Chapter 8: RATIOS, RATES, PROPORTIONS, AND CONVERSIONS - BC

[Pages:16]Chapter 8: RATIOS, RATES, PROPORTIONS, AND CONVERSIONS

8.1 RATIOS p 2-3 8.2 RATES p 4-5 8.3 PROPORTIONS p 6-7 8.4 CONVERSIONS p 8-9 8.5 PERCENT OF CHANGE p 10-11 8.6 SIMPLE INTEREST p 12-13 Answer Key

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8.1 RATIOS

Key Vocabulary 8.1 colon: _________________________________________________________________ ratio: __________________________________________________________________

Think 8.1

Sentence: There are 12 men and 18 women in the math class.

Ratio Sentence: The ratio of men to women is 12 to 18.

Written as: 12:18 or 12 and simplified as: 2:3 or 2

18

3

For whole number ratios, leave ratio improper: 4 to 1 or 4:1 or 4 1

For mixed number ratios, convert mixed numbers to improper.

2

1 2

to 3

2

1 2

3

5 2

3

5 2

3 1

51 23

5 6

Try It 8.1

Write each ratio using a colon and as a fraction. Simplify by reducing fractions to lowest

terms.

Colon Fraction

Colon Fraction

1) 4 to 6: ________; __________

3) 16 to 8: ________; __________

5)

4

1 2

to

3:

________;

__________

2) 15 to 3: ________; __________

4) 6 to 2: ________; __________

6)

6

1 3

to

2

1 2

:________;

__________

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8.1 Practice Exercises

Write each ratio using a colon and as a fraction. Simplify by reducing fractions to lowest terms.

Colon Fraction

1) 18 to 10: ________; __________

2) 14 to 28: ________; __________

3) 10 to 5: ________; __________

4)

2

1 4

to 4 :

________; __________

5)

5

1 2

to 3 :

________; __________

6) 6 to 11: ________; __________

7) 8 to 2: ________; __________ 8) 9 to 12: ________; __________ Write the sentences as a ratio. Simplify by reducing fractions to lowest terms. 9) Last year, the softball team won 20 out of 28 games. What is the ratio of wins to

losses? : _______________________________________________________ 10) Write an original sentence to show the ratio 24 to 18.

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8.2 PROPORTIONS

Key Vocabulary 8.2

proportion: ____________________________________________________________

equal cross products: ____________________________________________________

Think 8.2

To read a proportion created by two equal ratios, use the word "as" in place of the equal "=' SIGN.

2 8 reads "2 is to 3 as 8 is to 12." 3 12

To determine if a proportion is correct, use cross multiplication. If the cross products

are equal, then the proportion is correct.

2

8 (2)(12) = 24 and (3)(8) = 24; therefore, 2 = 8

3 12

3 12

2 10 (2)(22) = 44 and (3)(10) = 30; therefore, 2 10

3 22

3 22

Try It 8.2

Use cross multiplication to determine if proportion are equal. Circle = or . 1) 3 to 9 : ______________________ = or

4 12 2) 8 to 32 : ______________________ = or

3 12 3) 7 to 35 : ______________________ = or

5 20 4) 6 to 24 : ______________________ = or

9 45 5) 4 to 20 : ______________________ = or

5 25 6) 9 to 45 : ______________________ = or

6 36

4

8.2 Practice Exercises

Use cross multiplication to determine if the proportions are equal. Circle = or .

1)

3 to 15 : ______________________ = or

8 40

2)

4 to 24 : ______________________ = or

9 63

3)

2 to 14 : ______________________ = or

7 56

4)

6 to 18 :______________________ = or

5 15

5)

12 to 48 : ______________________ = or

8 56

6)

10 to 30 : ______________________ = or

6 18

7)

7 to 42 : ______________________ = or

8 48

8)

4 to 28 : ______________________ = or

10 80

9)

8 to 32 : _____________________ = or

3 18

10) Adam sold 8 boxes of tools in 3 hours. Sarah sold 48 boxes of tools in 21 hours.

Set up a proportion for the two rates and determine is the proportion is equal.

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8.3 RATES

Key Vocabulary 8.3

rate:___________________________________________________________________

per: ___________________________________________________________________

units:__________________________________________________________________

Think 8.3 Formulas for Common Rates:

mileage miles gallons

heart rate beats hour

speed miles hour

unit cost dollars pound/ounces

240 miles in 3 hours : miles 240 80 miles per hour hours 3

360 miles in 14 gallons : miles 360 26 miles per gallon gallons 14

304 beats in 4 minutes : beats 304 76 beats per minute minutes 4

$18.90 for 6 pounds : dollars $18.90 $3.16 per pound pound 6

Try It 8.3

Find each rate and label the units. 1) 375 miles on 15 gallons: _________________________________ 2) 320 beats in 4 minutes: __________________________________ 3) $1.75 for 5 ounces: _____________________________________ 4) $12.80 for 16 ounces: ___________________________________ 5) 204 miles in 3 hours: ____________________________________ 6) 330 miles in 4 hours: ____________________________________

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8.3 Practice Exercises

Find the rates. 1) $12 for 4 pounds 2) $1.40 for 7 pencils 3) 216 miles in 3 hours 4) 120 chairs for 30 tables 5) 18 tons poured in 8 hours 6) 825 miles on 15 gallons 7) $98 sales in 1 week 8) 1,360 words in 20 minutes 9) 410 heart beats in 6 minutes

Cost per pound _____ Cost per pencil _____ Miles per hour _____ Chairs per table _____ Tons poured per hour_____ Miles per gallon _____ Sales per day _____ Words per minute _____ Beats per minute_____

10) Find the best deal on cartons of eggs.

a) $21 for 6 cartons

b) $20 for 5 cartons

c) $18 for 4 cartons

d) $24 for 7 cartons

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8.4 CONVERSIONS

Key Vocabulary 8.4

conversion: _____________________________________________________________

Metric Units: ____________________________________________________________

Standard Units: __________________________________________________________

Think 8.4

Different units are used to measure length, volume, weight, and other measurements.

For example, a floor can be measured in inches, feet, yards, centimeters, and meters. (Others apply as well)

To convert from one measurement unit to another, write the unit values ratio in

fraction form. Then multiply by the new data value, and simplify.

1 yard = 3 feet

3 yards equals how many feet?

yards : 1 x 3 3yards feet 3 3 9 feet

1 yard = 0.9144 meters

3 yards equals how many meters?

yards : 1 x 3 3 yards meters 0.9144 3 2.74 meters

1 gallon = 3.7854 liters

2 gallons equals how many liters?

gallons : 1 x 2 2 gallons liters 3.7854 2 7.57liters

Try It 8.4

Convert the following measurements units.

1) 1 mile = 1.6093 kilometers 2 miles = _____ kilometers

2) 1 inch = 2.54 centimeters 4 inches = _____ centimeters 3) 1 teaspoon = 5 milliliters 8 teaspoons = _____ milliliters

4) 1 pound = 16 ounces 5) 1 cup = 16 tablespoons 6) 1 liter = 4 cups

3 pounds = _____ ounces 3 cups = ________ tablespoons 12 liters = ___________ cups

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