SOLVING PROPORTIONS USING CROSS PRODUCTS

Section 8.5

Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2.

In the Real World

Solving Proportions Using Cross Products

In the proportion = , the products 2 • 6 and 3 • 4 are called

cross products. Notice that the cross products are equal. This

suggests the cross products property.

23

46

Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2.

In the Real World

Solving Proportions Using Cross Products

NOTE BOOK

If = where b and d are nonzero numbers,

then ad = bc.

ab

cd

Words The cross products of a proportion are equal.

Numbers

Algebra

Cross Products Property

34

1520

=

4 • 15 = 60

3 • 20 = 60

Solving Proportions Using Cross Products

Solving a Proportion Using Cross Products

Use the cross products property to solve .29

3d

=

2d = 9 • 3

9 • 32

2d2

=

d = 13.5

Cross products property.

Divide each side by 2.

Simplify.

Write original proportion.29

3d

=

Solving Proportions Using Cross Products

Writing and Solving a Proportion

Science To find the weight w of a 60 pound dog on the moon, as described earlier, write and solve a proportion using the weight of the person.

Person Dog

10517.5

=weight on Earth

weight on moon

60w

Cross products property.

Divide each side by 105.

105w = 17.5 • 60

105w105

17.5 • 60105

=

w = 10

ANSWER A 60 pound dog would weigh 10 pounds on the moon.

Simplify.

Solving Proportions Using Cross Products

Writing and Solving a Proportion

Penguins At an aquarium, the ratio of rockhopper penguins to African penguins is 3 to 7. If there are 50 penguins, how many are rockhoppers?

SOLUTIONFirst, determine the ratio of rockhoppers to total penguins.

310

33 + 7

=

Set up a proportion to find the number r of rockhoppers.

310

=r

50rockhoppers

total penguins

For every 10 penguins, 3 are rockhoppers.Solve .3

10=

r50

3 • 50 = 10r

10r10

3 • 5010

=

15 = r

Cross products property.

Divide each side by 10.

Simplify.

ANSWER There are 15 rockhoppers at the aquarium.

Solving Proportions Using Cross Products

NOTE BOOK

Cross Products Property

Solving Proportions Using Cross Products

1. Write proportion

Make sure the bottom numbers represent the same item and the top numbers represent the same items.

2. Cross Multiply

3. Divide

4. Write out your answer