Basic Mathematics for College Students

 

482 Chapter 5 Summary and Review

Find the unit price of each item.

19. 5 pairs cost $11.45.


20. $3 billion in a 12-month span


21. AIRCRAFT Specifications for a Boeing B-52
    Stratofortress are shown below. What is the ratio
    of the airplane’s wingspan to its length?

Crew: 6

Length: 160 ft

Wingspan: 185 ft

Maximum takeoff

weight: 488,000 lb

Maximum speed:

595 mph

Maximum altitude: more than

50,000 ft

Range: 7,500 mi

22. PAY RATES Find the hourly rate of pay
    for a student who earned $333.25 for working
    43 hours.


23. CROWD CONTROL After a concert is over, it
    takes 48 minutes for a crowd of 54,000 people to
    exit a stadium. Find the unit rate of people exiting
    the stadium.


24. COMPARISON SHOPPING Mixed nuts come
    packaged in a 12-ounce can, which sells for $4.95, or
    an 8-ounce can, which sells for $3.25. Which is the
    better buy?

SECTION 5.2 Proportions

A proportionis a statement that two ratios or

two rates are equal.

DEFINITIONS AND CONCEPTS EXAMPLES

Write each statement as a proportion.

as



⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

$300 is to 500 minutes as $3 is to 5 minutes

$300

500 minutes



$3

5 minutes

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

The word “to”is used to separate the numbers

to be compared in a ratio (or rate).

3 is to 5

3

5

6 is to 10 ⎭⎪⎬⎪⎫

6

10

⎭⎪⎬⎪⎫

Each of the four numbers in a proportion is

called a term.The first and fourth terms are

called the extremes,and the second and third

terms are called the means.

First term (extreme) Third term (mean)

Second term (mean) Fourth term (extreme)

 

1

2



3

6

 

Since a proportion is an equation,a proportion

can be true or false. A proportion is true if

its ratios (or rates) are equivalent and false if its

ratios (or rates) are not equivalent.

One way to determine whether a proportion is

true or false is to use the fraction simplifying

skills of Chapter 3.

The two products found by multiplying

diagonally in a proportion are called cross

products.

Another way to determine whether a

proportion is true or false involves the cross

products. If the cross products are equal,the

proportion is true. If the cross products are not

equal,the proportion is false.

Determine whether the proportion is true or false.

Method 1Simplify any ratios in the proportion that are not in simplest

form. Then compare them to determine whether they are equal.

Simplify the ratio on the right side.

Since the ratios on the left and right sides of the proportion are not

equal, the proportion is false.

Method 2Check to see whether the cross products are equal.

Cross products

5  15  75

Since the cross products are not equal, the proportion is not true.

3

5



15

27

3  27  81

 

15

27



3

1

 5

3

1

 9



5

9

3

5



15

27