Solving Proportions

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7-4
Solving Proportions
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
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Warm Up Find two ratios that are equivalent to
each given ratio.
Possible answers
10 12
20 24
3 5
1.
2.
45 30
90 60
24 27
8 9
3.
4.
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Problem of the Day Replace each with a digit
from 1 to 7 to write a proportion. Use each digit
once. The digits 2 and 3 are already shown.
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Learn to solve proportions.
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Vocabulary
cross product
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Unequal masses will not balance on a fulcrum if
they are an equal distance from it one side will
go up and the other side will go down.
Unequal masses will balance when the following
proportions is true
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One way to find whether ratios, such as those on
the previous slide, are equal is to find a common
denominator. The ratios are equal if their
numerators are equal after the fractions have
been rewritten with a common denominator.
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Additional Example 1A Using Cross Products to
Identify Proportions
Tell whether the ratios are proportional.
A.
60
Find cross products.
60
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 ratios.
Find the cross products.
4 5 20
1 15 15
20 ? 15
The ratios are not equal. The mixture will not be
correct.
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Try This Example 1A
Tell whether the ratios are proportional.
A.
20
Find cross products.
20
20 20
Since the cross products are equal, the ratios
are proportional.
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Try This 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 ratios.
Find the cross products.
3 4 12
1 12 12
12 12
The ratios are equal. The mixture will be correct.
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When you do not know one of the four numbers in a
proportion, set the cross products equal to each
other and solve.
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Additional Example 2 Solving Proportions
Solve the proportion.
6p 12 5
Find the cross products.
Solve.
6p 60
p 10
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Try This Example 2
Solve the proportion.
14 3 2g
Find the cross products.
Solve.
42 2g
21 g
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Additional Example 3 Physical Science Application
Allyson weighs 55 lbs and sits on a seesaw 4 ft
away from its center. If Marco sits 5 ft away
from the center and the seesaw is balanced, how
much does Marco weigh?
Set up the proportion.
Let x represent Marcos weight.
Find the cross products.
55 4 5x
Multiply.
220 5x
Solve. Divide both sides by 5.
44 x
Marco weighs 44 lb.
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Try This Example 3
Robert weighs 90 lbs and sits on a seesaw 5 ft
away from its center. If Sharon sits 6 ft away
from the center and the seesaw is balanced, how
much does Sharon weigh?
Set up the proportion.
Let x represent Sharons weight.
Find the cross products.
90 5 6x
Multiply.
450 6x
Solve. Divide both sides by 6.
75 x
Sharon weighs 75 lb.
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Lesson Quiz
Tell whether each pair of ratios is proportional.
yes
1.
2.
no
Solve each proportion.
3.
4.
n 30
n 16
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