Chapter 2 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Chapter Chapter 22Section Section 66

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


Ratios and Proportions

11

33

22

2.62.62.62.6Write ratios.Solve proportions.Solve applied problems by using proportions.


Objective 11

Slide 2.6 - 3

Write ratios.


Write ratios.

A ratio is a comparison of two quantities using a quotient.

The last way of writing a ratio is most common in algebra.

Percents are ratios in which the second number is always 100. For example, 50% represents the ratio 50 to 100, 27% represents the ratio 27 to 100, and so on.

Slide 2.6 - 4

The ratio of the number a to the number b (b ≠ 0) is written

,a to b ,:a b or .a

b


Write a ratio for each word phrase.

3 days to 2 weeks

12 hr to 4 days

EXAMPLE 1Writing Word Phrases as Ratios

Solution:

Solution:

Slide 2.6 - 5

2 7 14weeks days days 3 days

weeks

3

14

days

days

3

14

4 24 96days hours hours 4

hours

days

12

96

hours

hours

1

8


EXAMPLE 2

Solution:

Finding Price per Unit

$2.79$0.116

24

$3.89$0.108

36

The 36 oz. size is the best buy. The unit price is $0.108 per oz.

$1.89$0.158

12

Slide 2.6 - 6

The local supermarket charges the following prices for a popular brand of pancake syrup. Which size is the best buy? What is the unit cost for that size?


Objective 22

Solve proportions.

Slide 2.6 - 7


Solve proportions.

Slide 2.6 - 8

A ratio is used to compare two numbers or amounts. A proportion says that two ratios are equal, so it is a special type of equation. For example,

3 15

4 20

is a proportion which says that the ratios and are equal.3

4

15

20

In the proportion

a, b, c, and d are the terms of the proportion. The terms a and d are called the extremes, and the terms b and c are called the means. We read the proportions as “a is to b as c is to d.”

, ,0a c

b db d

a c

b d


Beginning with this proportion and multiplying each side by the common denominator, bd, gives

Solve proportions. (cont’d)

We can also find the products ad and bc by multiplying diagonally.

For this reason, ad and bc are called cross products.Slide 2.6 - 9

d bda

bb

c

d

ad

bca c

b d

a c

b d .ad bc


Solve proportions. (cont’d)

Slide 2.6 - 10

If then the cross products ad and bc are equal.

Also, if then

,a c

b d

,ad bc , 0 .a c

b db d

From this rule, if then ad = bc; that is, the product of

the extremes equals the product of the means.

a c

b d

If , then ad = cb, or ad = bc. This means that the two

proportions are equivalent, and the proportion can

also be written as

Sometimes one form is more convenient to work with than the other.

a b

c d

a c

b d

, .0a b

c dc d


13 119 1547

17 91 1547

21 45 945

15 62 930

EXAMPLE 3

Solution: False

Deciding whether Proportions Are True

21 62

15 45

Slide 2.6 - 11

13 91

17 119

Solution: True

Decide whether the proportion is true or false.


EXAMPLE 4

Solution:

Finding an Unknown in a Proportion

35

6 42

x

42 6 35x

Slide 2.6 - 12

4

42 42

2 210x

5x The solution set is {5}.

The cross-product method cannot be used directly if there is more than one term on either side of the equals symbol.

Solve the proportion .


EXAMPLE 5

The solution set is

Solving an Equation by Using Cross Products

Slide 2.6 - 13

6 2.

2 5

a

6 5 2 2a 3030 4 05 3a 5 2

5 5

6a

26

5a

Solution:

26.

5

When you set cross products equal to each other, you are really multiplying each ratio in the proportion by a common denominator.

Solve


Objective 33

Solve applied problems with proportions.

Slide 2.6 - 14


EXAMPLE 6

Solution: Let x = the price of 16.5 gal of fuel.

Applying Proportions

Slide 2.6 - 15

$37.68

12 16.5

x

gal gal

12 621.

12 12

72x

51.81x

16.5 gal of diesel fuel costs $51.81.

Twelve gal of diesel fuel costs $37.68. How much would 16.5 gal of the same fuel cost?

Chapter 2 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

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