Concepts
1 BasicFunctions
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Unit 1B
Review of Operations with
Fractions
Copyright © Cengage Learning. All rights reserved.
1.8
Multiplication and Division of Fractions
Copyright © Cengage Learning. All rights reserved.
Multiplication and Division of Fractions
Multiplying Fractions
To multiply fractions, multiply the numerators and multiply
the denominators. Then reduce the resulting fraction to
lowest terms.
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Example 1
Multiply:
To simplify the work, consider the following alternative
method:
This method divides the numerator by 15, or (5  3), and
the denominator by 15, or (5  3). It does not change the
value of the fraction.
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Multiplication and Division of Fractions
Dividing Fractions
To divide a fraction by a fraction, invert the fraction
(interchange numerator and denominator) that follows the
division sign (). Then multiply the resulting fractions.
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Example 5
Divide:
Invert
and multiply.
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Multiplication and Division of Fractions
When both multiplication and division of fractions occur,
invert only the first fraction that follows a division sign ().
Then proceed according to the rules for multiplying
fractions.
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Applications Involving Multiplication
and Division of Fractions
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Applications Involving Multiplication and Division of Fractions
Lumber is usually measured in board feet. One board foot
is the amount of wood contained in a piece of wood that
measures one inch thick and one square foot in area, or its
equivalent. (See Figure 1.28.)
One board foot
Figure 1.28
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Applications Involving Multiplication and Division of Fractions
The number of board feet in lumber may be found by the
formula
The 12 in the denominator comes from the fact that the
simplest form of one board foot can be thought of as a
board that is 1 in. thick  12 in. wide  1 ft long.
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Applications Involving Multiplication and Division of Fractions
Lumber is either rough or finished. Rough stock is lumber
that is not planed or dressed; finished stock is planed on
one or more sides.
When measuring lumber, we compute the full size. That is,
we compute the measure of the rough stock that is required
to make the desired finished piece.
When lumber is finished or planed, in. is taken off each
side when the lumber is less than in. thick.
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Applications Involving Multiplication and Division of Fractions
If the lumber is
off each side.
in. or more in thickness, in. is taken
(Note: Lumber for framing houses usually measures in.
less than the name that we call the piece. For example, a
“two-by-four,” a piece 2 in. by 4 in., actually measures in.
by in.)
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Example 11
Find the number of board feet contained in 6 pieces of
lumber 2 in.  8 in.  16 ft (Figure 1.29).
Figure 1.29
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Example 11
cont’d
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