Chapter 7: Similarity

Section 7-1:Ratios and Proportions

Objectives

To write ratios and solve proportions.

Vocabulary

Ratio

Proportion

Extended Proportion

Cross-Product Property

Scale Drawing

Scale

Ratio

A ratio is a comparison of two quantities.

If you are comparing a to b, you may write as a proportion:

Fraction form:_______ (b ≠ 0)

Ratio form: a : b

Example

A photo is 8 in. wide and 5 1/3 in high. It is enlarged to a poster that is 2 ft. wide and 1 1/3 ft. high. What is the ratio of the width of the picture to the width of the poster?

Proportion

A proportion is a statement that two ratios are equal.

You can write a proportion in the following forms:

a c

b d : :a b c d

Extended Proportion

When three or more ratios are equal, you can write them as an extended proportion.

Example:

6 1 12 7

24 4 48 28

Properties of Proportions:

Cross-Product Property

The product of the extremes is equal to the product of the means.

Also known as “Cross-Multiplying”

Solve the proportion:

12

5 7

x

Solve the proportion:

3

8 4

y y

Solve the proportion:

5 20

3z

Solve the proportion:

18 6

6n n

Solve the proportion:

3 4 1

1 5 2 3

x

x x

Scale Drawing

A scale drawing is a drawing in which all lengths are proportional to corresponding actual lengths.

Scale

A scale is the ratio of any length in a scale drawing to the corresponding actual length.

The lengths may be different units.

Geography Example

Students at the University of Minnesota in Minneapolis built a model globe 42 ft. in diameter using a scale of 1: 1,000,000.

About how tall is Mount Everest on the model if it is actually about 29,000 ft tall?