    "Please, Readily Excuse, My Dear Aunt Sally" As hopefully you've already realized, the newest version of the order of operations is state below. THE ORDER OF OPERATIONS (Topmost First) Parentheses or other Marks of Inclusion (Innermost First) Roots or Exponents Multiplication or Division (Leftmost First) Addition or Subtraction (Leftmost First)     Restated it's: Parentheses first, next Roots or Exponents, then Multiply or Divide (left to righ) then Add or Subtract (left to right): Please, Readily Excuse, My Dear Aunt Sally.     Some properties of numbers permit "short cuts" to this order.

"Short Cuts"

Again, the commutative and associative properties of numbers permit flexability. The order of operations must still be maintained, but, while working with one operation, some flexability exists.

•   Multiplication is commutative and associative so you can switch the order or regroup and the result is the same.
 Example #1: Simplify: 2 x 13 x 5 2 x 13 x 5 = 26 x 5= 130 or 2 x 13 x 5 = 2 x 5 x 13= 10 x 13= 130
 Example #2: State the area of a triangle with a base of 9' and a height of 8'. Use the formula: Area equals half the base time the height. (½)(9)(8)       (½)(9)(8)   (4.5)(8)         (½)(72)     36 sq. ft.     36 sq. ft.
•   Addition is commutative and associative so you can switch the order or regroup and the result is the same.
 Example #1: Simplify: 4 + 2 + 8 + 16 4 + 2 + 8 + 16 =   6 + 8 + 16 =   14 + 16 =     30 or 4 + 2 + 8 + 16 = 4 + 16 + 2 + 8 =  20 + 10 =     30
•   Given the use of signed numbers, addition and subtraction really need not be completed left to right.
 Example #1: Simplify: -3 + 7 + 1 - 6 - 3 + 4 -3 + 7 + 1 - 6 - 3 + 4 =   4 + 1 - 6 - 3 + 4 =     5 - 6 - 3 + 4 =       - 1 - 3 + 4 =         - 4 + 4 = 0 or -3 + 7 + 1 - 6 - 3 + 4 = -3 - 6 - 3 + 7 + 1 + 4 =     - 12 + 12 = 0 PREMDAS Questions: Please do the following and record the result. 1. Simplify: 3 - 4 x 5 + 6 ÷ (-3) 2. Simplify:   (-2 + 5)² 3. Simplify:   { 2 + (-4 + 6)·(5 + 3(-2))}(-1) 4. State the result if you: Loose \$10, win \$4, loose \$2 twice, win \$3, win \$3, win \$4, loose \$6. 5. Simplify each then comment on the reason the answers are different. a. -2² b. (-2)² c. 6. Simplify each then comment on the reason the answers are different. a. 4 -5² b. 4(-5)² c. 7. Simplify: 8. 1st: then:              © 2005, Agnes Azzolino www.mathnstuff.com/math/spoken/here/2class/80/c80g.htm