4-4 Solving Proportions

Vocabulary

cross product

4-4 Solving Proportions

For two ratios, the product of the first term in one ratio and the second term in the other is a cross product. If the cross products of the ratios are equal, then the ratios form a proportion.

5 · 6 = 30

2 · 15 = 30=2

56

15

4-4 Solving Proportions

You can use cross products to solve proportions with variables.

4-4 Solving Proportions

Use cross products to solve the proportion.

Additional Example 1: Solving Proportions Using Cross Products

15 · m = 9 · 5

15m = 45

15m15

= 4515

m = 3

The cross products are equal.

Multiply.

Divide each side by 15 to isolate the variable.

= m5

915

4-4 Solving Proportions

Check It Out: Example 1

Use cross products to solve the proportion.

6·14 = 7m;m = 12=

67

= m14

847

A.

B.

9·7 = 6r;r = 10.5=

96

= r7

636

4-4 Solving Proportions

It is important to set up proportions correctly. Each ratio must compare corresponding quantities in the same order.

Suppose a boat travels 16 miles in 4 hours and 8 miles in x hours at the same speed. Either of these proportions could represent this situation.

16 mi4 hr

= 8 mix hr

16 mi8 mi

= 4 hrx hr

4-4 Solving Proportions

Additional Example 2: Problem Solving Application

If 3 binders of the same size take up 4 inches of space on a shelf, how much space will be needed for all 26 of these binders?

11 Understand the Problem

Rewrite the question as a statement.• Find the space needed for 26 binders.

List the important information:• 3 binders take up 4 inches of space.

4-4 Solving Proportions

22 Make a Plan

Set up a proportion using the given information. Let x represent the inches of space needed.

3 binders4 inches

= 26 bindersx

bindersinches

Additional Example 2 Continued

4-4 Solving Proportions

Solve33

34

= 26x

3 · x = 4 · 26

3x = 104

3x3

= 1043

x = 34 23

She needs 34 23

inches for all 26 binders.

Write the proportion.

The cross products are equal.

Multiply.

Divide each side by 3 to isolate the variable.

Additional Example 2 Continued

4-4 Solving Proportions

Look Back44

34

= 2634 2

3

4 · 26 = 104

3 · 34 23

= 104

The cross products are equal, so 34 23

is theanswer

Additional Example 2 Continued

4-4 Solving Proportions

Check It Out: Example 2A

A stack of 33 CDs is 1.5 inches high. How many CDs would be in a stack that is 3.5 inches high?

1.5 33

= 3.5x

1·5x = 33 x 3.5

x

77 CDs=

115.51.5

=

x

4-4 Solving Proportions

Check It Out: Example 2BMaria drives at a constant speed for 3 hours and travels 175 miles. How far would she drive in 4.5 hours at the same speed?

= 4.5x

3x = 175 . 4.5

x

262.5 miles=

787.53

=

x

3175

4-4 Solving Proportions

Lesson Quiz: Part I

Use cross products to solve the proportion.

1. 2520

= 45t

2. x9

= 1957

3. 23

= r36

4. n10

=288

t = 36

x = 3

r = 24

n = 35

4-4 Solving Proportions

Lesson Quiz: Part II

5. Carmen bought 3 pounds of bananas for $1.08. June paid $1.80 for her purchase of bananas. If they paid the same price per pound, how many pounds did June buy?5 pounds