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8-1: Ratios and Equivalent Ratios { IWBAT read and write ratios and equivalent ratios Ratio – A comparison of two quantities 9 girls and 7 boys Three ways to write ratios: 1. 9:7 2. 9 to 7 3. Ratio 9 7 Two ratios that are equal to each other 9 9 ∙ 5 45 = = 7 7 ∙ 5 35 9 45 = 7 35 Equivalent Ratios 5:8 _____ 15:24 1) Rewrite as in fraction form and make equal to each other 5 15 = 8 24 2) Cross-multiply (multiply diagonally) 120 = 120 3) If cross-products are equal, the ratios are equivalent (=). If cross-products are not equal (≠) Are the ratios equivalent? 1) 3 12 9 ____ 36 2) 108 = 108 4 6 16 ______ 20 80≠96 3) 9 to 8 ____ 45 to 40 9 45 _____ 8 40 360 = 360 Examples 8-2 and 8-3: Proportions { IWBAT solve proportions using equivalent ratios using Cross-Products (Cross-Multiplication) 4 12 , 5 15 Use the cross-multi plying method 4 12 , 5 15 60 = 60 Yes Do these ratios make a proportion? 1) 3 9 , 8 21 63 ≠ 72 No 2) 2 18 , 3 27 3) 5 40 , 8 64 54 = 54 320 = 320 Yes Yes Examples 2 = 3 21 1) Simplify vertically and/or horizontally, if possible 2 = 1 7 2) Cross-multiply = 14 3) Solve for , if needed Find the missing number 1) 6 9 8 = 2) 9 15 = 10 3) 8.5 3.2 = 8 5) Three boxes of cereal cost $10.50. What does one box cost? Examples 4) 2.6 4 = 4.8 8-4: Too Much or Too Little Information { IWBAT determine which information is missing and identify extraneous information in problems. 8-5: Rates { IWBAT use rates to solve problems. Rate – A ratio that compares two quantities that have different units of measure Unit Rate – A rate where the second quantity is a unit of one (denominator) Vocabulary You travel 99 miles in 90 minutes. What is your average rate of speed in miles per hour? 99 90 1) Write as a rate in fraction form 2) Divide 3) Rewrite as a phrase or as a fraction with labels 9.5 9.5 miles per minute 9.5 Find the Unit Rate 1) 90 miles in 75 minutes 2) 252 miles every 9 gallons 3) 48 chairs for 6 tables 4) 96 students in 3 classrooms 5) Respiration rate is the number of breaths you take per minute. You count 48 breaths in 3 minutes and your friend counted 34 breaths in 2 minutes. Who had the higher respiration rate? Examples 8-6: Unit Price { IWBAT find unit prices to determine the better buy. Unit Price – The cost per item Similar to unit rate but money amount always is the numerator Round to the nearest cent (hundredth), if necessary Vocabulary Find the unit price. Round to the nearest cent. $60.00 for 12 books 1) Write as a rate in fraction form with the price in the numerator 2) Divide 3) Rewrite as a phrase or as a fraction with labels $60 12 $5 $5 per book $5 Unit Price 1) $46.20 for 6 shirts 3) $1.47 for 1.5 lb broccoli Examples 2) $14.28 for 12 lb of turkey 4) $0.60 for 12 oz of rolls 12 bananas for $1.80 or 15 bananas for $2 1) Find the unit price for each item. $1.80 12 $2 15 2) Compare. The better buy is the cheaper (lesser) amount. $0.15 $0.13 15 bananas for $2 is the better buy. Which is the better buy? 1) 3 tacos for $3.50 or 4 tacos for $5.00 2) 12 books for $119.40 or 6 books for $53.34 Examples 8-7: Make a List { IWBAT solve problems by making an organized list 8-8: Similar Figures { IWBAT use proportions to solve problems involving similar figures Similar Figures – Figures that have the same shape but not necessarily the same size. Vocabulary 8-9: Scale Drawings { IWBAT interpret scale drawings. Scale Drawing – a reduction or enlargement of an actual object. Scale – a ratio that compares a measure on a drawing with the actual measure. Vocabulary 8-10: Using Maps { IWBAT use map scales and proportions to find actual distances