Section 8-1 Ratios and Proportions SPI 31A: identify corresponding parts of congruent geometric figuresSPI 32C: determine congruence or relations between triangles or quadrilaterals given a diagramSPI 22B: apply ratio and proportion to solve real-world problems

Objectives:• write ratios/proportions to find dimensions from scale drawings

Ratio: comparison of two numbers by division Scale Drawing: scale compares each length in the drawing to the actual length.

Proportion: an equation that states two ratios are equal.

Cross-Product Property: shortcut for finding a variable when one fraction is set equal to another.

Ratio (comparison of 2 numbers by division)

The ratio of two quantities a and b, can be written as:

a to b a:bb

a

What is the ratio of girls to boys if there are 13 girls and 22 boys?

13 to 22 13:2222

13

Real-world and Ratios

In the plains of Africa, zoologist tagged zebras to discover that there exists 178 female zebras to 148 male zebras.

What is the ratio of male to total number of zebra?

There are 148 male zebras.

There is a total of 326 zebras.

The ratio is 148 to 326 148:326326

148

74 to 163 74:163163

74

Real-world Connection to Ratios

Photography: A photo that is 8 in wide and 5 1/3 inches high 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 photo to the width of the poster?

Width of photoWidth of poster

= 8 in2 ft

= 8 in24 in

1 3

The ratio of the width of the photo to the width of the poster is 1:3 or 1/3.

=

Proportions (an equation that states two ratios are equal)

Use Multiplication Property of Equality to Solve Proportions

84

3 x

884

38

x

x6

Cross Products of Proportions(Use ONLY when one ratio or

fraction equals another)

84

3 x

x 483

x424

4

4

4

24 x

x6

Properties of Proportions govern when two equations are equivalent

Properties of Proportions

Use Cross-Products to Solve the Proportions

1. Solve the proportion:

2. Solve the proportion:

596 c

96

5 c

7.5c

456

c

7

2

5

4

xx)2(5)4(7 xx

105287 xx

19x

xxxx 51055287 10282 x

281028282 x382 x

Distributive Property

Simplify

SPE

Simplify

SPE

Simplify

Setting up to Write a Proportion

If people could jump as high as a flea, how high could a person, that is 5 feet tall jump if a flea that is .125 inches tall can jump to a height of 13 inches?

Jump heightTallness

13 .125

x 5

=

513125. x65125. x

125.

65

125.

125.x

520x

Answer the questionA person could jump to a height of 520 feet.

Real-world Connection and

Scale Drawings

The bedroom in the scale drawing is 7/8 in by 5/8 in.

Find the actual dimensions of the bedroom.

Drawing length (in)Actual length (ft)

= 1 in16 ft

7/8 in x

x = (7/8)(16)

x = 14

= 1 in16 ft

5/8 in y

y = (5/8)(16)

y = 10The actual size of the

bedroom is 14 ft by 10 ft