Find two ratios that are equivalent to each given ratio.

35

1.

4530

3. 9060

32

,

1012

2. 2024

56

,

89

4. 2427

1618

,

915

610

,Possible answers:

Warm Up

Pre-Algebra

7.4

Solving Proportions

Learn to solve proportions.

cross product

Vocabulary

Cross Products

The cross product represents the numerator of the fraction when a common denominator is found by multiplying the denominators.

Helpful Hint

Tell whether the ratios are proportional.

410

615

A.

Since the cross products are equal, the ratios are proportional.

60

=?

60 = 60

Find cross products.60410

615

Example: Using Cross Products to Identify Proportions

A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?

4 parts gasoline1 part oil

=? 15 quarts gasoline5 quarts oil

4 • 5 = 20 1 • 15 = 15

20 ≠ 15

The ratios are not equal. The mixture will not be correct.

Set up ratios.

Find the cross products.

Example: Using Cross Products to Identify Proportions

Tell whether the ratios are proportional.

Since the cross products are equal, the ratios are proportional.

20

20 = 20

Find cross products.2024

510

24

510

A. =?

Try This

Tell whether each pair of ratios is proportional.

4842 =? 16

141. 20

15 =? 34

2.yes no

Lesson Quiz

A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct?

3 parts tea 1 part sugar

=? 12 tablespoons tea4 tablespoons sugar

3 • 4 = 12 1 • 12 = 12

12 = 12

The ratios are equal. The mixture will be correct.

Set up ratios.

Find the cross products.

Try This

When you do not know one of the four numbers in a proportion, set the cross products equal to each other and solve.

Solving with Cross-Products

Solve the proportion.

6p = 12 • 5

p = 10

6p = 60

Find the cross products.

Solve.

56

p12

=

; the proportion checks.56

1012

=

Example: Solving Proportions

Solve the proportion.

14 • 3 = 2g

21 = g

42 = 2g

Find the cross products.

Solve.

23

14g

=

; the proportion checks.23

1421

=

Try This

Solve each proportion.

3. 4.n = 30 n = 164518

n12 = n

2469 =

Lesson Quiz

Allyson weighs 55 lbs and sits on a seesaw 5 ft away from its center. If Marco sits 4 ft away from the center and the seesaw is balanced, how much does Marco weigh?

5x5

2205

=

44 = x

Set up the proportion.

Let x represent Marco’s weight.

Find the cross products.

Multiply.

Solve. Divide both sides by 5.

Marco weighs 44 lb.

220 = 5x

55 • 4 = 5x

x4

555

=

pounds length

= pounds length

Example: Physical Science Application

Robert weighs 90 lbs and sits on a seesaw 6 ft away from its center. If Sharon sits 5 ft away from the center and the seesaw is balanced, how much does Sharon weigh?

6x6

4506

=

75 = x

Set up the proportion.

Let x represent Sharon’s weight.

Find the cross products.

Multiply.

Solve. Divide both sides by 5.

Sharon weighs 75 lb.

450 = 6x

90 • 5 = 6x

x5

906

=

poundslength

= poundslength

Try This

5. Two weights are balanced on a fulcrum. If a 6lb weight is positioned 1.5 ft from the fulcrum, at what distance from the fulcrum must an 18 lb weight be placed to keep the weights balanced?

0.5 ft

Lesson Quiz