Download Solving Proportions

Solving Proportions
2-7
Vocabulary
Review
Write each unit rate in words.
1. 65 mi/h
sixty-five
2. 7 ft/day
seven
3. $3.99/lb
three dollars ninety-nine
4. 11 km/s
eleven
per
per
per
per
Vocabulary Builder
A proportion always has
an equal sign.
Definition: A proportion is an equation that states that two ratios
are equal.
a
c
What It Means: Any equation of the form b 5 d , where b 2 0and d 2 0, is a
proportion. You read a proportion “a is to b as c is to d.”
Related Word: proportional (adjective)
Use Your Vocabulary
Complete each statement with the correct word from the list below.
proportion
ratios
proportional
5. A scaled map of the roads in a city is 9 to the actual roads.
6. When making fruit punch, you have to be sure that the amount of
ginger ale is in 9 to the amount of fruit juice.
5
15
5
15
7. Because 8 is not equal to 20 , the 9 8 and 20 do not form a proportion.
Chapter 2
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1
6
5
5 30
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proportion (noun) pruh PAWR shun
Problem 1 Solving a Proportion Using the Multiplication Property
Got It? What is the solution of the proportion 7x 5 45 ?
8. Use the justifications at the right to solve the proportion.
x
4
755
Write the original equation.
x
? 45
?75
Multiply each side by
28
.
Simplify.
5 5
x5
Divide.
a
c
In the proportion b 5 d , the products ad and bc are called cross products. You can
use the following property of cross products to solve proportions.
Property Cross Products Property of a Proportion
9. Complete the table.
Words
The cross products of a proportion are equal.
If
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Algebra
ART
a
c
, where b lj 0 and d lj 0, then ad â
â
b
d
FPO
8
2
, so 2 Ƃ
â
3
12
Example
â3Ƃ
, or 24 â
.
.
Problem 2 Solving a Proportion Using the Cross Products Property
y
Got It? What is the solution of the proportion 3 5 35 ?
10. Use the model to help you find the cross products.
5
y
3
â
3
5
3
y
3
11. Solve the proportion 3 5 5 .
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Lesson 2-7
Problem 3 Solving a Multi-Step Proportion
Got It? What is the solution of the proportion n5 5 2n 61 4 ?
12. Complete the reasoning model below.
Write
Think
First I write the original proportion.
Next I use the Cross Products Property.
)n â5(
(
Ƃn â10 Ƃ
Then I use the Distributive Property.
I simplify both sides.
Now I divide each side by Ź4.
â10n à
6n Ľ
à
Ľ
Ƃn â
Ľ4
â
Ľ4
nâ
Finally, I simplify.
When you model a real-world situation with a proportion, you must write the
proportion carefully. Be sure that the order of what is compared in each ratio
is the same.
100 mi
x mi
100 mi
5h
Correct: 2 h 5 5 h
Incorrect: 2h 5 x mi
13. Suppose you can buy 3 pounds of meat for $12. Cross out the proportion below that
will NOT help you find the cost of 5 pounds of meat.
12 dollars
x dollars
5 5 lb
3 lb
12 dollars
5 lb
5 x dollars
3 lb
3 lb
5 lb
5 x dollars
12 dollars
14. Suppose you need 9 pieces of wood to build 4 birdhouses. Cross out the proportion
below that will NOT help you find the number of pieces of wood you will need to
build 15 birdhouses.
15 birdhouses
4 birdhouses
5 9 pieces
x pieces
9 pieces
x pieces
5 15 birdhouses
4 birdhouses
9 pieces
x pieces
5 4 birdhouses
15 birdhouses
15. Suppose you can knit 3 scarves from 5 packages of yarn. Let x 5 the number of
scarves you can knit from 12 packages of yarn. Complete the proportion.
5 packages
3 scarves 5
Chapter 2
64
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
I subtract 10n from each side.
)
Problem 4
Using a Proportion to Solve a Problem
Got It? An 8-oz can of orange juice contains about 97 mg of vitamin C. About how
many milligrams of vitamin C are there in a 12-oz can of orange juice?
16. Let c =
.
17. Circle the proportion you will use to solve this problem.
c mg
8 oz
12 oz 5 97 mg
c mg
12 oz
8 oz 5 97 mg
97 mg
12 oz
8 oz 5 c mg
8 oz
12 oz
97 mg 5 c mg
18. Solve the problem using the proportion you chose.
19. There are about
mg of vitamin C in a 12-oz can of orange juice.
Lesson Check • Do you UNDERSTAND?
Reasoning When solving 5x 5 34 , Lisa’s first step was to write 4x 5 5(3). Jen’s
first step was to write 20 Q 5x R 5 20 Q 34 R . Will both methods work? Explain.
20. Circle the property that Lisa used. Underline the property that Jen used.
Multiplication Property
Cross Products Property
x
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21. Solve: 4x 5 5(3).
3
22. Solve: 20 Q 5 R 5 20 Q 4 R .
23. Will both methods work? Explain.
____________________________________________________________________
Math Success
Check off the vocabulary words that you understand.
proportion
cross products
Cross Products Property
Rate how well you can solve proportions.
Need to
review
0
2
4
6
8
Now I
get it!
10
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Lesson 2-7