Page 219 - Basic College Mathematics with Early Integers

Objectives 3.3 MULTIPLYING AND DIVIDING FRACTIONS

Multiply Fractions.

Evaluate Exponential Expressions Objective Multiplying Fractions
with Fractional Bases.
Let’s use a diagram to discover how fractions are multiplied. For example, to multiply
Divide Fractions. 1 3 1 3 3
and , we find of . To do this, we begin with a diagram showing of a rectangle’s
2 4 2 4 4
Multiply and Divide Given
area shaded.
Fractional Replacement Values.
3
Solve Applications That Require 4 of the rectangle’s area is shaded.
Multiplication of Fractions. 1 3 1
To find of , we heavily shade of the part that is already shaded.
2 4 2

3
By counting smaller rectangles, we see that of the larger rectangle is now heavily
8
shaded, so that
#
1 3 3 1 3 3 1 3 1 3 3
of is , or # = Notice that # = = .
#
2 4 8 2 4 8 2 4 2 4 8
Multiplying Fractions

To multiply two fractions,multiply the numerators and multiply the denominators.
If a, b, c, and d represent numbers, and b and d are not 0, we have
#
a c a c
# =
#
b d b d
PRACTICE 1–2 Examples Multiply.
Multiply.
#
2 5 2 5 10 Multiply numerators.
3 5 1 1 1. # = =
#
1. # 2. # 3 11 3 11 33 Multiply denominators.
7 11 3 9
This fraction is in simplest form since 10 and 33 have no common factors other
than 1.
#
1 1 1 1 1
2. # = = This fraction is in simplest form.
#
4 2 4 2 8
Work Practice 1–2
6 14
PRACTICE 3 Example 3 Multiply and simplify: #
6 7 7 27
Multiply and simplify: #
77 8 Solution:
#
6 14 6 14
# =
#
7 27 7 27
We can simplify by finding the prime factorizations and using our shortcut
procedure of dividing out common factors in the numerator and denominator.
1 1 Copyright 2012 Pearson Education, Inc.
# # #
#
#
6 14 2 3 2 7 2 2 4
Answers = = =
#
#
# # #
7 27 7 3 3 3 3 3 9
15 1 3
1. 2. 3. 1 1
77 27 44
Work Practice 3
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