Equations with Decimals

Show your work for each problem.

1.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
. Divide both sides by : .
2.
Solve:
Answer: 8
. Divide both sides by : . Check: \checkmark
3.
To eliminate decimals in , multiply all terms by:
1. a)
2. b)
3. c)
4. d)
Answer:
has 2 decimal places (the maximum). Multiply by to clear all decimals.
4.
Solve:
Answer: 3
1. Multiply all terms by 10 to clear decimals. What equation do you get? 3x + 9 = 18
2. Subtract 9 from both sides. What is 3x equal to? 9
3. Divide by 3. What is x? 3
5.
Solve:
Answer: 1.6
. Subtract : .
6.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Add : . Divide by : .
7.
Solve:
Answer: 6
1. What power of 10 eliminates all decimals? 100
2. After multiplying by 100, what equation do you get? 25x + 50 = 200
3. Subtract 50 from both sides. What is 25x equal to? 150
4. Divide 150 by 25. What is x? 6
8.
Solve:
Answer: 3
Add 0.3: . Divide by 0.6: .
9.
Solve:
Answer: 3
1. Multiply all terms by 10 to clear decimals. What is the new equation? 15x + 25 = 70
2. Subtract 25 from both sides. What is 15x equal to? 45
3. Divide by 15. What is x? 3
10.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 1.6: . Divide by 0.8: .
11.
Solve:
Answer: 8
Multiply by 100: . Divide by 75: .
12.
Solve:
Answer: 4
1. Multiply all terms by 10. What is the equation? 5x + 3 = 2x + 15
2. Subtract 2x from both sides. What do you get? 3x + 3 = 15
3. Subtract 3 from both sides. What is 3x equal to? 12
4. Divide by 3. What is x? 4
13.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by 10: . Subtract 8x: . Add 6: . Divide: .
14.
Solve:
Answer: 4
Multiply by 100: . Subtract 45: . Divide by 15: .
15.
Solve:
Answer: 5
1. Multiply all terms by 10. What is the equation? 25x - 15 = 15x + 35
2. Subtract 15x from both sides. What do you get? 10x - 15 = 35
3. Add 15 to both sides. What is 10x equal to? 50
4. Divide by 10. What is x? 5
16.
A store sells items for 2.75 euros each. After buying some items, you paid a total of 16.50 euros. How many items did you buy?
Answer: 6
1. Write the equation. If n = number of items, what is it? 2.75n = 16.50
2. Multiply both sides by 100. What equation do you get? 275n = 1650
3. Divide 1650 by 275. How many items? 6