An in Depth Look at Ratios and Proportions and Their Applications

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Ratio and Proportion

• An in Depth Look at Ratios and Proportions and
  Their Applications

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Ratio and Proportion
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Ratios
are the comparison of two or more numbers.
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Which ratio shows the ratio of 2 fish to 3 bear?
A
B
C
D
E
5
Which ratio shows the ratio of 1 soccer ball to 3
basketball?
A
B
C
D
E
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Which ratio shows the ratio of 3 butterflies to 1
apple?
A
B
C
D
E
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Three Ways to Write a Ratio
The ratio of 3 boys to 5 girls can be written as

• a) 3 to 5
• b) 3 5

c)
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Equal Ratios
Equal ratios are like equivalent fractions. They
name the same quantity.
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Equal Ratios
Examples of Equal Ratios
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Proportions
Two equal ratios form a proportion.
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Proportions
In a proportion the product of the means is equal
to product of the extremes.
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Proportions
3 5 6 10
Means
Extremes
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Proportions
Means
Extremes
6 x 5 3 x 10
30 30
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Proportions
Determine if the following are proportions.
1)
2)
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Proportions
3 x 60 5 x 36
4 x 15 8 x 8
180 180
60
64
Yes, it is a proportion.
No, it is not a proportion.
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Special Ratios
Corresponding sides of Similar Triangles have the
same ratio.
Corresponding Angles of Similar Triangles have
congruent angles
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Special Ratios

Triangle D
TriangleA
A is similar to D
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Special Ratios
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Special Ratios
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Special Ratios
E
B
A
C
D
F
ltA ?ltD ltC ? ltF ltB ? ltE
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Proportions
D
A
5
4
y
x
C
B
3
F
E
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Use a proportion to find x and y.
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Proportions
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Special Ratios
Constant Ratio
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Special Ratios
Another type of special ratio is a constant ratio
or rate. Distance rate x time is an example of
a constant ratio.
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Special Ratios
Time 1 2 3 4
Distance 60 120 180 240
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Special Ratios