sec. 8.3 proportions

Copy and complete the statement to write an equivalent ratio.

5.310

?20

=

ANSWER310

620

=

ANSWER 3224

86

=

6.24?

6= 8

Learning Target:Students will learn how to write

proportions and solve proportions using cross products property.

Proportion: an equation that shows two ratios are equivalent.

a : b = c : d

Cross Product Property:- The cross products of a proportion

are equal.

If , then a d = b c.

EXAMPLE 1

Use cross products to decide whether the ratios form a proportion.

a. 35

1218

?=

Answer:3 18 = 5 12

54 = 6054 does not equal 60 therefore the

ratio is NOT a proportion.

EXAMPLE 1

Use cross products to decide whether the ratios form a proportion.

b. 810

2025

?=

Answer:10 20 = 8 25

200 = 200200 does equals 200 therefore the

ratio is a proportion.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

412

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

4 5

412

20x

.

=

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

4 5

412

20x

=

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

4 5

412

20x

=

12 5

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

4 5

412

20x

=

12 5

12 5 = 60, so x = 60.

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 1 Use equivalent ratios.

4 5

412

20x

=

12 5

12 5 = 60, so x = 60.

The solution is 60.ANSWER

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 2 Use cross products.

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 2 Use cross products.

412

20x

=

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 2 Use cross products.

412

20x

=

.

4x = 240

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 2 Use cross products.

412

20x

=

4x = 240

.

EXAMPLE 2

Solve the proportion4

1220x

=

METHOD 2 Use cross products.

412

20x

=

4x = 240

.

x = 60

EXAMPLE 4

Solve the proportion2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

=

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

6.3 1.4 = x

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

6.3 1.4 = x Write the related division equation.

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

6.3 1.4 = x Write the related division equation.

4.5 = x

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

6.3 1.4 = x Write the related division equation.

4.5 = x Divide.

2.11.4

x3

= .

EXAMPLE 4

Solve the proportion

SOLUTION

2.11.4

x3

= Write the cross products.

6.3 = 1.4x They are equal.

6.3 1.4 = x Write the related division equation.

4.5 = x Divide.

The solution is 4.5.ANSWER

2.11.4

x3

= .

GUIDED PRACTICE for Example 4

135 = 6a

Write the related equation. Use it to solve the proportion.

22.56

a6

=8. 9. 30y

5060

=

ANSWER

a 1356

=

a = 22.5

ANSWER

1800 = 50y

y 180050

=

y = 36

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

SOLUTION

Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

SOLUTION

Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

Write a verbal model.

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

SOLUTION

Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

Write a verbal model.Distance traveled

Time traveled

Total distance

Total time=

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

SOLUTION

Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

Write a verbal model.Distance traveled

Time traveled

Total distance

Total time=

Substitute values.

EXAMPLE 3

Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?

SOLUTION

Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.

Write a verbal model.Distance traveled

Time traveled

Total distance

Total time=

Substitute values.5 mi

3 h

20 mi

t h=

EXAMPLE 3

Write the cross products.

EXAMPLE 3

5

3

20

t=

Write the cross products.

EXAMPLE 3

5

3

20

t=

They are equal.

Write the cross products.

EXAMPLE 3

5

3

20

t=

They are equal.

Write the cross products.

5 t 60=

EXAMPLE 3

5

3

20

t=

They are equal.

Write the cross products.

5 t 60=

Solve using mental math.

EXAMPLE 3

5

3

20

t=

They are equal.

Write the cross products.

5 t 60=

t = 12 Solve using mental math.

EXAMPLE 3

5

3

20

t=

They are equal.

Write the cross products.

5 t 60=

t = 12 Solve using mental math.

It will take you 12 hours to travel 20 miles.ANSWER

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

for Examples 1, 2, and 3

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

for Examples 1, 2, and 3

ANSWER

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

for Examples 1, 2, and 3

4 mi

2 h

20 mi

t h=

ANSWER

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

for Examples 1, 2, and 3

4 mi

2 h

20 mi

t h=

ANSWER

4

2

20

t=

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

for Examples 1, 2, and 3

4 mi

2 h

20 mi

t h=

ANSWER

4

2

20

t=

4 t 40=

GUIDED PRACTICE

7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

4 mi

2 h

20 mi

t h=

ANSWER

4

2

20

t=

4 t 40=

t = 10h

for Examples 1, 2, and 3

Can you write proportions and solve proportions using cross products

property.