Lesson 3.6- Ratios and Proportions, pg. 155

Objectives:To determine whether two ratios

form a proportion.To solve proportions.

Vocabulary

Ratio: a comparison of two numbers by division.

Examples: x to y x : y x/yProportions: an equation stating that two

ratios are equal.

Example: 8

14

4

7

a

b

c

d

Extremes: in the ratios , a and d are the extremes.

Means: in the ratios ,c and b are the means.

Rate: the ratio of two measurements having different units of measure.

Scales: a ratio or rate used when making a model of something that is too large or too small to be conveniently shown at actual size.

a

b

c

d

Ex. 1: Determine whether ratios form a proportion.

1.

7

8

49

56and

Another way to determine whether two ratios form a proportion is to use cross products. If the cross products are equal, then the ratios form a proportion.

Ex. 2: Use cross products.

1. 2. 0 25

0 6

125

2

.

.,

. 4

5

16

20,

Solve Proportions

You can write proportions that involve a variable. To solve proportions, use cross products and the techniques used to solve other equations.

Ex. n

3

6

9

Ex. 3: Solve a proportion.

n

12

3

8 2. 1. 3

4

6x

3. 4. 1

019

12

.n

6

14

7

3

x

Ex. 4:

1. The Lehmans’ minivan requires 5 gallons of gasoline to travel 120 miles. How much gasoline will they need for a 350-mile trip?

2. Seth earns $152 in 4 days. At that rate, how many days will it take him to earn $532?

NBA #20, page 158, problems 12-34 even