Page 246 - Basic College Mathematics with Early Integers

S E C T I O N 3.5 I ADDING AND SUBTRACTING UNLIKE FRACTIONS 223

2 4
Example 1 Add: + PRACTICE 1
5 15
2 8
Add: +
Solution: 7 21
Step 1: The LCD of the fractions is 15. In later examples, we shall simply say,
for example, that the LCD of the denominators 5 and 15 is 15.
2 2 # 3 6 4 4
Step 2: = = , = ; This fraction already has a denominator of 15.
5 5 3 15 15 15
3
Multiply by 1 in the form
3
2 4 6 4 10
Step 3: += + =
5 15 15 15 15
Step 4: Write in simplest form.

1
10 2 # 5 2
= =
15 3 # 5 3
1
Work Practice 1

2 3
Example 2 Add: + PRACTICE 2
15 10
5 2
Solution: Add: +
6 9
Step 1: The LCD of the denominators 15 and 10 is 30.
4
2 2 2 = 3 3 3 9
Step 2: = # = # =
15 15 2 30 10 10 3 30

2 3 4 9 13
Step 3: + = + =
15 10 30 30 30
13
Step 4: is in simplest form.
30
Work Practice 2

1 1
Example 3 Add: - + PRACTICE 3
6 2
1 9
Solution: The LCD of the denominators 6 and 2 is 6. Add: - 5 + 20

#
1 1 -1 1 3
- + = +
#
6 2 6 2 3 Recall that
-1 3
= + 1 -1 1
6 6 - = =
6 6 -6
2
=
6
2
Next, simplify .
6
1
2 2 1
= =
6 2 # 3 3
1 Answers
2 19 1
Work Practice 3 1. 3 2. 18 3. 4