Vocabulary

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Vocabulary
proportion cross products
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An equation that states that two ratios are
equivalent is called a proportion. For example,
the equation, or proportion, states
that the ratios and are equivalent.
Ratios that are equivalent are said to be
proportional, or in proportion.
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Notes Last sentence
Proportion
a d b c
Cross Products
One way to find whether two ratios are equivalent
is to find their cross products.
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Additional Example 1A Using Cross Products to
Identify Proportions
Tell whether the ratios are proportional.
Find the cross products.
60 60
Since the cross products are equal, the ratios
are proportional.
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Additional Example 1B 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?
Set up equal ratios.
Find the cross products.
20 ? 15
The ratios are not equal. The mixture will not be
correct.
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Check It Out! Example 1A
Tell whether the ratios are proportional.
Find the cross products.
20 20
Since the cross products are equal, the ratios
are proportional.
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Check It Out! Example 1B
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?
Set up equal ratios.
Find the cross products.
12 12
The ratios are equal. The mixture will be correct.
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Additional Example 2 Using Properties of
Equality to Solve Proportions
The ratio of the length of the actual height of a
person to the length of the shadow cast by the
person is 13. At the same time, a lighthouse
casts a shadow that is 36 meters long. What
should the length of its shadow be?
1 3
Write a ratio comparing height of a person to
shadow length.
height of person length of shadow
Set up the proportion. Let x represent the shadow
length.
Since x is divided by 36, multiply both sides of
the equation by 36.
12 x
The length of the lighthouses shadow should be
12 meters.
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Check It Out! Example 2
For most cats, the ratio of the length of their
head to their total body length is 15. If a cat
is 20 inches in length, what should the total
length of their head be?
1 5
Write a ratio comparing head length to total
length.
head length total length
Set up the proportion. Let x represent the length
of the cat's head.
Since x is divided by 20, multiply both sides of
the equation by 20.
4 x
The length of the cat's head should be 4 inches.
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Additional Example 3 Using Cross Products to
Solve Proportions
Allyson weighs 55 pounds and sits on a seesaw 4
feet away from it center. If Marco sits on the
seesaw 5 feet away from the center and the seesaw
is balanced, how much does Marco weigh?
Set up a proportion using the information. Let w
represent Marcos weight.
55 4 5w
Find the cross products.
Divide both sides by 5.
44 w
Simplify.
Marco weighs 44 lb.
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Check It Out! Example 3
Austin weighs 32 pounds and sits on a seesaw 6
feet away from it center. If Kaylee sits on the
seesaw 4 feet away from the center and the seesaw
is balanced, how much does Kaylee weigh?
Set up a proportion using the information. Let w
represent Kaylees weight.
32 6 4w
Find the cross products.
Divide both sides by 4.
48 w
Simplify.
Kaylee weighs 48 lbs.
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Additional Example 4 Business Application
Nate has 225 envelopes to prepare for mailing. He
takes 30 minutes to prepare 45 envelopes. If he
continues at the same rate, how many more minutes
until he has completed the job?
Let x represent the number of minutes it takes to
complete the job.
Set up the proportion.
30 225 45x
Find the cross products.
Divide both sides by 45.
150 x
Simplify.
It will take 150 minutes to complete the job.
Nate has already spent 30 minutes, so it will
take him 150 30 120 more minutes to finish
the job.
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Check It Out! Example 4
Nemo has to make 160 muffins for the bake sale.
He takes 21 minutes to make 24 muffins. If he
continues at the same rate, how many more minutes
until he has completed the job?
Let m represent the number of minutes it takes to
complete the job.
Set up the proportion.
21 160 24m
Find the cross products.
Divide both sides by 24.
140 m
Simplify.
It will take 140 minutes to complete the job.
Nemo has already spent 21 minutes, so it will
take him 140 21 119 more minutes to finish
the job.