Algebra 1 HonorsAlgebra 1 HonorsFinal Exam ReviewFinal Exam Review

Chapter 4Chapter 4Presented By:Presented By:

Justin LoveJustin Love&&

Liz MosesLiz Moses

May 7, 2009

Key Terms:Key Terms: RatioRatio RateRate

Unit RateUnit Rate Unit AnalysisUnit Analysis ProportionProportion

Extremes of ProportionsExtremes of Proportions Means of ProportionsMeans of Proportions

Cross ProductsCross Products Similar FiguresSimilar Figures

ScaleScale

Homework Part I:Homework Part I:– Define Key TermsDefine Key Terms

Pages 183-191 (or in Pages 183-191 (or in glossary)glossary)

Chapter 4, Section 1Chapter 4, Section 1

Ratio and ProportionRatio and Proportion

Using Unit Using Unit RatesRates

Unit RatesUnit Rates: : a rate with a rate with a denominator of 1)a denominator of 1)

RatioRatio: : a comparison of a comparison of two numbers by division.two numbers by division.

RateRate: : the ratio of the ratio of aa to to bb if if aa and and bb are measured in are measured in different units.different units.

Price of Apple JuicePrice of Apple Juice

PricePrice VolumVolumee

Cost/OzCost/Oz

$.72$.72 16 oz16 oz 4.54.5¢/oz¢/oz

$1.20$1.20 32 oz32 oz ????????¢/¢/ozoz

$1.60$1.60 64 oz64 oz ????¢/????¢/ozoz

The table at the right gives prices for different sizes of the same brand of apple juice. Find the unit rate (cost/oz) for the 32 oz and the 64 oz size.

How?: divide cost by oz, and move the decimal to the right 2 places

cost

Now….What size is best economical choice?

$.72ounces 16 oz

= $.045 =4.5¢¢

Unit Rates and Unit Rates and Conversions….Conversions…. When converting from one unit to another, as in When converting from one unit to another, as in

hours to minutes or minutes to hours, you must hours to minutes or minutes to hours, you must decide which conversion factor will produce the decide which conversion factor will produce the appropriate unit. This process is called appropriate unit. This process is called unit unit analysisanalysis..

To change one unit of measure to another, you can To change one unit of measure to another, you can use rates that equal 1. For Example:use rates that equal 1. For Example:

7 h=

7 h1

60 min1 h

= 420 min Divide the common unit, which is hours (h), The result is minutes.

Try: You and your friends go on a road trip and drive for 5 Hours. How many minutes were you driving?

Bonus: If you were driving at an average speed of 63 MPH, How

many miles did you travel?

Converting Converting Rates…..Rates…..

Try: A sloth travels Try: A sloth travels at 0.15 MPH. at 0.15 MPH. Convert this speed Convert this speed into Feet-Per-Minute.into Feet-Per-Minute.

A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s speed in MPH? You need to convert feet to miles, and seconds to hours……

Solving Solving Proportions….Proportions….

A A proportionproportion is an equation is an equation that states two rations are that states two rations are equal.equal.

a c=b dFor this proportion, a and d are the extremes of the proportion, and b and c are the means of the proportion.

Proportions may also be written

like this: a : b = c : dUsing the

Multiplication Property of Equality:

t 5=9 6

Try: 18 m=50 15

Using Using Cross Cross

Products…Products…

The products of ad and bc are the

cross products of the proportion

a c b d=

Solving Multi-Step Solving Multi-Step ProportionsProportions

To solve a proportion To solve a proportion with variable with variable expressions with more expressions with more than one term, you will than one term, you will use cross products and use cross products and the Distributive the Distributive Property.Property.

Chapter 4, Section 2Chapter 4, Section 2

Proportions and Similar Proportions and Similar Figures.Figures.

Finding the Finding the Length of a Length of a

SideSideIn the Figure below, In the Figure below, ABCABC ~ ~ DFEDFE. .

Find Find DEDE..C

A B

21 cm

18 cm

15 cm

E

D F

x

10 cm

Applying Applying SimilaritySimilarity

EX: EX: A tree Casts a shadow 7.5 feet long. A woman A tree Casts a shadow 7.5 feet long. A woman 5ft tall casts a shadow 3 feet long. How tall is the 5ft tall casts a shadow 3 feet long. How tall is the tree?tree?

You can use proportions to find dimensions of objects that are difficult to measure directly…

Finding Finding Distances on Distances on

MapsMaps

A A scale drawingscale drawing is similar to an actual object or place. The is similar to an actual object or place. The ratio of a distance in the drawing to the corresponding ratio of a distance in the drawing to the corresponding actual distance is the actual distance is the scalescale of the drawing. of the drawing.

The scale of a map is 1 inch = 10 miles. Aprx How far is it from Valkaria to Wabasso if the two cities are 1.75 inches apart on the map?

Chapter 4, Section 3Chapter 4, Section 3

Proportions and Percent Proportions and Percent EquationsEquations

Finding the Finding the Percent…Percent…

Remember: a Remember: a percent is a ratio percent is a ratio that compares a that compares a number to 100.number to 100.

What percent of 80 is 18?

Finding Finding the Part…the Part…

You can use a You can use a proportion to proportion to find the part (is) find the part (is) or the whole (of) or the whole (of) in a percent in a percent problem…problem…Find 75% of 320.

Finding Finding the the

Whole….Whole….Surface water accounts for 77.6% of our countries total Surface water accounts for 77.6% of our countries total

water supply. The surface water supply is about 264.4 water supply. The surface water supply is about 264.4 billion gallons per day. Find the total water supply.billion gallons per day. Find the total water supply.

Finding the Finding the Whole…Whole…

Try: Try: Carlos worked 31.5 hours at a hospital as a Carlos worked 31.5 hours at a hospital as a volunteer. This represents 87.5% of his school’s volunteer. This represents 87.5% of his school’s requirement for community service. How many requirement for community service. How many hours does his school require for community service?hours does his school require for community service?

Using a Using a Percent Percent

Equation…Equation…What percent of 170 is 68?What percent of 170 is 68?

You can also solve a percent problem by translating the words into an equation.

Percents Greater than 100% Percents Greater than 100% and Less than 1%and Less than 1%

a. a. What percent of What percent of 90 is 135?90 is 135?

b. b. What is .48% of 250?What is .48% of 250?

Using Using EstimationEstimation

……

You can estimate some You can estimate some percents using percents using fractions. For example, fractions. For example, if you wanted to find if you wanted to find 26.1% of a number, you 26.1% of a number, you could multiply ¼ times could multiply ¼ times the number to estimate the number to estimate the answer.the answer.

PercentPercent 5%5% 10%10% 20%20% 25%25%

FractionFraction 1/20 1/20 1/10 1/10 1/51/5 1/41/4

PercentPercent 33.333.3

Percents and Fractional Equivalents.