Page 248 - Basic College Mathematics with Early Integers

S E C T I O N 3.5 I ADDING AND SUBTRACTING UNLIKE FRACTIONS 225

Objective Writing Fractions in Order

One important application of the least common denominator is to use the LCD to
help order or compare fractions.

Example 7 Insert 6 or 7 to form a true sentence. PRACTICE 7
Insert 6 or 7 to form a true
3 9

4 11 sentence.
5 11
Solution: The LCD for these fractions is 44. Let’s write each fraction as an
8 20
equivalent fraction with a denominator of 44.
#
#
33
3 3 11 = 9 9 4 36
= = =
#
#
4 4 11 44 11 11 4 44
Since 33 6 36, then
33 36
6 or
44 44
3 9
6
4 11
Work Practice 7
Example 8 Insert 6 or 7 to form a true sentence. PRACTICE 8
2 1 Insert 6 or 7 to form a true
- - sentence.
7 3
17 4
Solution: The LCD of the denominators 7 and 3 is 21. - - 5
20
#
#
2 2 3 6 -6 1 1 7 7 -7
- =- =- or - =- =- or
#
#
7 7 3 21 21 3 3 7 21 21
Since -6 7 -7, then
6 7
- 7 - or
21 21
2 1
- 7 -
7 3
Work Practice 8
Objective Evaluating Expressions Given Fractional
Replacement Values

7 2
Example 9 Evaluate x - y if x = and y = . PRACTICE 9
18 9 5
Evaluate x - y if x = and
7 2 11
Solution: Replace x with and y with in the expression x - y. 4
18 9 y = .
7 2 9
x - y = -
18 9
The LCD of the denominators 18 and 9 is 18.Then
#
7 2 7 2 2
- = -
#
18 9 18 9 2
7 4
= -
18 18
1
3 3 1
= = = Simplified
#
18 3 6 6 Answers
1 1
7. 7 8. 6 9.
Work Practice 9 99