Page 198 - Basic College Mathematics with Early Integers

S E C T ION 3 .1 I INTRODUCTION TO FRACTIONS AND MIXED NUMBERS 175

The statements below apply to positive fractions.
The fractions in Example 13, parts a, b, and c, are proper fractions. Notice that
the value of each is less than 1. This is always true for proper fractions since the
numerator of a proper fraction is less than the denominator.
The fractions in Example 13, parts d and e, are improper fractions. Notice that
improper fractions are greater than or equal to 1. This is always true since the
numerator of an improper fraction is greater than or equal to the denominator.
Note: We will graph mixed numbers at the end of this chapter.

Objective Reviewing Division Properties of 0 and 1

Before we continue further, don’t forget from Section 1.7 that the fraction bar indi-
cates division. Let’s review some division properties of 1 and 0.
= 1 because 1 9 = 9 -11 #
9
#
9 1 =-11 because -11 1 =-11
0 6
#
= 0 because 0 6 = 0 is undefined because there is no number that
6 0
when multiplied by 0 gives 6.
In general, we can say the following.

Let n be any integer except 0.
= 1 0
n
n n = 0
n n
= n is undefined.
1 0

Examples Simplify. PRACTICE 14–19
Simplify.
15 -2 0
14. = 1 15. = 1 16. = 0 9 -6
15 -2 -5 14. 15.
9 -6
-9 41 19
17. =-9 18. = 41 19. is undefined 0 4
1 1 0 16. 17.
-1 1
Work Practice 14–19 -13 -13
18. 19.
0 1
Notice from Example 17 that we can have negative fractions. In fact,
= -5,
5
-5 5 = -5, and - = -5
1 -1 1
Remember, for
Because all of the fractions equal -5 , we have example, that
-5 5 5 2 -2 2
= = - - = =
1 -1 1 3 3 -3
This means that the negative sign in a fraction can be written in the numerator, in
the denominator, or in front of the fraction. Remember this as we work with nega-
tive fractions.

Answers
14. 1 15. 1 16. 0 17. 4
18. undefined 19. -13