The document discusses ratios, proportions, and solving proportions. It provides examples of ratios, defines a proportion as two equal ratios, and explains how to check if proportions are true by seeing if the fractions are equal in lowest terms. It also discusses using cross multiplication to solve proportions, finding missing terms in proportions, similar figures and proportional sides, and applying proportions to find missing angle measures and side lengths.

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6.1 Ratios &
Proportion

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A RATIO is a quotient
that compare 2 quantities.
3
4
3 to 4 3 : 4
These are all the same.

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A Proportion is an equation
of two equal ratios.
gallons
miles
gallons
miles
2
25
4
50
=

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Proportion is true if
fractions are equal when in
lowest terms.
3 4 5
6 8 10
= =
all
reduce
to 1/2

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the Extremes.
the Means.
12
8
3
2
=

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The product of the means
equals the product of the
extremes.
Cross products are equal.
12
8
3
2
=
2 • 12 = 3 • 8
24 = 24

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To Solve Proportions
n
3
6
9
=
Find n
9 n = (3) (6)
9 n = 18
n = 2

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7
4
=
w
5000 - w
7 ( 5000 - w) = 4 w
35,000 = 11 w
3182 = w
35000 - 7 w = 4 w

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3: 8 = n : 6
3 = n
8 6
18 = 8 n
18/8 = n
2.25 = n

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Similar Figures
A B
C D
E F
G H
Corresponding <s =
Sides are proportional

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A B
C D
E F
G H
ABCD ~ EFGH
10
12
13
Find GH small 10
big 13
= 12
GH

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small 10
big 13
= 12
GH
10 GH = (12)(13)
10 GH = 156
GH = 15.6
mathbyart.com

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A B
C D
E F
G H
ABCD ~ EFGH
110
Find m<E
<A = <E m<E = 1100
~
110

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A
B C
D
E F
AB C ~ DEF
8 6
5
Find EF

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A
B C
D
E F
AB C ~ DEF
8 6
5
small
big
6
8
= EF
5

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6
8
= EF
5
x
(6)(5) = 8x
30 = 8x
30/8 = x
3.75 = x
mathbyart.com

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The desire to succeed
means nothing
without the
will to
prepare!
thought for the day