Page 231 - Basic College Mathematics with Early Integers

208 C HAPTE R 3 I FRACTIONS

For example,

1 2 1 + 2 3 Add the numerators.
+ = =
4 4 4 4 Keep the denominator.
4 2 4 - 2 2 Subtract the numerators.
- = =
5 5 5 5 Keep the denominator.

As usual, don’t forget to write all answers in simplest form.

PRACTICE 1–3 Examples Add and simplify.

Add and simplify.
2 3 2 + 3 5 ; Add the numerators.
6 2 1. + = =
1. + 7 7 7 7 ; Keep the common denominator.
13 13
1
#
5 1 3 7 3 + 7 10 2 5 5
2. + 2. + = = = =
#
8 8 16 16 16 16 2 8 8
1
20 6 7
3. + + 7 6 3 7 + 6 + 3 16
11 11 11 3. + + = = or 2
8 8 8 8 8
Work Practice 1–3
Concept Check Find and correct the error in the following:
1 1 2
+ =
5 5 10

PRACTICE 4–5 Examples Subtract and simplify.
Subtract and simplify.
8 1 8 - 1 7 ; Subtract the numerators.
11 6 4. - = =
4. - 9 9 9 9 ; Keep the common denominator.
12 12
1
7 2 7 5 7 - 5 2 2 1
5. - 5. - = = = =
#
15 15 8 8 8 8 2 4 4
1
Work Practice 4–5
From our earlier work, we know that
-12 12 12
= =- since these all simplify to -2.
6 -6 6
PRACTICE 6
In general, the following is true:
8 4
Add: - + -a a a
17 17 = =- as long as b is not 0.
b -b b
Answers
8 3 5
1. 2. 3. 3 4. Example 6 11 6
13 4 12 Add: - +
8 8
1 4
5. 6. -
3 17 11 6 -11 + 6
Solution: - + = Copyright 2012 Pearson Education, Inc.
8 8 8
Concept Check Answer
-5 5
We don’t add denominators together; = 8 or - 8
1 1 2
correction: + = .
5 5 5 Work Practice 6