This document provides information about integers, absolute value, and opposites: - Absolute value refers to the distance of a number from zero on the number line and is always positive. It is represented by vertical bars around a number. - To evaluate expressions with absolute value, simplify values within the bars first before combining terms. - The opposite of an absolute value expression is found by placing a negative sign before the absolute value bars.

1. Integers, Absolute
Value, and
Opposites
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2. Integers & Absolute Value
What is absolute value?
The distance of a number from zero
on a number line.

3. Absolute Value Notation
The notation we use to show absolute value is a pair
of vertical bars like those seen below.
| |

4. Absolute Value
Because absolute value refers to distance on a
number line, it is always a positive number.
I'm positive!
|-3|
Are you
sure?

5. What does absolute value look like?
the absolute
value of 7 | 7 | = 7
the absolute
value of – 7 | – 7 | = 7
Integers & Absolute Value

6. What does absolute value look like?
7 units 7 units
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Integers & Absolute Value

7. Reading an
Absolute Value Expression
To read the expression |-9| you would say,
“the absolute value of negative nine.”
How would you read |14| ?
“the absolute value of fourteen”
`

8. Recap: Absolute Value
• The absolute value of a number is its
distance from zero.
• Distance is always positive!!
• Absolute value is represented by 2
lines surrounding the number.
2=-2 2 = 2-2 and 2 are
both a distance
of 2 units from
zero!

9. Evaluating Absolute Value
Expressions
When evaluating an expression that contains absolute
value bars, simplify the values within the bars first.
Example #1: |-12| + |-3|
= 12 + 3
= 15
Example #2: |18| - |-5|
= 18 – 5
= 13

10. Absolute Value
Evaluate the expression.
Example 1: | 3 |
Example 2: | - 68 |
Example 3: | 6 | + | - 9 |
Example 4: | - 11 | - | - 8 |
Integers & Absolute Value
3
68
6 + 9 = 15
11 – 8 = 3

11. Absolute Value
Evaluate the expression.
Practice 1: | 16 |
Practice 2: | - 74 |
Practice 3: | 12 | + | - 14 |
Practice 4: | - 23 | - | - 18 |
Practice 5: | - 19 | - | - 15 |
Integers & Absolute Value

12. Absolute Value
Evaluate the expression.
Practice 1: | 16 | = 16
Practice 2: | - 74 | =74
Practice 3: | 12 | + | - 14 | = 12 + 14 = 26
Practice 4: | - 23 | - | - 18 | = 23 – 18 = 5
Practice 5: | - 19 | - | - 15 | = 19 – 15 = 4
Integers & Absolute Value

13. Absolute Value Video
Integers & Absolute Value

14. How can we use absolute value
in everyday life when talking about
elevation, direction and distance?

15. When measuring the distance
between two values, one lying
above zero and one lying below
zero, we simply take the absolute
value of each and then add the
values.

16. Measuring Distance
Jamie walked 8 yards towards her locker,
then realized she left her binder in class.
She walked back to class to get it, and
then she walked 12 yards to her locker.
Write the answer using absolute value
notation.
│+8│+│-8│+│+12│
8 + 8 + 12
She walked 28 yards.

17. Measuring Distance
Amy dove in the pool 6 feet. Then she
came up 4 feet before swimming back
down 5 feet. She swam back up 7 feet.
What is the total distance she swam?
Write the answer using absolute value
notation.
│-6│+│+4│+│-5│+ │+7│
6 + 4 + 5 + 7
She swam 22 feet.

18. The pilot ascended 3000 feet in the air.
After ten minutes, he ascended 7000 more
feet. He then descended 5000 feet in the
air before ascending 6000 feet. What is
the distance the pilot traveled in all? Write
the answer using absolute value notation.
│+3000│+│+7000│+│-5000│+│+6000│
3000 + 7000 + 5000 + 6000
The place traveled 21,000 feet.

19. Jessica loves to ride her scooter through her
neighborhood! On Saturday she rides 50 yards
North to her aunt’s house, and then 30 yards South
to her best friend’s house. She spends the night. On
Sunday she rides 20 yards East to the store, and
then 20 yards west back to her friend’s house. How
many yards did Jessica ride her scooter in all this
past weekend?
│+50│+│-30│+│+20│+ │-20│
50 + 30 + 20 + 20
Jessica rode 120 yards.

20. Woman 2005 2007 Change
from
2005-2007
Kate 93 88
Maddie 77 74
Tess 100 100
Awbree 91 95
The following table shows the weight change
from 2005 to 2007 for four different women.
Which woman had the greatest change in weight from 2005 to 2007?
- 5
-3
0
4
Kate

21. The OPPOSITE of
Absolute Value

22. Absolute Value
• The absolute value of a number is its
distance from zero.
• Distance is always positive!!
• Absolute value is represented by 2
lines surrounding the number.
2=-2 2 = 2
-2 and 2 are
both a distance
of 2 units from
zero!

23. 23
• numbers that are the same
distance from zero
• two exact numbers with different
signs
Opposite Numbers

24. The Opposite of…
• If you see a number written like, -(-5)
that means the opposite of -5 which
would be 5.
• The same is true with an absolute value
sign.
OPPOSITE
• What does –(-56) equal?
• What does -|5| equal?
- -2 = -2
“the opposite of negative 56”
56
“the opposite of the absolute value of 5”
-5

25. Evaluate the expression.
Example 1: -| -3 |
Example 2: (- 68)
Example 3: -| - 9 |
Example 4: -(-12)
Example 5: -| 9 |
Integers & Absolute Value

26. Absolute Value
Evaluate the expression.
Example 1: -| 3 | = -3
Example 2: (- 68) = -68
Example 3: -| - 9 | = -9
Example 4: -(-12) = 12
Example 5: - | 9 | = –9
Integers & Absolute Value

27. Use < , > , or = to compare the two expressions.
Example 1: -| 3 | ___ -| 10 |
Example 2: (- 68) ___ - 68
Example 3: | - 11 | ___ - (-9)
Example 4: - | - 77 | ___ - ( -77)
Comparing Absolute value

28. Use < , > , or = to compare the two expressions.
Example 1: -| 3 | > -| 10 |
Example 2: (- 68) = - 68
Example 3: | - 11 | > = - (-9)
Example 4: - | - 77 | < - ( -77)
Comparing Absolute value