Page 212 - Basic College Mathematics with Early Integers

S E C T I O N 3.2 I FACTORS AND SIMPLEST FORM 189

Cross Products
# #
25 16 40 10
16 = 10
40 25

Notice that these cross products are equal:
#
#
25 16 = 400, 40 10 = 400
In general, this is true for equivalent fractions.

Equality of Fractions
# #
8 6 24 2
6 2

24 8

#
#
Since the cross products (8 6 = 48 and 24 2 = 48 ) are equal, the fractions
are equal.
Note: If the cross products are not equal, the fractions are not equal.

8 19
Example 11 Determine whether and are equivalent. PRACTICE 11
11 26 4 5
Determine whether and
Solution: Let’s check cross products. are equivalent. 13 18
#
#
26 8 11 19
8 19
= 208 = 209
11 26
8 19
Since 208 Z 209, then Z .
11 26
“Not equal to”
symbol
Work Practice 11

Objective Solving Problems by Writing Fractions
in Simplest Form

Many real-life problems can be solved by writing fractions. To make the answers
clearer, these fractions should be written in simplest form.

Example 12 Calculating Fraction of Parks in Wyoming State PRACTICE 12
There are six national parks
There are currently 58 national parks in the United States. Two of these parks are
(including historic) in
located in the state of Wyoming. What fraction of the United States’ national
Washington state. See
parks can be found in Wyoming? Write the fraction in simplest form. (Source:
Example 12 and determine
National Park Service)
what fraction of the United
Yellowstone States’ national parks are
National Park 90 located in Washington state.
25
Write the fraction in simplest
Grand Teton
Casper form.
National Park
25
80
80 Answers
Cheyenne 3
11. not equivalent 12.
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