Chapter 7:

Similarity

7-1Ratios and Proportions

ObjectiveTo write ratios and solve

proportions

• Ratio:– A comparison of two numbers– Notation: words, colon, fraction or decimal (b 0)

Proportion:– An equation stating two ratios are equal– Example:

ba :

3

2

6

4

b

aba to

Write the ratio in simplest form.

Solving a Proportion

Steps:

1. Cross multiply

2. Divide

Solve the following proportions:

133

56

19

x

5619133 x

8x

xx

x 10

7

4

56

497

305

3

18x

1064133 x

8x 5.17x

Additional Examples

20

50

24

306 x

6120 = 24(x + 50)

6120 = 24x + 1200

4920 = 24x

205 = x

14

23

21

51 x

714 = 21(x – 23)

714 = 21x – 483

1197 = 21x

57 = x

In a photograph, Dan is 2.5 inches tall and his sister Emma is 1.5 inches tall. Dan’s actual height is 70 inches.

What is Emma’s actual height?

2.5

1.5

70=

x

Dan’s picture height

Emma’s picture height

Dan’s actual height

Emma’s actual height

2.5x = 105

x = 42 inches

Example 1

Extremes and Means

The first and last numbers in a proportion are the

extremes.

The middle two numbers in a proportion are the

means.

Properties of Proportions

Write an equivalent proportion.

7-1 p. 436: 15-31 odd