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Order of Operations

When we speak about operations mathematically, it means things like add, subtract, multiply, divide, squaring, etc. Remember: If it isn't a number it is probably an operation.


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 will get a wrong answer !

So, long ago people agreed to follow rules when doing calculations, and they are:
Do things in Parentheses First. Example:
yes 6 × (5 + 3)=6 × 8=
48
 
no 6 × (5 + 3)=30 + 3=
33
(wrong)
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
yes 5 × 22=5 × 4=
20
 
no 5 × 22=102=
100
(wrong)
Multiply or Divide before you Add or Subtract. Example:
yes 2 + 5 × 3=2 + 15=
17
 
no 2 + 5 × 3=7 × 3=
21
(wrong)
Otherwise just go left to right. Example:
yes 30 ÷ 5 × 3=6 × 3=
18
 
no 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)

source: mathisfun.com

» WFM Glossary