M098
Carson Elementary and Intermediate Algebra 3e
Section 3.2
Objectives
1.
2.
3.
4.
Write a percent as a fraction or decimal number.
Write a fraction or decimal number as a percent.
Translate and solve percent sentences.
Solve problems involving percents.
Vocabulary
Percent
A ratio representing some part out of 100
Prior Knowledge
Ratio: A ratio is a comparison of two quantities using a quotient.
Proportion: An equation in the form
a
c
 , where b ≠ 0 and d ≠ 0
b d
Cross Product: The cross product can be used to solve for a missing quantity
New Concepts
Converting a fraction to a decimal, and from a decimal to a percent
FRACTION
to
Divide
DECIMAL
to
PERCENT
move decimal to the right 2 places
START HERE:
Example 1
3
Write as a decimal
4
The fraction
3
is the
4
same as 3 divided by 4,
so do the division,
adding a decimal and
zeroes as necessary.
0.75
4 3.0
To convert a decimal to
a percent, move the
decimal point two
places to the right and
write with a percent (%)
sign.
0.75  75%
3
 0.75
4
Example 2
7
Write as a decimal
8
The fraction
7
is the
8
same as 7 divided by 8,
so do the division,
adding a decimal and
zeroes as necessary.
0.875
8 7.00
To convert a decimal to
a percent, move the
decimal point two
places to the right and
write with a percent (%)
sign.
0.875  87.5%
7
 0.875
8
C.Stewart 2011
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M098
Carson Elementary and Intermediate Algebra 3e
Section 3.2
Hundredths
Thousandths
Ten Thousandths
0 .
Tenths
Place value reminder:
1
2
3
4
Converting a percent to a decimal, and from a decimal to a fraction
(To use this chart, move from the RIGHT to the LEFT)
FRACTION
read it
write it
reduce it
from
DECIMAL
from
PERCENT
move decimal 2 places to the left
START HERE:
Example 1
To convert a decimal to a
fraction, read the decimal,
write it as a fraction, then
reduce it. The decimal 0.64 is
read “sixty-four hundredths*:”
0.64 
64
100
Now, reduce the fraction:
To convert a percent to a
decimal, move the decimal
two places to the left. If
there is no decimal written, it
is implied to be after the
number.
Write 64% as a decimal.
64%  0.64
64
16

100 25
Example 2
To convert a decimal to a
fraction, read the decimal,
write it as a fraction, then
reduce it.
38
19
0.38 

100
50
To convert a percent to a
decimal, move the decimal
two places to the left.
Write 38% as a decimal.
38%  0.38
Example 3
To convert a decimal to a
fraction, read the decimal,
write it as a fraction, then
reduce it.
The decimal 0.155 is read as
“one-hundred fifty-five
thousandths”
0.155 
C.Stewart 2011
To convert a percent to a
decimal, move the decimal
two places to the left.
Write 15.5% as a decimal.
15.5%  0.155
155
31

1000 200
page 2
M098
Carson Elementary and Intermediate Algebra 3e
Section 3.2
Solve percent problems using proportions.
To solve a percent problem, we can use one of the following proportions:
percent
part
is
percent
or


100
whole
of
100
Example 1:
What number is 15% of 36?
To use the proportion, identify the key words:
What number is 15% of 36?
We will use the first proportion. Fill in the 3 parts of the
proportion that you identified:
What number is
of 36
x
15

36 100
15 percent
Stays 100
Now, we use what we know about proportions to solve for
the missing number. By cross multiplying, we get the
following:
100 x  15  36
100 x  540
100 x
540

100
100
x  5.4
Therefore, 5.4 is 15% of 36.
Example 2:
48 is 120% of what number?
Identify the key words:
48 is 120% of what number?
We will use the first proportion. Fill in the 3 parts of the
proportion that you identified:
48 is
of what number
48 120

x
100
120 percent
Stays 100
Again, we use what we know about proportions to solve
for the missing number. By cross multiplying, we get the
following:
120 x  48  100
120 x  4800
120 x
4800

120
100
x  40
Therefore, 48 is 120% of 40.
C.Stewart 2011
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M098
Carson Elementary and Intermediate Algebra 3e
Section 3.2
Example 3
Heidi left an 11% tip of $1.65
for a meal. What was the cost
of the mean before the tip?
With word problems such as this one, it is sometimes
more helpful to use the second proportion:
11 percent
Stays 100
11
1.65

100
x
1.65 is the part
Unknown whole
Now use the cross products to solve:
11x  165
x  15
Therefore, the meal cost $15. The total cost, including the
tip, was $16.65.
C.Stewart 2011
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