Complex Fractions

Show your work for each problem.

1.
Which of the following is a complex fraction?
1. a)
2. b)
3. c)
4. d)
Answer:
is a complex fraction because both the numerator () and denominator () are fractions.
2.
Simplify:
Answer: 2
3.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
4.
Simplify:
Answer: 3/2
1. What is the reciprocal of ? 9/4
2. Multiply: = ? 18/12
3. Simplify 3/2
5.
Simplify:
Answer: 8
6.
Simplify:
Answer: 1
1. First, add the fractions in the numerator. = ? 3/4
2. Now simplify 1
7.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
, then
8.
Simplify:
Answer: 4/3
. Then
9.
Simplify using the LCD method:
Answer: 5
1. What is the LCD of 2, 3, and 6? 6
2. Multiply numerator by 6: = ? 5
3. Multiply denominator by 6: = ? 1
4. Final answer: = ? 5
10.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
(where )
11.
Simplify:
Answer: (x+1)/(x-1)
1. What is the LCD of all fractions in this expression? x
2. Multiply the numerator by : = ? x+1
3. Multiply the denominator by : = ? x-1
4. Write the final simplified form (x+1)/(x-1)
12.
Simplify:
Answer: x+y
Multiply by :
13.
Simplify:
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by : Numerator: . Denominator: . Answer:
14.
Two resistors of 6 ohms and 12 ohms are in parallel. Find the total resistance using
Answer: 4
1. What is as a fraction with denominator 12? 2/12
2. Add = ? 3/12
3. Simplify = ? 1/4
4. Find = ? 4
15.
Simplify:
Answer: b/a
(where )
16.
Simplify:
Answer: x
1. Note that . What is the LCD? (x+1)(x-1)
2. Add the fractions in the numerator with LCD : = ? 2x/(x^2-1)
3. Now divide: = ? x