Ratios and Proportions

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Ratios and Proportions

• SISD
• TAKS / Math-180 Module 12

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Ratios Proportions Determine if ratios are
proportional

• - One way to tell whether two ratios are
  proportional is to show that the cross products
  are equal.

EXAMPLE 1 Are the ratios proportional?
EXAMPLE 2 Are the ratios proportional?
Check cross products.
Check cross products.
5 x 4 20
2 x 10 20
5 x 3 15
7 x 4 28
15 28 Therefore, the two ratios are
NOT proportional.
20 20 Therefore, the two ratios are
proportional.
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Applications
A tree casts a 32.5 foot-long shadow at the same
time a 24 foot flagpole casts a 15 foot-long
shadow. Set up and solve a proportion to find
the height of the tree.
24 feet
15x 32.5 24
x
15x 780
15 feet
15 15
x 52 The tree is 52 feet tall.
32.5 feet
4
Mrs. Hanleys geometry class is trying to
approximate the height of the Washington
Monument. They notice that the monument casts a
333 foot-long shadow at the same time a 5
foot-tall student casts a foot-long shadow.
Approximate the height of the Washington Monument
by setting up and solving a proportion.
5 ft
3h 333 5
h
3h 1665
3 ft
3 3
h 555 The Washington Monument is approximately
555 feet-tall.
333 ft
5

• Michael is making a model of his fathers car.
  The car is 4.5 feet-tall and 11 feet-long. How
  long will the model car be if he uses a scale of
  1 inch to 2 feet.

x inches
2x 1 11
2x 11
2 2
x 5.5 The model will be 5.5 inches-long.
11 feet
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• Michael is making a model of his fathers car.
  The car is 4.5 feet-tall and 11 feet-long. How
  tall will the model car be if he uses a scale of
  1 inch to 2 feet.

x
2x 4.5 1
4.5 ft
2x 4.5
2 2
x 2.25 The model will be 2.25 inches tall.
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Mrs. Garcia wants to make a small flower garden
similar to the triangular garden already in her
yard. She wants the new one smaller but still
proportional. If the longest side of the small
garden is 6 feet long, what will be the
dimensions of the other two sides of her new
garden?
6 ft
b
24b 18 6
a
24a 16 6
24b 108
24 ft
24a 96
18 ft
24 24
24 24
b 4.5 Side b will be 4.5 feet-long.
a 4 Side a will be 4 feet-long.
16 ft
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Try This!

• This problem is 39 from the July 2006 Released
  Mathematics TAKS Exit Level Exam.

In 2002, people in Laredo, Texas, erected the
tallest flagpole in the United States. It can be
seen from miles away.
According to the information in the drawing, what
is the approximate height of the flagpole? (The
drawing is not drawn to scale.)

• 308 feet
• 295 feet
• 205 feet
• 197 feet

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THE END