate o credit cards. Readig Assigmet Chapter : Percet Notatio Uit Lesso People lear i a variety of ways. For this reaso, each sectio i each uit of this course will iclude multiple resources, such as required readig assiged i the textbook; optioal media assigmets that will iclude the hardest cocepts i the uit; homework with five help aids to the right of the problem, which iclude Help Me Solve This ; View a Example ; Textbook, which opes the e-textbook to the page where the cocept is taught; Ask My Istructor ; ad the optio to prit the questio. The best way to lear math is by practicig. Each uit will ot oly provide istructio ad guidace o how to solve problems, but also umerous opportuities to practice solvig them o your ow through o-graded assigmets. At the ed of each sectio will be a Exercise Set. Aswers ad guidace for solutios are provided i idicated sectios of the textbook, as well as i the studet solutios maual that accompaies the textbook. Whe you click o Uit V i your course, you will see a TO DO LIST to assist you i startig your course. Click each chapter as listed i Chapter Cotets i MyMathLab. A Chapter Opeer will be available for review. Next click o the sectios withi the Chapter to ope the followig: video presetatio, multimedia e- Text (e-book with aimatios ad videos to illustrate cocepts), ad your study pla. The above holds true for every chapter ad every sectio i the textbook. Each Chapter also cotais a mid-chapter review, chapter summary ad review, ad a chapter test with test prep videos ad after Chapter 2, there will be a Cumulative Review that will cover all cocepts up to ad icludig the curret chapter. Uit V covers Chapter i the textbook. MAT 0390, Itermediate Algebra 1
CHAPTER EIGHT: PERCENT NOTATION Sectio.1, Percet Notatio Percet Notatio ca be writte three ways: 1. Ratio: % = the ratio of to 100 = 100 2. Fractio otatio: % = x 1 100 = 100 3. Decimal otatio: % = x 0.01 = 0.01 Example: Write three kids of otatio for 70%. 1. Ratio = 70 100 2. Fractio otatio = 70 x 1 = 70 100 100 3. Decimal otatio = 70 x 0.01 = 0.7 Covertig betwee percet otatio ad decimal otatio is very importat i everyday math. You ca utilize ratio or decimal otatio to accomplish this coversio. Example: Write decimal otatio for 7%. 7% = 7 100 = 0.7 OR 7% = 7 x 0.01 = 0.7 Study the boxes o pages 514 for further guidace o covertig from percet otatio to decimal otatio ad from decimal otatio to percet otatio. Let s covert betwee fractio otatio ad percet otatio. Example: Covert 3 to percet otatio. 5 Divide the umerator by the deomiator. 0.6 5 )3.0-3 0 0 Covert the decimal otatio to percet otatio. 0.6 * 100 = 60% Percet otatio 3 5 = 60% Review examples 9-16, pages 516-51. Look carefully at the chart at the bottom of page 51, etitled Fractio, Decimal, ad Percet Equivalets. You will fid these very helpful. The families of fractios will help you too. MAT 0390, Itermediate Algebra 2
FAMILIES OF FRACTIONS The Family of Thirds: 1 3 = 0.33333 3 repeatig = 1 3 % Example: 66.3333% = 66 1 3 % 2 3 = 0.66666 6 repeatig = 2 3 % Example: 76. 666666 = 76 2 3 % Family of Niths (otice the patter): 1 9 = 0.1111% 1 repeatig = 1 9 % 2 9 = 0.2222% 2 repeatig = 2 9 % 3 9 = 1 = 0.3333% 3 repeatig (I believe you kow this oe by ow.) 3 4 9 = 0.4444% 4 repeatig = 4 % (Do you see the patter?) 9 You fiish the rest. 5 = 9 6 = 9 7 = 9 = 9 The Family of Odd Eighths: They are termiatig decimals, but a good family to kow. The eve eighths you should kow. See the patter: 1 = 0.125 3 = 0.375 5 = 0.625 7 = 0.75 MAT 0390, Itermediate Algebra 3
Sectio.2, Solvig Percet Problems Usig Percet Equatios I sectio 5., you were poited to this: Studets repeatedly state that their biggest obstacle is to traslate words ito algebraic expressios/ equatios. The chart o page 366 is oe of the most importat charts i the book. Study it carefully. The practice traslatig phrases to algebraic expressios o pages 367-36 i Examples 1 ad 2. If you mastered this cocept, the Sectio.2 will be easy for you. Page 525 gives you the key words i percet traslatios. Make sure that you lear these key words. Oce your equatio is set up, follow the rules for solvig equatios: You must show the additio/subtractio/divisio steps o both sides of the equatio to receive full credit. You must show your work algebraically. This sectio is simply a exteded review of solvig equatios. Sectio.3, Solvig Percet Problems Usig Proportios I this sectio, we will solve percet problems usig proportios. May studets state that this is their favorite way to solve percet problems. Remember that a percet is a ratio of some umber to 100. For example, 46% is the ratio of 46 to 100, which ca be represeted by the fractio 46 100. The umbers 67,620,000 ad 147,000,000 have the same ratio as 46 ad 1000.How do you determie that fact? Remember cross products? If the cross products are equal, the ratios are equal. 