Order of Operations 11/12

from mathisfun.com:

Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like ...

7 + (6 × 52 + 3)

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?

Warning: Calculate them in the wrong order, and you can get a wrong answer !

So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Parentheses First

 4 × (5 + 3)=4 × 8=

32

  4 × (5 + 3)=20 + 3=

23

(wrong)

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract

 5 × 22=5 × 4=

20

  5 × 22=102=

100

(wrong)

Multiply or Divide before you Add or Subtract

 2 + 5 × 3=2 + 15=

17

  2 + 5 × 3=7 × 3=

21

(wrong)

Otherwise just go left to right

 30 ÷ 5 × 3=6 × 3=

18

  30 ÷ 5 × 3=30 ÷ 15=

2

(wrong)

How Do I Remember It All ... ? PEMDAS !

P

Parentheses first

E

Exponents (ie Powers and Square Roots, etc.)

MD

Multiplication and Division (left-to-right)

AS

Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)