ratiosandpropday1 2014
TRANSCRIPT
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Holt McDougal Geometry
7-1 Ratio and Proportion
Write and simplify ratios.
Use proportions to solve problems.
Objectives
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Holt McDougal Geometry
7-1 Ratio and Proportion
ratioproportionextremesmeanscross products
Vocabulary
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Holt McDougal Geometry
7-1 Ratio and Proportion
A ratio compares two numbers by division. The ratio
of two numbers a and b can be written as a to b, a:b,
or , where b ≠ 0. For example, the ratios 1 to 2,
1:2, and all represent the same comparison.
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Holt McDougal Geometry
7-1 Ratio and Proportion
In a ratio, the denominator of the fraction cannot be zero because division by zero is undefined.
Remember!
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Holt McDougal Geometry
7-1 Ratio and Proportion
A proportion is an equation stating that two ratios
are equal. In the proportion , the values
a and d are the extremes. The values b and c
are the means. When the proportion is written as
a:b = c:d, the extremes are in the first and last
positions. The means are in the two middle positions.
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PROPORTION
TWO EQUAL RATIOS
a = c
b d
MEANS: b,c
EXTREMES: a,d
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Use the proportion given to complete each statement 2
5
y
x
?
?
5
2.
5.
c
ya
?
?
5.
?
?.
xd
y
yxb
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Cross Products Property
The product of the means equals the
product of the extremes.
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Properties of Proportions
ab
cd
=
1. ad = bc
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PROPERTIES OF PROPORTION
Exchange Property
You may exchange the means
or the extremes.
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Properties of Proportions
ab
cd
=
a
c
b
d=
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PROPERTIES OF PROPORTION Reciprocal Property
Take the reciprocal of both ratios.
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Properties of Proportions
ab
cd
=
b
a
d
c=
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PROPERTIES OF PROPORTION “Add One” Property
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Properties of Proportions
ab
cd
=
a + b
bc + d
d=
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Holt McDougal Geometry
7-1 Ratio and Proportion
Example 3A: Solving Proportions
Solve the proportion.
Cross Products Property
Simplify.
Divide both sides by 56.
7(72) = x(56)
504 = 56x
x = 9
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Holt McDougal Geometry
7-1 Ratio and Proportion
Example 3B: Solving Proportions
Solve the proportion.
Cross Products Property(z – 4)2 = 5(20)
Simplify.(z – 4)2 = 100
Find the square root of both sides.(z – 4) = 10
(z – 4) = 10 or (z – 4) = –10 Rewrite as two eqns.
z = 14 or z = –6 Add 4 to both sides.
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Holt McDougal Geometry
7-1 Ratio and Proportion
Check It Out! Example 3a
Solve the proportion.
Cross Products Property
Simplify.
Divide both sides by 8.
3(56) = 8(x)
168 = 8x
x = 21
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Holt McDougal Geometry
7-1 Ratio and Proportion
Check It Out! Example 3b
Solve the proportion.
Cross Products Property
Simplify.
Divide both sides by 8.
2y(4y) = 9(8)
8y2 = 72
y2 = 9
Find the square root of both sides.y = 3
Rewrite as two equations.y = 3 or y = –3
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Holt McDougal Geometry
7-1 Ratio and Proportion
Check It Out! Example 3c
Solve the proportion.
Cross Products Property
Simplify.
Divide both sides by 2.
d(2) = 3(6)
2d = 18
d = 9
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Holt McDougal Geometry
7-1 Ratio and Proportion
Check It Out! Example 3d
Solve the proportion.
Cross Products Property(x + 3)2 = 4(9)
Simplify.(x + 3)2 = 36
Find the square root of both sides.(x + 3) = 6
(x + 3) = 6 or (x + 3) = –6 Rewrite as two eqns.
x = 3 or x = –9 Subtract 3 from both sides.
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Holt McDougal Geometry
7-1 Ratio and Proportion
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