Equations with Fractions

Show your work for each problem.

1.
What is the first step to solve ?
1. a)Subtract 5 from both sides
2. b)Add 5 to both sides
3. c)Divide both sides by 5
4. d)Multiply both sides by 5
Answer: Multiply both sides by 5
Since is divided by 5, we multiply both sides by 5 to isolate . This gives us .
2.
Solve:
Answer: 21
Multiply both sides by 3: , so .
3.
Solve:
Answer: 30
Multiply both sides by 6: , so .
4.
Solve:
Answer: 36
1. What operation is being applied to x? division
2. What is the inverse operation? multiplication
3. Multiply both sides by 4. What is x? 36
5.
What is the LCD of and ?
1. a)2
2. b)3
3. c)5
4. d)6
Answer: 6
The LCD (Least Common Denominator) of 2 and 3 is 6, because 6 is the smallest number that both 2 and 3 divide into evenly.
6.
Solve:
Answer: 12
1. What is the reciprocal of ? 3/2
2. Multiply both sides by . What is ? 12
3. So x equals? 12
7.
Solve:
Answer: 20
Multiply both sides by : .
8.
After multiplying by LCD 6, what equation do you get?
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply each term by 6: , , . So we get .
9.
Solve:
Answer: 8
1. What is the LCD of 2 and 4? 4
2. Multiply all terms by 4. What is ? 2x
3. What is ? x
4. Now solve . What is x? 8
10.
Solve:
Answer: 18
Multiply by LCD 6: , so and .
11.
Which equation is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply both sides by 3: , which gives .
12.
Solve:
Answer: 10
1. What is the LCD of 4 and 3? 12
2. Multiply both sides by 12. What is the left side? 3(x+2)
3. What is the right side? 4(x-1)
4. Distribute both sides. Left side becomes? 3x+6
5. Right side becomes? 4x-4
6. Solve . What is x? 10
13.
Solve:
Answer: 12
LCD is 12. Multiply: , so and .
14.
Solve:
Answer: 20
1. What is the LCD of 2 and 5? 10
2. Multiply all terms by 10. What is ? 5x
3. What is ? 2x
4. Now solve . What is x? 20
15.
A recipe uses cup of sugar for 12 cookies. How much sugar for 18 cookies?
1. a) cup
2. b)1 cup
3. c)2 cups
4. d) cup
Answer: 1 cup
Set up proportion: . Cross-multiply: cup.
16.
Solve:
Answer: 2.75
Cross-multiply: . Expand: . Subtract : . Add 4: . Divide by 8: .
17.
Solve:
Answer: 12
1. What is the LCD of 4 and 2? 4
2. Multiply all terms by 4. The equation becomes? 3x - 8 = 2x + 4
3. Subtract 2x from both sides. What do you get? x - 8 = 4
4. Add 8 to both sides. What is x? 12