pre-algebra chapter 6 notes.ppt

7/29/2019 pre-algebra chapter 6 notes.ppt

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PRE-ALGEBRACHAPTER 6

January 2013


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Ratios &

Unit Rates


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Key Definitions

Ratio: a comparison of two quantities by

division

Unit Rate: the rate for one unit of a given

quantity


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Examples

Write each ratio as a fraction in simplest form.

1. 14 to 6


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Examples


2. 7:21


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Examples


4. 4:10


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Examples


5. 15 cats : 50 dogs


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Examples


6. 21 hired out of 105 applicants


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Examples


7. 66 miles on 4 gallons


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Examples


8. 48 wins : 18 losses


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Examples


10. 22 players : 2 teams


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Examples

Express each rate as a unit rate.

11. 96 students in 3 buses


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Examples


13. $52.50 in 7 hours


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Examples


14. 416 miles in 8 hours


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Examples


15. $94.99 for 7 pizzas


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Examples


16. 103.68 miles in 7.2 hours


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Examples

Express each ratio in simplest form.

17. Dena counted 14 robins

out of 150 birds.


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Examples


18. Mr. and Mrs. Romero bought a 1,200square-foot house for $111,600. How much did

they pay per square foot?


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SolvingProportions


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Key Definitions

Proportion: a statement of equality of tworatios

Cross Product: the product of two numbers

on the diagonal when comparing two ratios


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Examples

Tell whether each pair of ratios isproportional.


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Examples

Solve each proportion.


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Examples

Solve each proportion.One hundred nautical miles equals about 115 standard,

or statute, miles. How many statute miles equal 381

nautical miles? Round your answer to the nearest whole

number.


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Examples

Solve each proportion.One hundred rods is about 275 fathoms. About how

many fathoms is 25 rods?


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Examples

Solve each proportion.At the Copy Shoppe, 18 copies cost $1.08. at this rate,

how much will 40 copies cost?


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Examples

Solve each proportion.On a recent day, the exchange rate for U.S. dollars to

European euros was 1.32 dollars per euro. On that day,

about how many euros would you get for 25 dollars?


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Examples

Solve each proportion.Recently, the exchange rate for Mexican pesos to U.S.

dollars was 10.737 pesos = 1 dollar. If you were

vacationing in Mexico and had 250 pesos left, how many

dollars would you receive?


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Similar Figures

Similar figures have same shape, not

necessarily same size.

Corresponding angles have equal measuresCorresponding sides are in proportion

Indirect measurement = using similar figures tocompute distances that are difficult to measure

directly.


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Key Definitions

Scale Drawing: a two-dimensional drawing thataccurately represents an object. (It is mathematically similar

to the object.)

Scale: gives the ratio of the dimensions in the drawing tothe dimensions of the object.

Scales can use the same units or different units.

All dimensions are reduced or enlarged using the same

scale.


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Key Definitions

Reduction: a scale drawing that is smaller than the actualobject

Enlargement: a scale drawing that is larger than the

actual object


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ExamplesThe scale of a drawing is in = 12 ft.

Find the actual measurement.

8 inches


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ExamplesThe scale of a drawing is in = 12 ft.

Find the actual measurement.

18 inches


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ExamplesThe scale of a drawing is 2 cm = 15 m.Find the length each measurement would be on a scale drawing.

225 m


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ExamplesThe scale of a drawing is 2 cm = 15 m.Find the length each measurement would be on a scale drawing.

622.5 m


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6-4 Fractions, Decimals, Percents

Percent = ratio that compares a number to 100

Write as a fraction or mixed number 5%

125%

58%

72%

144%


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Write as a decimal

1.5%

62.5%

125%

45%


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Write Each Decimal as a Percent

0.333

METHOD 1 = REWRITE AS AFRACTION

METHOD 2 = MOVE DECIMAL POINT


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Write each decimal as a percent

0.4

0.023

1.75


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Write a Fraction as a Percent

5/16

3/11


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Proportions and Percents

Find 65% of 245


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Proportions and Percents

Find 25% of 124

Find 43% of 230

Find 12.5% of 80


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Finding a Percent

What percent of 60 is 52?


14 is what percent of 15?


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Finding a Whole Amount

207 is 46% of what number?




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Percents in Equations

What is 85% of 62?


What is 145.5% of 20?


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Commission Problem

A real estate agent makes a 4.5%

commission on property she sells. How

much commission does she make on thesale of a house that sells for $132,500.


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Solving a Percent Problem

In a survey, 952 people, or 68%, preferred

smooth peanut butter to crunchy. How

many people were surveyed?


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Percent ofChange

Seventh Grade

Mrs Dishman


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Key Definitions

Percent of Change: the amount, stated as a percent, that a

number increases or decreases

Percent of Increase: a percent change describing anincrease in quantity; when the amount goes up

Percent of Decrease: a percent change describing andecrease in quantity; when the amount goes down

fi i i


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Key Definitions

To Find % of Change

Amount of change

Original amount

E l


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Examples

Find each percent of change. Round the answers to the

nearest tenth of a percent, if necessary.

1.) from 100 to 114

E l


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2.) from 2.0 to 3.2

E l


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3.) from 4,000 to 8,500

E l


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5.) 202 to 192

E l


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6.) 96 to 78

E l


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7.) 77 to 13

E l


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9.) 38 to 95

E l


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10.) 60.3 to 95

E l


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11.) -7 to -10


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Markup and Discount

MARKUP = amount of increase a store puts

on an item.

A music stores percent of markup is 67%.A CD costs the store $10.15. Find the

markup.


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Markup and Discount

A computer store pays $6 for a computer

mouse. The percent of markup is 75%.

Find the mouses selling price.


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Markup and Discount

When an item goes on sale, the amount of

the price decrease is the discount.

Athletic shoes that are regularly $85.99 areon sale for 20% off. Find the discount.


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6-9 Applications of Rational

Numbers Examples provided in class..

Documents

pre-algebra chapter 6 notes.ppt