Class Note for MATH 302A at UA
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Date Created: 02/06/15
Pnnmnki pm Hunnwud 39hmmns ms mum F39rupunhns Pruhlen Farmquot arm Cunveri Homework B Class Notes due Wednesday April 30 a Text problems Ratios and Prop ions in 61 4 5 8 12 23 35 0 Due 51 Math 302A April 25 2008 Mth mu Rallusand prawn Math mix a izrpngt Honuwofr c an mummi Pnnmnkins mums hymn Ew I39linwrsmns a s Emmiw E39s Humim amaan mum F39rupunhns Pruhlen Farmquot arm ammoquot Additive Comparisons vs Multiplicative Comparisons Units Suppose that one car costs 10000 and another costs 15000 Rates We39re looking at relationships for example 60 mph This Label the comparisons as additive and multiplicative is a lot harder to visualize that g mile 0 The second car costs 5000 more than the first 1 B The second car costs 15 times as much as the first a The second car costs 50 more than the first Mth mu Rallusand prawn m an Honuwofr cumin 5 mum Pnnmnmns mum hymn Ems Wm B Huuuvmm 39mens ms mum F39rupununs Pruhl n Farmquot aim ammoquot Definitions Fractions vs Ratios A ratio is a relationship between two amounts or quantities like What are the wholes7 a b ab When the two amount in a ratio represent different quantities we often refer to such ratios as rates We usually see a per in there like 60 mileshour When we set two ratios together we have a proportion a bc d abcd Mth mu Rallusand prawn Math mix Rams and inning gt Honuwofr Cunluangins mumm Prupullluns Prulnums Ew I39hnwrsmns Emmiw E Humevmm 39hmmns ms Dglxmmns Prupullluns mums ram6m Epu39 Cunverslu sum E Solvmg 3 Proportion Other Places Ratios Show Up Solve a CookIng If a repre makes a certaIn amount how would you 289 X get tWIce the amount7 300unces 500unces Wh d h H 7 0 Maps or anything of thIs Idea If 1 Inch represents 20 mIles at oest Is te us how many Inches represent 30 mIles7 a SImIlar TrIangles HorIxLwofr 5 s Pnnmnmns Pruhlems v Es lnnllnn E Humevmm Ihmpxnsons own F39rupununs Pruhlen Inn4m Elma cumsu sum E Ratio Problems Percent Suppose the ratIo of men to women In a room Is 2 3 Percent means per hundred O lfthere are 10 more women than men how many men are In 50 the room7 50 means 50 per hundred or 100 B lfthere are 24 men how many women are In the room7 2 o O lf12 more men enter the room how many women must enter 2 means 2 per hundred or m to keep the ratIo of men to women the same7 315 315 means 315 per hundred or i 100 HorIxLwofr c valan rm 5 Pnnmnmns mung putm Ew m Es lnnllnn E Humevmm Ihmpxnsons nun MW Pruhlen putm E1165 cums Easy Percents Exploration 65 a 1 100 Work In groups on exploratIon 6 5 sales and percent decrease a 333 666 and quotWeasel 1 1 3 725quot 750quot 775quot a 4 A 2 A 4 A 1 2 3 4 a g 20g 40g 60g 80 1 3 5 7 7 1250 7 3750 7 6250 7 8750 0 8 A 8 A 8 A 8 A 1 2 a i 7 i 7 10 10A10 20 etc Mth mu Rallusand prawn Math am Rams and Prunurums Hernewer eas DMIIKIKIUHS Prununmns prairnms Erws Ornvershns Emmetw E Hurrime 39mexnsons Denna F39rupunhns prahiere pene Erma cams situation E Conversions Converting to Percent 9 T0 WHte fraCtlonS 35 deCImalS 0r Percents To write decimals as fractions or percents a ab means 3 3 Divide and write the answer to get the demmal Thequot multiply by 100 to get the percent a Read the decimal Without the word point Simplify if 0 Example 4860 48 60 08 80 necessary a We can also move the decimal point over 0 To write a percent multiply by 100 a To turn 45 into a percent multiply by 100 and move the 6 Example 0 09 9100 9 decimal point two places over to the right 3 You try 7 0071 0 59 e we see this decimal point moving when we use suentific notation a You try 49 4 320 Mth mu Rallusand prawn Mth am Rams and prawngt Hernewer 39 5 s Prununmns prairnms Erws Ornvershns Emmetw E Hurrime 39mexnsons Denna F39rupunhns prahiere pene Ew39 canrers situation E To Decimal A Problem To write a decimal from a percent divide by 100 What if you have 3 257 Move the decimal point to the left two 0 Rewrite 25 as 04 Now 3 25 3 4 To write a fraction read the decimal Without the word point Simplify if necessary Example 591 5 91 5 91100 You try 3 62 0 6 0 Mth mu Rallusand prawn Mth am Rams and prawngt Honuwofr c name an 5 Emma E Humevmm 39hmmnsons new pana Pruhlen pene Ewa cane Estimating More Estimating A newspaper story reports that 8 of 7968 students work full time Strategl 3 find a close number 7968 is about 8000 Strategl 1 Use 10 as a benchmark 1 of 8000 is what7 10 of 7968 is 796 8 or about 797 What can we do then7 Strategl 2 Use 1 as a benchmark 1 of 7968 is 79 68 or about 80 So 8 is 8 1 8 80 640 Strategl 4 find a range 8 is between 10 and 5 5 of 8000 is 400 10 of 8000 is 800 So 8 of 7968 is between 400 and 800 Mth mu Rallusand prawn Mth am Rams and prawngt Humnur Cuniuan 5 mumnus Pnnmnmns prunnms Percent gum rnnaysmns a Exact Answer ercent art Write and solve a proportion plT p whole 8 7 x 100 7 7968 Mth mu Rams and Pmlmrliuns Humnur Cuniuan 5 mumnus Pnnmnmns prunnms Percent gum rnnaysmns 5 Exploration 6 7 Work on exploration 6 7 part 1 In groups Mth mu Rams and Pmlmrliuns Humnur Cuniuan 5 mumnus Pnnmnmns prunnms Percent gum rnnaysmns 5 Another Example My sister has 72 stuffed animals on her bed but she generally only sleeps With 4 at a time What percent of her animals does she sleep With7 Human ounwmsnus Dyan qu F39rupununs Pruhlen Farmquot awn Cunverslulis Emma Solving Percent Problems For most percent problems convert to proportions then solve Math am 1 PruIJurIiuns Human ounwmsnus Dyan qu F39rupununs Pruhlen Farmquot apua Cunverslulis An Example My friend makes 68 baskets a week and wants to sell no more than 30 What is the maximum number of baskets she can sell7 nth a Human ounwmsnus Dyan qu F39rupununs Pruhlen Farmquot apua Cunverslulis Another Example There is a 20 oflc sale at the mall I39ve wanted this really cool sweater that is 120 but couldn39t afford it How much is the discount amount7 What is the sale price7 E Mth mu Rallusand Prupurlluns Math am Rams and imam gt Honuwofr 5 Dumb Gunman Pnnmnmns mum hymn Ezy I39unwrsmns 5 Another Example The college bookstore makes a profit by charging students 25 more than the book actually cost wholesale If your book cost 140 how much dld the bookstore pay for It7 Mth mu Rams and pmme
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