### Order of Operations – PEMDAS

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“Operations” means 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?

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

Order of Operations

Do things in Parentheses First.

Example: Then Exponents (Powers, Roots)

Example: Then Multiply or Divide which comes first.

Example 1: Example 2: How Do I Remember It All … ? PEMDAS !

 P Parentheses first E Exponents (ie Powers and Square Roots, etc.) MD Multiplication and Division (which comes first) AS Addition and Subtraction (which comes first) You can remember by saying “Please Excuse My Dear Aunt Sally”.

Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract),

It all means the same thing! It doesn’t really matter how you remember it, just so long as you get it right.

Example: How do you work out 3 + 6 × 2 ?

First 6 × 2 = 12, then 3 + 12 = 15

Example: How do you work out (3 + 6) × 2 ?

Parentheses first:

First (3 + 6) = 9, then 9 × 2 = 18

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and Division rank equally, so just go left to right:

First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3

Oh, yes, and what about 7 + (6 × 52 + 3) ?

 7 + (6 × 52 + 3) Start inside Parentheses, and then use Exponents First 7 + (6 × 25 + 3) Then Multiply 7 + (150 + 3) Then Add 7 + 153 Parentheses completed, last operation is an Add 160 DONE !

### Commutative, Associative and Distributive Laws

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Commutative Laws

The “Commutative Laws” say you can swap numbers over and still get the same answer …