46 1000 = 67,620,000 147,000,000 46 147,000,000 = 1000 67,620,000 6,762,000,000 = 6,762,000,000 Example: Traslate to a proportio ad solve. 23% of 5 is what? # of Hudredths base amout (a) Set up the proportio by fidig the cross products, ad solve. 23 a 100 5 100a = 115 (This is the equatio to solve (115 = 23 x 5) 100a = 115 (Reduce by dividig each side by 100.) 100 100 a = 1.15 MAT 0390, Itermediate Algebra 4
Study the key terms base ad amout carefully. It is very easy to traspose those. Example: What percet of 50 is 16? = 16 100 50 16 100 50 50 = 1600 50 = 1600 50 50 = 32% Note that whe solvig percet problems usig proportios, is a percet ad eeds oly a % sig. Sectio.4, Applicatios of Percets I this sectio, we will look at real-world applicatios ad solve these usig proportio equatios or the percet equatio (see Sectio.2). Remember that i sectio 5. these istructios were give: Studets repeatedly state that their biggest obstacle is to traslate words ito algebraic expressios/ equatios. The chart o page 366 is oe of the most importat charts i the book. Now is the time to implemet what you leared o page 366. Read each example carefully. Take otes o how the proportios are set up; if those ratios are icorrect, you will get a wrog aswer. You eed to master this ow for future success i this course ad future math courses. It is strogly advised that you use the studets solutios maual ad work the odd-umbered problems o pages 542-544. If you eed further help with ay of these, cotact your istructor. Sectio.5, Percet of Icrease or Decrease I this sectio, we will solve applied problems ivolvig percet of icrease or percet of decrease. Percet of Decrease The Dow Joes Idustrial Average (DJIA) pluged from 11,143 to 10,365 o September 29, 200. This was the largest oe-day drop i its history. Example: What was the percet of decrease? First, let s fid out how much the decrease was: 11,143 10,365 = 77 Next, we create our Proportio Equatio: 100 = 77 11143 77 100 11143 11143 = 7700 11143 11143 = 7700 11143 MAT 0390, Itermediate Algebra 5
~ 6.91 % ~ 7% Percet Equatio: Example: 77 is what percet of 11,143? 77 = 11,143p 77 = 11,143p 11143 11143 0.0691 ~ p 0.07 * 100 ~ p P ~ 7% Traslatig for Success, page 549 Sectio.6, Sales Tax, Commissio, ad Discout Taxes are a big issue i all of our lives. We have sales tax, city tax, couty tax, state tax, ad federal tax. Sice we deal with taxes every day, we eed to kow how to figure the taxes i all of these areas. Example: The sales tax o the purchase of a GPS avigator is $55.93. The GPS avigator costs $799. That is the sales tax rate? You ca solve this i oe of two ways. First way: r = 55.93 799 r = 0.07 r = 0.07 * 100 r = 7% (sales tax rate) Secod way: Set up a proportio equatio: 55.93 = 799r 55.93 = 799r 799 799 0.07 = r 0.07 * 100 = r 7% = r (sales tax rate) May sales people work for a base salary + commissio. Some sales people work o graduated commissio. Let s work a problem with a graduated commissio. MAT 0390, Itermediate Algebra 6
Example: Miguel s commissio is icreased accordig to how much he sells. He receives a commissio of 5% for the first $2000 of sales ad % for the amout over $2000. What is his total commissio o sales of $6200? C = (6200-2000)(0.0) + 2000(0.05) C = 4200(0.0) + 100 C = 336 + 100 C = $436 We all love to buy thigs at a discout. Pay close attetio to defiitios o page 556 of origial or marked price, the rate of discout, the discout, ad the sale price. Note that discout problems are a type of percet of decrease problem. Example: A leather sofa marked $2379 is o sale at 33 1 % off. What is (a) the discout? (b) The sale price? 3 Look back at the family of fractios to help with the percet. (a) Discout = Rate of discout x Origial price D = 33 1 % x 3 $2379 D = 1 3 x $2379 D = 2379 3 D = $793 (b) Sale price = Origial price Discout S = $2379 $793 S = $156 Here is a secod way to solve Step B of this problem: S = $2379 (2379 1 3 ) S = $2379 $793 S = $156 The secod method solves the problem i a more efficiet method; the first method ivolves more work. Sectio.7, Simple Iterest ad Compoud Iterest, Credit Cards If you have to take out a loa, always try to get simple iterest. The amout of moey that you borrow is the pricipal (P). The iterest rate = r. Time = t, which represets 1 year. The simple iterest formula is I = Prt (Iterest = Pricipal x rate x time) Example: What is the simple iterest o $2500 ivested at a iterest rate of 6% for 1 year? P = $2500,r = 6% = 0.06, t = 1 (t will always be a base of 1 year) I = Prt I = 2500 * 0.06 * 1 I = $150 The simple iterest for 1 year is $150. MAT 0390, Itermediate Algebra 7
