Absolute Value

Show your work for each problem.

1.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
because is 6 units away from zero on the number line. Absolute value is always non-negative.
2.
Which expression equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
(the distance from to zero). The other options: , , and .
3.
Which statement is TRUE?
1. a)
2. b)
3. c)
4. d)
Answer:
because and are both 3 units from zero. They are opposites, so they have the same absolute value.
4.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. First compute , then take the absolute value to get .
5.
Which pair of numbers has the GREATEST distance between them?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
, , , . The pair and has the greatest distance of units.
6.
What is ?
Answer: 9
. Since is already positive, its absolute value is simply . It's 9 units from zero.
7.
What is ?
Answer: 12
. The number is 12 units away from zero, so its absolute value is .
8.
What is ?
Answer: 11
. The absolute value of is , and the absolute value of is .
9.
What is the distance between and on the number line?
Answer: 13
Distance . Or count: from to is 13 units.
10.
What is ?
Answer: 5
.
11.
Find and explain your answer.
Answer: 7
1. Where is on the number line? left of zero
2. How many units is from zero? 7
3. What is ? 7
12.
Calculate step by step.
Answer: 2
1. What is ? 5
2. What is ? 3
3. What is ? 2
13.
Find the distance between and on the number line.
Answer: 10
1. What is ? 10
2. What is ? 10
3. The distance is? 10
14.
Simplify:
Answer: 8
1. What is ? 4
2. What is ? 8
3. What is ? 2
4. What is ? 6
5. What is ? 6
6. What is ? 8
15.
A thermometer reads 23 degrees Celsius. The actual temperature is 18 degrees Celsius. Find the absolute error.
Answer: 5
1. What is the difference: measured - actual? 5
2. What is the absolute value of this difference? 5
3. The absolute error is how many degrees? 5