1. Winter, 2011 Ms. Ellmer

2. Background: Ratios and proportions have many uses in many industries. They can be used to read a map, mix chemicals in painting and landscaping, mix cleaners in home improvement projects, scaled drawings, and finding unit prices while grocery shopping. Vocabulary: Ratio: A comparison of two numbers. Written in 3 ways: 1. a to b 2. a:b 3. a b Unit Rate: Any number over 1 with units “something per something else” Scale Drawing/Scale: compares each length in a drawing to the actual length. Dimensional Analysis/Factor-Label Method: a process using proportions to cancel units of measurement. 2

3. How to Use It: In Science, unit rates allow you to “cancel your units,” or use dimensional analysis to get the units you want. Ex.1 40.56(km) ∙ (1 mi) = (hr) 1.6 (km) 25.35 mi/hr …..on a 10 speed bike!!!!! 3

4. Ex.2 Page 143 (Algebra I) Lance Armstrong! In 2004, Lance Armstrong won the Tour de France completing the 3391 km course in about 83.6 hours. Find Lance’s average speed using v=d/t. d=3391 km t = 83.6 hr v = ? v = d t v = (3391 km) (83.6 hr) v = 40.6 km/hr 4

5. Vocabulary Continued: Proportion: is an equation that states that two ratios are equal, written as: a = c bd And you read it as, “a is to b as c is to d” What is the difference between a set of ratios and a proportion????? THE = SIGN IS IN THE PROPORTION ONLY!!!!!! 5

6. Ex.3 Solve for x. 1:16 = ? : 36 1= x 16 36 What should we do now? Yep, cross multiply and start flexing your algebra muscles! x = 2.25 6

7. The proportions can get really big and have variables….no problemo! Ex. 4 Solve each proportion. 2X-2= 2X-4 14 6 6(2X-2) = 14(2X-4) 12x – 12 = 28x – 56 -28x -16x – 12 = -56 + 12 = +12 -16x = -44 x = 2.75 7 Recipe to Solve Equations Step1: Get x term(s) alone on one side. Step2: Combine Like Terms. Step3: Isolate x using opposite functions. Step4: Plug x value back in to original question and check answer.

8. Are we done? Nope, go back in and check your answer…. 2(2.75)-2= 2(2.75)-4 14 6 0.25 = 0.25 YES!!!!! 8

9. The Golden Rectangle: a rectangle that can be divided into a square and a rectangle, studied by da Vinci (1452- 1519) The Golden Ratio: In any golden rectangle, the L:W is about 1.618:1 This is used largely in architecture, such as Sears Tower, Empire State Building, and the UN Building in NYC

10. How to Use It: Ex. The longer side of a golden rectangle is 20ft. Find the length of the shorter side. L = 1.618 W 1 20ft = 1.618 W 1 (20ft) ∙(1) = (1.618)(W) 20 = 1.618W 1.618 12.4 ft = W

11. Now, you do ODDS 1- 29 11