winter, 2011 ms. ellmer. background: ratios and proportions have many uses in many industries. they...
TRANSCRIPT
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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