ExerciseExercise

Write in fraction form: 2 : 7 as 6 : 21.Write in fraction form: 2 : 7 as 6 : 21. 2

727

6216

21==

What are the extremes?What are the extremes? 2; 212; 21What are the means?What are the means? 7; 67; 6Does the product of the extremes equal the product of the means? What is the product?

Does the product of the extremes equal the product of the means? What is the product? yes; 42yes; 42

2323

Use the rule for dividing rational numbers to find the quotient.

Use the rule for dividing rational numbers to find the quotient.

5050

2323

×× 1501

501

751

75==

ExerciseExercise

The scale for a drawing or map is the ratio of the drawing’s length to the actual length.

The scale for a drawing or map is the ratio of the drawing’s length to the actual length.

ScaleScale

A scale drawing is a drawing in which all of the lengths are at the same scale, or ratio, to the actual lengths of the object.

A scale drawing is a drawing in which all of the lengths are at the same scale, or ratio, to the actual lengths of the object.

Scale DrawingScale Drawing

A scale is a ratio.A scale is a ratio.

1 in.10 ft.1 in.10 ft.

1 in.120 in.1 in.

120 in.==

11201

120==

11201

120 of actual sizeof actual size

Find the length of a bridge in a drawing if the scale is 1 cm : 5 m and the actual length is 27 m.

Find the length of a bridge in a drawing if the scale is 1 cm : 5 m and the actual length is 27 m.Let b = the length of the bridge in the drawing.Let b = the length of the bridge in the drawing.1515

== b27b27

5b = 275b = 2755 55

b = 5.4 cmb = 5.4 cm

Example 1Example 1

The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns?

The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns?Let n = the actual distance between the two towns.Let n = the actual distance between the two towns.

Example 2Example 2

The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns?

The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns?

2152

15== 3.6n

3.6n

2n = 542n = 5422 22

n = 27 kmn = 27 km

Find the distance from Carville to Danville.Find the distance from Carville to Danville.

CarvilleCarvilleDanvilleDanville

5 cm5 cm

scale – 2 cm : 25 kmscale – 2 cm : 25 km

2252

25== 5n5n

2n = 1252n = 12522 22

n = 62.5 kmn = 62.5 km

Example 3Example 3

If a model airplane is constructed on a 1 in. : 25 ft. scale, what is the actual length of the airplane if the length of the model is 9 in.?

If a model airplane is constructed on a 1 in. : 25 ft. scale, what is the actual length of the airplane if the length of the model is 9 in.?

225 ft.225 ft.

ExampleExample

If a map is drawn on a 1 in. : 50 mi. scale, what is the distance between towns if the distance on the map is 2.5 in.?

If a map is drawn on a 1 in. : 50 mi. scale, what is the distance between towns if the distance on the map is 2.5 in.?

125 mi.125 mi.

ExampleExample

How far apart on a map with a scale of 1 in. : 50 mi. should two towns be drawn if they are actually 275 mi. apart?

How far apart on a map with a scale of 1 in. : 50 mi. should two towns be drawn if they are actually 275 mi. apart?

5.5 in.5.5 in.

ExampleExample

A map is to be made with a scale of 1 in. to 40 mi. How far apart will two cities appear on the map if they are actually 55 mi. from each other?

A map is to be made with a scale of 1 in. to 40 mi. How far apart will two cities appear on the map if they are actually 55 mi. from each other?Let n = the map distance.Let n = the map distance.1

401

40== n

55n55

40n = 5540n = 554040 4040

n = 1 in.n = 1 in.3838

Example 4Example 4

Find the scale used if two cities that are 60 mi. apart appear on a map in. apart.

Find the scale used if two cities that are 60 mi. apart appear on a map in. apart.3

434

60 mi.60 mi.

3434 ÷ 60÷ 603

434

xx3434

== 1601

6011

2020

1801

80==

Example 5Example 5

The scale is 1 in. : 80 mi.The scale is 1 in. : 80 mi.

