The document provides information about integers and order of operations. It defines integers as positive and negative numbers including zero. It explains how to compare integers using less than, greater than, and equal signs. It also defines absolute value as the distance from zero on a number line and provides examples. Rules for multiplying, dividing, adding, and subtracting integers are outlined. Finally, it discusses order of operations and provides examples of solving expressions using PEMDAS.

1. Nicknamed “Signed Numbers”
INTEGERS

2. What are Integers
• Integers are positive and negative numbers
and zero
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

3. Comparing Integers
• Each positive number has an opposite negative
number.
• Positive numbers are larger than negative numbers
• To compare integers, a less than sign (<), a greater than
sign (>) or an equal sign is used.
 Think of an alligator.
• Examples:
 -5 < 2
 9 > -3
 -7 < -5
• You can think about it this way: if you spend $7, you will have less
money left over than if you spent only $5.

4. Absolute Value
• Absolute Value is the distance an integer is
from zero on a number line
 The absolute value is always a positive
• Expressed with bars on both sides of the
number
– Example: |5|=5
– Example: |-7|=7
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

5. Absolute Value
Check my work:
1. |9|=9
2. |-3|= -3
3. |-2|=2
4. |25|= -25
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

6. Why Learn Integers?
 Some word problems require integers.
 At 8:00 a.m. it was 10 degrees below zero. By 3:00
p.m., the temperature had risen 35 degrees. What
was the temperature at 3:00 p.m.?
 -10 + 35 = +25 degrees above zero.
 Most importantly, Algebra requires knowing integers.

7. Integer Rule Handout

9. Multiplying and Dividing have the
same rules
 If SAME signs = Positive Answer
+2 x +3 = +6 + + +
-2 x - 3 = +6 - -
 If Different signs = Negative Answer
+2 x-3 = -6 + - -
- 2 x +3 = -6 - +

10. Multiplying/Dividing - Practice
1) 5 x -2 = -10 DIFFERENT signs
2) 12 4 + 3 or 3 SAME signs
3) 20 10 -2 DIFFERENT signs

11. Multiplying/Dividing
Tabe D. pg. 77

13. Adding Integers
Rule Add/Subtract
Same signs = 1+3= 4
add numbers - 1 +-3 = - 4
Different signs = -3+4= 1
take the difference 3 +- 4 = -1
When adding, always keep sign of the largest
absolute value

14. Adding Integers - Practice
1) 5 + 2- = 3 DIFFERENT signs
Take the difference
2) -12 + - 3 = - 15 SAME signs
Add numbers
3) -7 + 4 = -3 DIFFERENT signs
Take the difference

15. Adding Integers
Tabe D. pg 75

16. Subtracting Integers
Rule Add/Subtract
Change it! -1 - 3 =
subtraction sign - 1 +3 =
to plus sign
Switch it!
sign of 2nd number - 1 + -3 =
Solve it! using adding rules
- 1 +-3 = -4
Another way to say this: Rewrite the subtraction problem as an addition
problem in which you add the opposite of the number being subtracted.

17. Subtracting Integers - Practice

18. Subtracting Integers
Tabe. D. pg 76

19. Assignment -- Integers
IXL.com -- Integers
Get a Smart Score of 100 on all of these!
Level H. I.6 (Adding)
I.8 (Subtracting)
Level J. C.3 (Add/Subtract)
C.7 (Mult/Division)
Level H. X.3 (All Integers)

20. INTEGER JEOPARDY

21. Powers

22. Properties of Powers

23. Opposite Operations
• Addition and Subtraction
• Multiplication and Division
• Exponents and …

24. Square Roots

25. Common Square Roots

26. Order of Operations
Please Excuse My Dear Aunt Sally
1. Parenthesis (4-2)
2. Exponent 4³
[
3.
4.
Multiply
Divide
4(3) or 4x3
4÷2 or 4/2
[
5.
6.
Add
Subtract
4+2
4-2

27. Left to Right
• 3x6÷2
– Multiply First
18 ÷2 =9
– Divide First
3x3=9
• 4 – 5 +6
– Add First
4+1=5
– Subtract First
-1 + 6 = 5

28. (8-3)² =
P
E
[
M
D
[
A
S

29. (6-4)² - 2 =
P
E
[
M
D
[
A
S

30. (6x2)(8÷2)² =
P
E
[
M
D
[
A
S

31. 50 ÷2+1²-3²=
P
E
[
M
D
[
A
S

32. 3 x 4 + 6 ÷ 2 + 5 – 1=
No Parenthesis- No Problem
E
[
M
D
[
A
S

33. PEMDAS – Guided Practice
2
1) (2 + 1) - 7 = 2
2
2) 4 - (6 + 2) = 8
3) (8 x 2) + (7 x 3) = 37
4) 8 x 2 – 10 – 3 = 3
2
5) 24 ÷ 2 + 6 =12

34. IXL.com
• Order of Operations Practice
– Level K. B. 2