Don

1
Dont Break the Laws of Math!

• Learn the
• Order of Operations

2
Why?

• Why do we need an order of operations?
• Consider the following problem

3

• There are two ways to solve this!
• The order of operations tells us which way is
  correct. We even have a good way to remember the
  order of operations.
  (next)

4
Judge Judy

• Please
• Excuse
• My dear
• Aunt Sally

5
Do this first!

• Please stands for parentheses and other
  grouping symbols.
• Parentheses ( )
• Brackets
• Braces
• The fraction bar (groups the problem into a top
  and a bottom)

6
Then do these

• Excuse stands for exponents.
• Exponents are a shorthand for repeated
  multiplication of a number by itself.

7
Next come this pair

• My Dear stands for
• Multiply and divide
• IN ORDER
• from left to right.
• Multiply is not more important do whichever
  comes first as you go from left to right.

8
Last but not least!

• Aunt Sally stands for
• Add and subtract
• IN ORDER
• from left to right.

9
Lets try it!

• Please excuse my dear Aunt Sally
• Since parentheses come first, it seems as if we
  should do something with the 5. But what?
• Trick 1
• Parentheses can be used 2 different ways
• As a grouping symbol (thats what Please means)
• As a multiplication sign (thats what this is)
• How can you tell which way its being used?
  (next)

10
Parentheses as a grouping symbol

• If the parentheses are being used as a grouping
  symbol, there will be some action going on
  inside.
• By action, I mean
• Addition ( 5 4)
• Subtraction ( 7 3)
• Multiplication ( 6 x 4 )
• Division ( 10 / 2 )

11
Parentheses as a multiplication symbol

• Once we start algebra and use x to mean the
  unknown number that were trying to find, we
  cant also use x to mean multiply.
• One way to indicate multiplication is with a
  number followed immediately by parentheses.
• 5 ( ) means 5 times whatever is inside the
  parentheses
• 2 of the most popular alternate multiplication
  signs are
• parentheses 4 ( 5 ) and
• a raised dot

12
S
M
A
M
Identify your operations and them perform them in
the correct order. Multiply first from left to
right. Then add and subtract in order.
13
A
D
M
E
Identify your operations and them perform them in
the correct order. Exponents first, then multiply
and divide, in order, from left to right. Add
last.
14
P
D
M
P
Identify your operations and them perform them in
the correct order. Parentheses first, then
multiply and divide, in order, from left to right.
The parentheses around the 5 in line 2 are
optional.
15
A
M
M
Identify your operations and them perform them in
the correct order. Multiply first and then add.

16
E
P
M
D
Identify your operations and them perform them in
the correct order. Parentheses first, then
exponents, then multiply and divide in order.
17
Order is important in court . . and in math!
Please excuse my dear Aunt Sally.