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c)
Since 12 = 2
⋅
6 = 2
⋅
2
⋅
3 and 18 = 2
⋅
9 = 2
⋅
3
⋅
3, the factor 2 appears twice in the LCD and
the factor 3 appears twice in the LCD. So the LCD is 2
⋅
2
⋅
3
⋅
3 or 36:
d)
To perform addition with the mixed number
first convert it into an improper fraction:
Note that
. Then add on the 2 to get
, which is the same as
.
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Now do Exercises 67–78
Calculator Close-Up
You can check these results with a graphing calculator. Note how a graphing calculator handles
mixed numbers.
Helpful Hint

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Recall the
place value
for decimal numbers:
So
6 Fractions, Decimals, and Percents
In the decimal number system, fractions with a denominator of 10, 100, 1000, and so on are written
as decimal numbers. For example,
Fractions with a denominator of 100 are often written as percents. Think of the percent symbol (%)
as representing the denominator of 100. For example,
Example 8 illustrates further how to convert from any one of the forms (fraction, decimal, percent) to
the others.
EXAMPLE
8
Changing forms
Convert each given fraction, decimal, or percent into its other two forms.
a)
b)
6%
c)
0.1
Solution
a)
So
. Note that a fraction can also be converted to a decimal by dividing the
denominator into the numerator with long division.
b)
c)

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Now do Exercises 79–90
Calculator Close-Up
A calculator can convert fractions to decimals and decimals to fractions. The calculator shown here
converts the terminating decimal 0.333333333333 into 1/3 even though 1/3 is a repeating decimal
with infinitely many threes after the decimal point.
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7 Applications
The dimensions for lumber used in construction are usually given in fractions. For example, a two-
by-four (2 × 4) stud used in framing walls is actually
. by
. by
. A two-by-twelve (2 ×
12) ﬂoor joist with a width of
and height of
comes in various lengths, usually 8, 10, 12,
14, and 16 feet. In Example 9 we find the height of a wall.
EXAMPLE
9
Framing a two-story house
In framing a two-story house, a carpenter uses a 2 × 4 shoe, a wall stud, two 2 × 4 plates, then 2 ×
12 ﬂoor joists, and a
plywood ﬂoor, before starting the second level. Use the dimensions in Fig.
1.24 to find the total height of the framing shown.
Figure 1.24
Solution
We can find the total height using multiplication and addition:

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The total height of the framing shown is
in.