Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 4 Ratios and Proportions
Dec 26, 2015
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Section 4.3
Understanding and Solving Proportions
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Write a Proportion
A proportion is a mathematical statement showing that two ratios are equal.
A proportion is written as an equation with a ratio on each side of the equal sign.
Remember to include the units when writing a rate. Also, keep in mind that the order of the units is important. Be sure that like units for each rate are in the same position.
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Example
Write each sentence as a proportion.
a. 2 is to 7 as 4 is to 14
b. 12 eggs is to 3 chickens as 4 eggs is to 1 chicken
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Solution Strategy
2
7=
414
12 eggs
3 chickens=
4 eggs1 chicken
Write each sentence as a proportion.
a. 2 is to 7 as 4 is to 14
b. 12 eggs is to 3 chickens as 4 eggs is to 1 chicken
like units
like units
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Determine Whether Two Ratios Are Proportional
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Example
Determine whether the ratios are proportional.
If they are, write a corresponding proportion.
18
30=? 610
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Solution Strategy
Determine whether the ratios are proportional.
If they are, write a corresponding proportion.
18
30=? 610
18
30=
610
180
180
The ratios are proportional.
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Example
Solve for the unknown quantity. Verify your answer.
x
24=34
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Solution Strategy
Solve for the unknown quantity. Verify your answer.
x
24=34
72
4x
4x = 72
x = 18
18
24=34
24 • 3 = 72
18 • 4 = 72
It checks!
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Example Apply your knowledge
A cake recipe requires 5 eggs for every 4 cups of flour. If a large cake requires 12 cups of flour, how many eggs should be used?
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Solution Strategy
x = number of eggs for large cake
5 eggs
4 cups of flour=
x eggs12 cups of flour
A cake recipe requires 5 eggs for every 4 cups of flour. If a large cake requires 12 cups of flour, how many eggs should be used?
like units
like units4x = 5 • 12
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Solution Strategy
x = 15
4x
4=604
4x = 5 • 12
4x = 60
The large cake requires 15 eggs.
5
4=1512
4 • 15 = 60
5 • 12 = 60
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Solving a Geometry Application Problem
One common application of proportions is solving problems involving similar geometric figures. Similar geometric figures are geometric figures with the same shape in which the ratios of the lengths of their corresponding sides are equal. Because these ratios are equal, they are proportional.
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Solving a Geometry Application Problem
The similar rectangles yield this proportion:7
14=1224
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Solving a Geometry Application Problem
The similar triangles yield these proportions:
1
2=36
1
2=
510
3
6=
510
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Example Using shadow proportions to find “difficult to measure” lengths
Kyle is 5.6 feet tall. Late one afternoon while visiting the Grove Isle Lighthouse, he noticed that his shadow was 8.5 feet long. At the same time, the lighthouse cast a shadow 119 feet long. What is the height of the lighthouse? (See the figure on the next slide.)
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Example Using shadow proportions to find “difficult to measure” lengths
8.5 ft shadow119 ft shadow
5.6 ft
x
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Solution Strategy
x = height of the lighthouse
5.6
8.5=
x119
Kyle is 5.6 feet tall. Late one afternoon while visiting the Grove Isle Lighthouse, he noticed that his shadow was 8.5 feet long. At the same time, the lighthouse cast a shadow 119 feet long. What is the height of the lighthouse?