Integers
Intrigued by Integers
Integers are whole numbers both positive ones and negative ones.
eg., 1, 1, 5, 5
Integers involve:
 adding and subtracting integers
 multiplying and dividing integers
 absolute value

properties:
 commutative property
 associative property
 distributive property
Commutative, Associative and Distributive Laws

Commutative Property or Law:
a + b = b + a
ab = ba
The order of operation for two numbers when adding and multiplying is not important to obtaining the correct answer.
 eg., 2 + 4 = 4 + 2 = 6

eg., 2 × 4 = 4 × 2 = 8

The advantage to the commutative property is that you can start with the larger number to make the addition easier.
eg., 4 + 2 = 6.

The order of operation for two numbers when adding and multiplying is not important to obtaining the correct answer.

Associative Property or Law:
(a + b) + c = a + (b + c)
(ab)c = a(bc)
The order of operation for addition and multiplication is not important to obtaining the correct answer.
 eg., 2 + 4 + 8 = (2 + 4) + 8 = 2 + (4 + 8) = (2 + 8) + 4 =14

eg., 2 × 4 × 8 = (2 × 4) × 8 = 2 × (4 × 8) = (2 × 8) × 4 = 64

The advantage to the associative property is that you can group the numbers together to make the addition easier.
 eg., 2 + 8 = 10 + 4 = 14.

The order of operation for addition and multiplication is not important to obtaining the correct answer.

Distributive Property or Law:
a(b + c) = ab + ac = a(b + c)
The order of operation for multiplying a number by an addition group is not important to obtaining the correct answer

eg., 2(4 + 8) = (2 × 4) + (2 × 8) = 2 × (4 + 8) = 2 × 12 = 24

eg., 2(4 + 8) = (2 × 4) + (2 × 8) = 2 × (4 + 8) = 2 × 12 = 24

The advantage to the distributive property is that you can do what's easiest.
 eg., (2 × 4 = 8) + (2 × 8 = 16) = 8 + 16 = 24 or 2 × (4 + 8 = 12) = 2 × 12 = 24

The order of operation for multiplying a number by an addition group is not important to obtaining the correct answer
Order of Operations
An easy way to remember the order of operations regarding mathematical expressions:
Please Excuse My Dear Aunt Sally
Parentheses  Exponents  Multiplication  Division  Addition  Subtraction
Parentheses  Exponents  Multiplication  Division  Addition  Subtraction
The Order:
eg., (8 + 8)  (2 × 2) × 2² + 3
 Do all the operations in parentheses or brackets first.
(16)  (4) × 2² + 3  Do any numbers involving exponents next.
16  4 × 4 + 3  Do multiplication and division operations next.
16  16 + 3  Do addition and subtraction operations last.
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Interested in Integers
Teaching Resources for Math for integer — teaching and practice worksheets.
Integer Worksheets
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