Ratio and Proportion

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7-1
Ratio and Proportion
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
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Warm Up Find the slope of the line through each
pair of points. 1. (1, 5) and (3, 9) 2. (6, 4)
and (6, 2) Solve each equation. 3. 4x 5x 6x
45 4. (x 5)2 81 5. Write in simplest
form.
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x 3
x 14 or x 4
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Objectives
Write and simplify ratios. Use proportions to
solve problems.
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Vocabulary
ratio proportion cross products
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The Lord of the Rings movies transport viewers to
the fantasy world of Middle Earth. Many scenes
feature vast fortresses, sprawling cities, and
bottomless mines. To film these images, the
moviemakers used ratios to help them build highly
detailed miniature models.
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A ratio compares two numbers by division. The
ratio of two numbers a and b can be written as a
to b, ab, or , where b ? 0. For example, the
ratios 1 to 2, 12, and all represent the
same comparison.
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Examples
In Mr. Alexanders Geometry class, there are 12
boys and 16 girls. Write the following ratios.
12
12
16
16
16
1. Boys to Girls
2. Girls to
3. Girls to Boys
Students
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In the United States House of Representatives
there are 435 seats. Of those, 70 are occupied by
women. Write the ratio of men to women in the US
House of Representatives.

• 365

70
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Solving problems with ratios!
To simplify a ratio, we divide out the common
factor. So, when we solve we are looking for that
factor.
How do we put the 4 back in?
Divide 4 out
So to make ratios big again we multiply!
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The ratio of the lengths of an isosceles triangle
is 447, and its perimeter is 52.5 cm. What are
the lengths of the sides of the triangle?
4
4
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We know we have a missing factor. What do we call
it?
How do we find perimeter?
x
x
x
15x 52.5
4(3.5) 14 4(3.5) 14 7(3.5) 24.5
X 3.5
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• One common ratio is slope, which is the
  comparison of the change in y to the change in x.
  This can also be expressed as

Rate of change
m
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Example 7
Write a ratio expressing the slope of the line.
6
4
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Example 8
Write the slopes as a ratio for points A(7, 9)
and B(2, -6).
Substitute the given values.

Simplify.
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A proportion is an equation stating that two
ratios are equal. When you cross multiply you
create equal cross products.
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Example 9 Solving Proportions
Solve the proportion.
Cross Products Property
4(65) k(10)
Simplify.
260 10k
Divide both sides by10.
k 26
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Example 10 Solving Proportions
Solve the proportion.
Cross Products Property
p(p) 4(9)
Simplify.
p2 36
Find the square root of both sides.
p ?6
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Example 11
Solve the proportion.
Cross Products Property
3(x 8) 4(x 3)
Distribute.
3x 24 4x 12
Subtract both sides by 3x.
24 x 12
Subtract both sides by 12.
12 x
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Example 12
Cross Products are 7a and 5b
5b
7a
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The following table shows equivalent forms of the
Cross Products Property.
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Example 13 Problem-Solving Application
The scale of a map of downtown Dallas is 1.5
cm300 m. If the distance between Union Station
and the Dallas Public Library is 6 cm, what is
the actual distance?
The answer will be the distance from the Union
Station to the Dallas Public Library.
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Example 13 Continued
Let x be the distance from the Union Station to
the Dallas Public Library. Write a proportion
that compares the ratios of the width to the
length.
Distance in cm
Distance in m
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Example 13 Continued
Cross Products Property
6(300) x(1.5)
Simplify.
1800 1.5x
Divide both sides by 1.5.
x 1200
The distance from the Union Station to the Dallas
Public Library is 1200 m.
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Example 13 Continued
Look Back
Check the answer in the original problem. The
ratio of the scale distance to actual distance is
61200, or 1200. The ratio of the given scale is
also 1200. So the ratios are equal, and the
answer is correct.
6/1200 .005 1.5/300 .005
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Example 14
The 250,000 budget for a local shelter is
allocated proportionally to the mens and womens
departments according to the population in the
shelter by gender. If there are 1946 women and
399 men in the shelter, what amount rounded to
the nearest dollar is allocated to the mens
department?
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Example 15
After an election in a small town, the newspaper
reported that 42 of the registered voters
actually voted. If 12,000 people voted, how many
people are registered to vote in the town?
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Example 16
A student wanted to find the height of a statue
of a pineapple in Nambour, Australia. She
measured the pineapples shadow at 8 ft 9in and
her own shadow at 2 ft. The students height is 5
ft 4 in. What is the height of the pineapple?
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Example 17
The Lincoln Memorial in Washington, D.C., is
approximately 57 m long and 36 m wide. If you
would want to make a scale drawing of the base of
the building using a scale of 1 cm 15 m, what
would be the dimensions of the scale drawing?
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Lesson Quiz
1. The ratio of the angle measures in a triangle
is 156. What is the measure of each
angle? Solve each proportion. 2. 3. 4.
Given that 14a 35b, find the ratio of a to b in
simplest form. 5. An apartment building is 90 ft
tall and 55 ft wide. If a scale model of this
building is 11 in. wide, how tall is the scale
model of the building?
15, 75, 90
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7 or 7
18 in.