solving proportions using cross products section 8.5
TRANSCRIPT
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