Use the LCM to rename these ratios with a common denominator.

Use the LCM to rename these ratios with a common denominator.

1212

2323andand

3636

4646

,,

ExerciseExercise

Use the LCM to rename these ratios with a common denominator.

Use the LCM to rename these ratios with a common denominator.

2323

3535andand

10151015

9159

15,,

ExerciseExercise

Use the LCM to rename these ratios with a common denominator.

Use the LCM to rename these ratios with a common denominator.

3434

2525andand1

313

,, ,,

20602060

45604560

,, 24602460

,,

ExerciseExercise

Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

2525

4104

106

156

15,,

ExerciseExercise

Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

Change these ratios to equivalent ratios by multiplying by 1 in the form of 2 over 2 and 3 over 3.

ExerciseExercise

4343

8686

129

129

,,

ProportionProportion

A proportion is a statement of equality between two ratios.

A proportion is a statement of equality between two ratios.

6868

9129

12==

The 2nd and 3rd are called the means.

The 2nd and 3rd are called the means.

1st1st

2nd2nd

3rd3rd

4th4th

The 1st and 4th are called the extremes.

The 1st and 4th are called the extremes.

Property of ProportionsProperty of Proportions

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

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

6868

9129

12== alsoalso6

868

9129

12== 8

686

129

129

==

6868

9129

12== alsoalso6

868

9129

12== 9

696

128

128

==

6868

9129

12== alsoalso6

868

9129

12== 6

969

8128

12==

Given = , write a

proportion by inversion of ratios and a proportion by alternation of terms.

Given = , write a

proportion by inversion of ratios and a proportion by alternation of terms.

3535

5353

20122012==

12201220

3123

125

205

20==

Example 1Example 1

Solve = for n.Solve = for n.8n8n

6156

158n8n

6156

15 ==

6n = 15 • 86n = 15 • 8

6n = 1206n = 120

6n6

6n6

1206

1206==

n = 20n = 20

Example 2Example 2

Solve = for x.Solve = for x.10827

10827

32x

32x

10827

10827

32x

32x ==

108x = 32(27)108x = 32(27)

108x = 864108x = 864

108x108

108x108

864108864108==

x = 8x = 8

Example 3Example 3

Solve = .Solve = .7272

4x4x x ≈ 1.14x ≈ 1.14

ExampleExample

Solve = .Solve = .9509

50x8x8 x = 1.44x = 1.44

ExampleExample

The ratio of adults to students on a bus is 2 to 7. If there are 8 adults, how many students are on the bus?

The ratio of adults to students on a bus is 2 to 7. If there are 8 adults, how many students are on the bus?

8n8n

2727 ==

2n = 562n = 56

2n2

2n2

562

562==

n = 28 studentsn = 28 students

Example 4Example 4

Sam can paint 200 ft. of privacy fence in 3 hr. To the nearest foot, how many feet can he paint in 5 hr.?

Sam can paint 200 ft. of privacy fence in 3 hr. To the nearest foot, how many feet can he paint in 5 hr.?

3 hr.5 hr.3 hr.5 hr.

200 ft.x ft.

200 ft.x ft. ==

3x = 200(5)3x = 200(5)

3x3

3x3

1,0003

1,0003==

x ≈ 333 ft.x ≈ 333 ft.3x = 1,0003x = 1,000

Example 5Example 5

A rectangle whose width is 5 ft. and whose length is 12 ft. is similar to a rectangle whose width is 8 ft. What is the length of the larger rectangle?

A rectangle whose width is 5 ft. and whose length is 12 ft. is similar to a rectangle whose width is 8 ft. What is the length of the larger rectangle?

19.2 ft.19.2 ft.

ExampleExample

What is the height of a tree if a 6 ft. man standing next to the tree makes an 8 ft. shadow and the tree makes a 50 ft. shadow?

What is the height of a tree if a 6 ft. man standing next to the tree makes an 8 ft. shadow and the tree makes a 50 ft. shadow?

37.5 ft.37.5 ft.

ExampleExample

If a car can go 250 mi. on 8 gal., how many gallons will it take to go on a 600 mi. trip?

If a car can go 250 mi. on 8 gal., how many gallons will it take to go on a 600 mi. trip?

19.2 gal.19.2 gal.

ExampleExample

If a 50 ft. fence requires 84 2” x 4”s, how many 2” x 4”s are needed for a 160 ft. fence?

If a 50 ft. fence requires 84 2” x 4”s, how many 2” x 4”s are needed for a 160 ft. fence?

269269

ExampleExample

The product of ratios is also a ratio. For example, suppose a production line can assemble 130 cars per hour. How many days, at 8 hr./day, will it take to produce 100,000 cars?

The product of ratios is also a ratio. For example, suppose a production line can assemble 130 cars per hour. How many days, at 8 hr./day, will it take to produce 100,000 cars?

97 days 97 days

ExampleExample