1. Integers and Absolute Values

2. Example 1. Study the pattern of the following subtraction sentences.
5 – 1 = 4
5 – 2 = 3
5 – 3 = 2
5 – 4 = 1
5 – 5 = 0
5 – 6 = ?

3. Example 1. Study the pattern of the following subtraction sentences.
5 – 1 = 4
5 – 2 = 3
5 – 3 = 2
5 – 4 = 1
5 – 5 = 0
5 – 6 = -1
This is an example of a negative number. A negative number is less than zero.

4. Integers

5. Numbers to the left of zero
Integers
Numbers to the left of zero
are less than zero.

6. Integers Numbers to the right of zero are more than zero.
Numbers to the left of zero
are less than zero.

7. Integers Numbers to the right of zero are more than zero.
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,… are called negative integers. The number negative 3 is written –3.

8. Integers Numbers to the right of zero are more than zero.
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,… are called negative integers. The number negative 3 is written –3.
The numbers 1, 2, 3, … are called positive integers. The number positive 4 is written +4 or 4.

9. Integers Numbers to the right of zero are more than zero.
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,… are called negative integers. The number negative 3 is written –3.
The numbers 1, 2, 3, … are called positive integers. The number positive 4 is written +4 or 4.
Zero is neither negative nor positive.

10. Example 2a: Name the coordinates of D, E, and B

11. Example 2b: Graph points F, U, and N on a number line if F has coordinate 1, U has coordinate –3, and N has coordinate 4.

12. Absolute Value Absolute Value
In words: The absolute value of a number is the distance the number is from the zero point on the number line.
In symbols: |4| = 4 and |-4| = 4

13. Example 3: Simplify
|9| + |-9|

14. Example 3: Simplify
|9| + |-9|
|9| + |-9| = 9 + 9

15. Example 3: Simplify
|9| + |-9||
|9| + |-9| = 9 + 9
= 18

16. Example 3: Simplify
|9| + |-9||
|9| + |-9| = 9 + 9
= 18
|13| - |-2|

17. Example 3: Simplify |9| + |-9|| |9| + |-9| = 9 + 9 = 18 |13| - |-2|
|13| - |-2| = 13 – 2

18. Example 3: Simplify |9| + |-9|| |9| + |-9| = 9 + 9 = 18 |13| - |-2|
|13| - |-2| = 13 – 2
= 11

19. Example 4: Evaluate the expression |x| - 7 if x = - 13

20. Example 4: Evaluate the expression |x| - 7 if x = - 13

21. Example 4: Evaluate the expression |x| - 7 if x = - 13
= 13 – 7

22. Example 4: Evaluate the expression |x| - 7 if x = - 13
= 13 – 7
= 6

23. Assignment: 18 – 46 even, 47 – 60 all