If the circumference of the earth is about 25,000 mi., what should be the scale of a globe if it is to have a circumference of 2.5 ft.?

If the circumference of the earth is about 25,000 mi., what should be the scale of a globe if it is to have a circumference of 2.5 ft.?

30 in. : 25,000 mi.30 in. : 25,000 mi.1 in. : 833.33 mi.1 in. : 833.33 mi.

ExampleExample

If that same globe has relief (e.g. it is raised where there are mountains), then how high should Mt. Everest be raised on the globe if it is 29,000 ft. high?

If that same globe has relief (e.g. it is raised where there are mountains), then how high should Mt. Everest be raised on the globe if it is 29,000 ft. high? 0.006 in.0.006 in.

ExampleExample

A blueprint of a house is drawn to a scale of 1 in. : 5 ft. If a bedroom is 10 ft. by 12 ft., what are its dimensions on the blueprint?

A blueprint of a house is drawn to a scale of 1 in. : 5 ft. If a bedroom is 10 ft. by 12 ft., what are its dimensions on the blueprint? 2 in. by 2.4 in.2 in. by 2.4 in.

ExampleExample

In the science classroom, which measures 20 ft. by 20 ft., the teacher wishes to hang a scale model of the solar system from the ceiling. She plans to hang the sun in the center of the room and Neptune, which is 2.8 billion mi. from the sun, in a corner 14 ft. away. Determine the scale of the model.

In the science classroom, which measures 20 ft. by 20 ft., the teacher wishes to hang a scale model of the solar system from the ceiling. She plans to hang the sun in the center of the room and Neptune, which is 2.8 billion mi. from the sun, in a corner 14 ft. away. Determine the scale of the model. 1 ft : 0.2 billion mi.1 ft : 0.2 billion mi.

ExampleExample

How far from the center of the room should Earth be placed if it is about 93 million mi. from the sun?

How far from the center of the room should Earth be placed if it is about 93 million mi. from the sun? 0.465 ft.0.465 ft.

ExampleExample

If a 2.5 in. x 3.5 in. photo is to be enlarged to 5 in. x 7 in., what enlargement setting would be used?

If a 2.5 in. x 3.5 in. photo is to be enlarged to 5 in. x 7 in., what enlargement setting would be used?Let p = the % enlargement.Let p = the % enlargement.2.5p = 52.5p = 5 200%

enlargement200%

enlargement2.52.5 2.52.5p = 2p = 2

Example 6Example 6

A 10 cm x 16 cm table of data is reduced using a copier setting of 67%. What are the dimensions of the new table?

A 10 cm x 16 cm table of data is reduced using a copier setting of 67%. What are the dimensions of the new table? 10(0.67)10(0.67)

6.7 cm x 10.7 cm6.7 cm x 10.7 cm

= 6.7 cm= 6.7 cm16(0.67)16(0.67) = 10.7 cm= 10.7 cm

Example 7Example 7

If a picture in a book is labeled and an object in the photo is 5 in. wide, how wide is the real object?

If a picture in a book is labeled and an object in the photo is 5 in. wide, how wide is the real object? 30 x 5 in.30 x 5 in.

= 12.5 ft. wide= 12.5 ft. wide

= 150 in.= 150 in.

1301

30

15012

15012

ft.ft.

Example 8Example 8

Find the size of a 3 in. by 5 in. photo if it is enlarged 250%. Find the size of a 3 in. by 5 in. photo if it is enlarged 250%.

7.5 in. by 12.5 in.7.5 in. by 12.5 in.

ExampleExample

What should the enlargement of a 3 in. by 4 in. photograph be if you wish to place in on 9 in. by 12 in. paper?

What should the enlargement of a 3 in. by 4 in. photograph be if you wish to place in on 9 in. by 12 in. paper? 300%300%

ExampleExample