Do Now 10/12/09Do Now 10/12/09

Copy HW in your planner.Copy HW in your planner. Text p. 165, #28-34 evens, #46-50 evensText p. 165, #28-34 evens, #46-50 evens Text p. 171-172, #16-38 evenText p. 171-172, #16-38 even

In your journal, consider the following. On a bright In your journal, consider the following. On a bright sunny day, how can you determine the height of a tall sunny day, how can you determine the height of a tall object (i.e. flagpole) without physically measuring the object (i.e. flagpole) without physically measuring the object?object?

ObjectiveObjective SWBAT find ratios and write and solve SWBAT find ratios and write and solve

proportionsproportions

SWBAT solve proportions using cross SWBAT solve proportions using cross productsproducts

RATIO-RATIO- uses division to compare uses division to compare

two quantitiestwo quantities

a to ba to b a:ba:b aabb

You can write ratios three different ways:You can write ratios three different ways:

Section 3.5 “Write Ratios and Section 3.5 “Write Ratios and Proportions”Proportions”

Try It Out…Try It Out…

SOLUTIONSOLUTION

VOLLEYBALLVOLLEYBALL

A volleyball team plays A volleyball team plays 1414 home matches and home matches and 1010 away away matchesmatches..

a.a. Find the ratio of home matches to away matches.Find the ratio of home matches to away matches.

== 7755a.a.

home matcheshome matches

away matchesaway matches

1414 1010 ==

b.b. Find the ratio of home matches to all matches.Find the ratio of home matches to all matches.

b.b.home matcheshome matches

all matchesall matches

1414 14 + 1014 + 10

== == 14142424 ==

771212

PROPORTION-PROPORTION- an equation that states that an equation that states that

two ratios are equivalent.two ratios are equivalent.

d

c

b

a

Try It Out…Try It Out…

1111 66

xx3030== Write original proportion.Write original proportion.

Multiply each side by Multiply each side by 30.30.

330330 66

== xx Simplify.Simplify.

5555 = = xx Divide.Divide.

1111 66

xx3030==3030 3030

xx3030Solve the proportion Solve the proportion 1111

66 == ..

Proportion Cross Products PropertyProportion Cross Products Property

A A CROSS PRODUCTCROSS PRODUCT is the product of the numerator is the product of the numerator of one ratio and the denominator of the other ratio in a of one ratio and the denominator of the other ratio in a proportion. proportion.

d

c

b

aIf , then bcad

Section 3.6 “Solving Proportions Section 3.6 “Solving Proportions Using Cross Products”Using Cross Products”

Write original proportion.

8 15 = x 6

Solve the proportion =8 x

615

Cross products property

Simplify.120 = 6x

Divide each side by 6.20 = x

=8 x

615

3x =

2x – 6

Cross products property 3(x – 6) = 2 x

3x – 18 = 2x Distributive property

Subtract 3x from each side. 18 = x

Solve the proportion

3x =

2x – 6

Write original proportion.

SCALESCALE - - the SCALE of a drawing, map, or model relates the SCALE of a drawing, map, or model relates the dimensions of the drawing, map, or model to the dimensions of the drawing, map, or model to the actual dimensions.the actual dimensions.

Write and solve a proportion to find the distance d between Cleveland and Cincinnati if the distance on the map is about 4.2 centimeters.

=4.2 d

1 centimeters85 kilometers

Cross products property

d = 357 Simplify.

1 d = 85 4.2

The ship model kits sold at a hobby store have The ship model kits sold at a hobby store have a scale of a scale of 1 ft : 600 ft.1 ft : 600 ft. A completed model of the A completed model of the Queen Elizabeth II is Queen Elizabeth II is 1.61.6 feet long. Estimate the feet long. Estimate the actual length of the Queen Elizabeth II. actual length of the Queen Elizabeth II.

Write and solve a proportion to find Write and solve a proportion to find the length the length gg of the Queen Elizabeth of the Queen Elizabeth IIII..

==1.61.6 gg

11600600

Cross products propertyCross products property

g g = 960= 960 Simplify.Simplify.

1 1 · · g g = 600 = 600 ·· 1.6 1.6

SOLUTIONSOLUTION

The actual length of the Queen Elizabeth II is about 960 feet.

Indirect MeasurementsIndirect Measurements

You measure the shadow of a telephone pole to be 24 ft. The shadow of a 5ft-tree is 4 ft. How tall is the telephone pole?

treeshadow

poleShadow

treeheight

poleHeight

SS

HH

ss

hh

30

1204

H

H

4

24

5

H

HomeworkHomework Text p. 165, #28-34 evens, #46-50 evensText p. 165, #28-34 evens, #46-50 evens Text p. 171-172, #16-38 evenText p. 171-172, #16-38 even

2424

HomeworkHomeworkReal-Life Applications WorksheetReal-Life Applications Worksheet

1) 1)

2) 2)

3) 3)

4) 4)

milesx

inches

miles

inch1312;

2

656

1

milesx

inches

miles

inch943;16

71

656

1

milesx

inches

miles

inch738;8

11

656

1

inchesmiles

x

miles

inch3.1;

8.852656

1

b. about 1 ¼ inches

c. the city locations on the maps are approximations