Winter, 2011Ms. Ellmer

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 b2. a:b3. 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.

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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!!!!!

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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 kmt = 83.6 hrv = ?v = d

tv = (3391 km)

(83.6 hr)v = 40.6 km/hr 4

Vocabulary Continued:Proportion: is an equation that states that two ratios are equal, written as:

a = c b d

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!!!!!!

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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 = 2.256

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 -28x-16x – 12 = -56 + 12 = +12-16x = -44 x = 2.75

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Recipe to Solve EquationsStep1: 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.

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!!!!!

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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

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 = 1.618W1.618 1.618

12.4 ft = W

Now, you do

ODDS 1- 29

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