Transcript mgpia3e_ppt_06_01

Chapter 6
Ratio, Proportion,
and
Percent
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
6.1
Ratio and Proportion
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Writing Ratios as Fractions
A ratio is the quotient of two quantities.
For example, a percent can be thought of as a ratio,
since it is the quotient of a number and 100.
53% = 53 or the ratio of 53 to 100
100
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Ratio
The ratio of a number a to a number b is their
quotient. Ways of writing ratios are
a to b,
a : b,
a
and
b
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Solving Proportions
A proportion is a statement that two ratios
are equal.
c
a
If and are two ratios, then
d
b
a c
=
b d
is a proportion.
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Solving Proportions
A proportion contains four numbers. If any
three numbers are known, the fourth number
can be found by solving the proportion. To
solve use cross products.
Multiply both sides
by the LCD, bd
a 
c
bd    bd  
b 
d
a
c
bc
=
b
d
ad
These are called
cross products.
ad = bc
Simplify
cross product
cross product
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Determining Whether Proportions are True
3 12
Is =
a true proportion?
8 32
3 12
=
8 32
?
3  32 = 8  12
96 = 96
True proportion
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Finding Unknown Numbers in Proportions
26 28
Solve
= .
x 49
26  49 = 28x
1274 = 28x
45.5 = x
Check:
Cross multiply.
Simplify the left side.
Divide both sides by 28.
26 28
= ?
45.5 49
26 52 4 28
=
= =
45.5 91 7 49
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Solving Problems by Writing Proportions
A 16-oz Cinnamon Mocha Iced Tea at a local coffee shop
has 80 calories. How many calories are there in a 28-oz
Cinnamon Mocha Iced Tea?
16 ounces 28 ounces

80 calories x calories
16x  80  28
16x  2240
x  140
Solve the proportion.
Cross multiply.
Simplify the right side.
Divide both side by 140.
A 28-oz Cinnamon Mocha Iced Tea has 140 calories.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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Helpful Hint
When writing proportions to solve
problems, write the proportions so that the
numerators have the same unit measures and
the denominators have the same unit
measures.
For example,
2 inches 7 inches

5 miles
n miles
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