Example: What is the simple iterest o a pricipal of $2500 ivested at a iterest rate of 6% for 3 moths? Remember that t = 1 year; 3 moths = 3 12 = 1 4 P = $2500 r = 6% = 0.06 t = 1 4 I = Prt I = 2500 * 0.06 * 1 4 I = 2500 0.06 4 I = $37.50 Whe iterest is paid o iterest, we call it compoud iterest. This type of iterest is usually paid o ivestmets. The Compoud Iterest Formula is A = P * (1 + r t ) Example: The Ibses ivest $4000 i a accout that pays 5 5 %, compouded quarterly. Fid the amout i the accout after 2 1 2 years. P = $4000 r = 5 5 % = 0.05625 = times a year; quarterly = 4 times a year A = P (1 + r t ) A = 4000 (1 + 0.05625 ) 4 (5 2 ) 4 A = 4000 (1 + 0.05625 ) 10) 4 A = 4000 (1.0140625) 10 A ~ $4599.46 The amout i the accout after 2 1 years is $4599.46. 2 Accordig to creditcards.com, the average credit card debt per household with credit card debt i the Uited States was $16,007 i 2009. The moey you obtai through the use of a credit card is ot free moey. There is a price (iterest) to be paid for the privilege. A balace carried o a credit card is a type of loa. A small chage i a iterest rate ca make a large differece i the cost of a loa. Whe you make a paymet o a credit card, do you kow how much of that paymet is iterest ad how much is applied to reducig the pricipal? Kowledge of credit cards is very importat to you. Study carefully Examples 6 o pages 566-567. Also, it may be helpful for you to work problems 1-49, odds, o pages 56-570. The aswers ca be foud i the back of the book. Summary ad Review, pages 571-576 Test, pages 577-57 Cumulative Review: Chapters 1-, 579-50 MAT 0390, Itermediate Algebra
Referece Bittiger, M. L., Elleboge, D. J., & Johso, B. L. (2012). Prealgebra (6th ed.). Bosto, MA: Addiso-Wesley. Learig Activities (No-Graded) Practice What You Have Leared After readig Chapter, improve your mastery of the cotet by workig the odd-umbered problems o the followig pages: Sectio.1, pages 519-524 Sectio.2, pages 529-530 Sectio.3, pages 535-536 Sectio.4, pages 542-544 Traslatig For Success, page 549 Sectio.5, pages 550-552 Sectio.6, pages 55-561 Sectio.7, pages 56-570 Oce you have completed the problems, you ca check your aswers i the back of the textbook to see how well you did. Review What You Have Leared Before attemptig the Homework ad the Uit Assessmets, study the chapter summaries, review the cocepts taught i the chapters, ad work the odd-umbered problems i the review exercises. Chapter Mid-Chapter Review, pp. 537-53 Chapter Summary ad Review, pages 571-576 Chapter Test (Practice) pages 577-57; Note: See the top of page 577 to fid the step-by-step solutios for each problem i the test. Cumulative Review: Chapter 1-, pages 579-50 Study Pla for Uit V Oce you have accessed the MAT 0390 course i MyMathLab, click o your chapter study pla to see your progress ad do practice exercises. Your study pla is updated each time you take a Assessmet. The study pla is optioal ad is geerated specifically for each studet. Its cotets are based o each studet s results i order to provide practice where it is eeded for the studet to obtai mastery of the uit cocepts. Other Resources ad Activities If you eed additioal guidace or iformatio, you may use all the resources located withi the MyMathLab. For example, clickig o Tools for Success o the toolbar o the left will brig up the Multimedia Library, which provide access to video lectures give by the authors of the book, PowerPoits, aimatio, ad iteractive figures o a variety of topics. Whe you click o Tools for Success at the very top of the page, it will also provide liks to a variety of helpful aids ragig from Traslatig for Success ad Visualizig for Success Iteractive Aimatios to Basic Math Review Card ad the Itroductory Algebra Review Card, which give a brief summary of may key math cocepts. MAT 0390, Itermediate Algebra 9
I the Chapter Cotets you will also be able to view the Aswer sectio from your textbook, view the Glossary from your textbook, ad view the Idex from your textbook. No-Graded Learig Activities are provided to aid studets i their course of study. You do ot have to submit them. If you have questios, cotact your istructor for further guidace ad iformatio. MAT 0390, Itermediate Algebra 10