1. Absolute Value

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3. Absolute Value What is the absolute value of 0?
Every number and its opposite are the same distance from zero on the number line.
The absolute value of a number is the distance between the number and zero on a number line.
So that means a number and its opposite have the same absolute value.
Because distances are always positive, the absolute value of a positive or negative number is ALWAYS positive.
Absolute value bars are used to show the absolute value of a number.
What is the absolute value of 0?
Absolute Value

4. Absolute Value of a Number
|10|
The absolute value of ten is written as:
On the number line, count the number of units from 10 to 0.
How many units is 10 from 0?
|10| = 10
What other number has an absolute value of 10? Why?
|-10| = 10 because -10 is 10 units from zero.
Absolute Value of a Number

5. Find the absolute value of the following numbers:
|16|
|-9|
|-25|
|11|
|-78|
|15|
|47|
|-12|

6. Mrs. Owens overdrew her checking account by $45.
Mrs. Owens received a call from her bank because she had a checkbook balance of -45 dollars.
What was the amount overdrawn?
|-45| = 45
Mrs. Owens overdrew her checking account by $45.

7. Maria was sick with the flu and her weight change as a result of it is represented by -4 pounds. How much weight did Maria lose?
4 pounds
Jeffrey owes his friend $5. How much is Jeffrey’s debt? $5

8. The elevation of Niagara Falls, which is located between Lake Erie and Lake Ontario, is 326 feet. How far is this above sea level?
326 feet
How far below zero is -16 degrees Celsius?
|-16|=16 -16°C is 16 degrees below zero.
Frank received a monthly statement for his college savings account. It listed a deposit of $100 as It listed a withdrawal of $25 as The statement showed an overall ending balance of $
How much did he take out?
$25
What is the total amount Frank has saved for college?
$75

9. I am thinking of two numbers. Both numbers have the same absolute value. What must be true about the two numbers?
Can the absolute value of a number ever be a negative number? Why or why not?
How can we use absolute value to determine magnitude? For instance, how far below zero is −8 degrees?

10. Jessie and his family drove up to a picnic area on a mountain
Jessie and his family drove up to a picnic area on a mountain. In the morning, they followed a trail that led to the mountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. After lunch, they hiked on a trail that led to the mountain overlook, which was 3,500 feet below the picnic area.
Locate and label the elevation of the mountain summit and mountain overlook on a vertical number line. The picnic area represents zero. Write a rational number to represent each location.
picnic area mountain summit mountain overlook a.
Use absolute value to represent the distance on the number line of each location from the picnic area.
Distance from the picnic area to the mountain summit. Distance from the picnic area to the mountain overlook. b.
What is the distance between the elevations of the summit and overlook? Use absolute value and a number line to explain your answer. c.

11. Comparing and Ordering Absolute Values:
When comparing and ordering absolute values, the numbers are ALWAYS positive and should be compared or ordered based on the positive value.

12. Compare the following:
|14| _____14
|44| _____ |-44|
|-4| _____ -2
5 _____|6|

13. Order the following values from greatest to least:
|-3| |-7| |0| |1|
Order the following from least to greatest:
|-13|

14. Adding and subtracting absolute values:
When adding and subtracting with absolute values, ALWAYS rewrite the problem with the absolute values. Then solve.

15. |10 – 5| 5
2. |–18| – |13|
3. |16| – |–2| 14
4. |–11| + |0| 11
5. |–26| + |–17| 43
6. |–1| + |–1| 2

16. 9. ⎪31⎥ + ⎪–5⎥ 36
10. ⎪–16⎥ – ⎪4⎥ 12
11. ⎪–28⎥ – ⎪–1⎥ 27
12. ⎪11–2⎥ 9
13. ⎪44⎥ + ⎪–34⎥ 78
14. ⎪–101⎥ – ⎪–1⎥
100