# Ordering Operations Using PEMDAS!

## What PEMDAS actually is

P- Parentheses

E- Exponents

M- Multiplication

(Multiplication and Division is reversible- whichever comes first!)

D- Division

(Addition and Subtraction is reversible-whichever comes first!)

S- Subtraction

PEMDAS is a short and fun way to understand and easily remember the order of operations.

## Order of Operations

1. Simplify what's inside (expressions) the grouping symbols. Grouping symbols include; parentheses ( ), brackets, [ ], and braces { } (rarely used).

2. Evaluate the powers, that are within the expression. This includes powers that are within grouping symbols.

3. Simplify any multiplication or division expressions from left to right (Inverse operations do not apply to the commutative property!). This too, includes multiplication and division operations within grouping symbols.

4. Simplify any addition and subtraction expressions from left to right (Again, inverse operations do not apply to the commutative property!).

## Example of Using PEMDAS

54-4×(5-2)cubed

54-4×(5-2)cubed=54-4×(3)cubed-----Evaluate inside of grouping symbols. 5-2 equals 3.

------------------ =54-4× 27----Evaluate powers. Evaluate 3 cubed, which is 27

------------------ =54-108------Simplify multiplication or division expressions. 4*27 is 108

------------------- =-54-----Simplify addition or subtraction. 54-108 equals -54

## Example of Step 1- PARTY-GOERS!

(9+5)÷[(6×4)+5]

• 6×4 would be first because it is within a set of parentheses, which is within a set of brackets.
• Why wasn't 9+5 solved first, after all it is within parentheses? 9+5 could not have been solved first because the brackets represent a higher order than the parentheses. The brackets are there because it already wants a complex numerical expression to be solved first.

## Example of Step 2- ELECT!

2(2+ 6 squared) - 5 squared

• 6 squared would be solved first because it is a power.
• Why wouldn't 5 squared be solved first? 5 squared could not be solved first because 6 squared is within a parentheses. Remember, the first step in order of operations, is to simplify what is in grouping symbols.

## Example of Step 3- MAINTAINED DRINKS!

5(5÷6×4)

• 5÷6 would be solved first because within the two inverses division and multiplication, here division is first. Remember, division and multiplication is reversible, solved left to right.

Tip:

(12)(3)+(5-4÷2)

• As you can see, within the first two sets of grouping symbols, expressions are already simplified. Whenever you see two sets of grouping symbols together like that, with nothing in them left to solve, you would multiply them.
• In this case 4÷2 would be solved first because it is division within grouping symbols.

## Example of Step 4- AT SODA-BARS!

3(7-6+5)+5-4

• 7-6 would be solved first, because we need to simplify addition or subtraction expressions.
• Why wouldn't 5-4 be solved first? 5+4 would not be solved first because, 7-6 is within parentheses.

## Need Extensive Help? Maybe Khan can help!

Introduction to Order of Operations

5+6×3+8=11×3+8