Transcript JUDGE JODY

Don’t Break the
Laws of Math!
Learn the
Order of Operations
Why?
Why do we need an order of
operations?
Consider the following problem:
2  3 5
2  3 5
There are two ways to solve this!
2  3 5
5 5
25
2  3 5
2+15
17
The order of operations tells us which
way is correct. We even have a good
way to remember the order of
operations.
(next…)
Judge Judy
• Please
• Excuse
• My dear
• Aunt Sally
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)
Then do these
‘Excuse’ stands for exponents.
Exponents are a shorthand for
repeated multiplication of a
number by itself.
3  3 3  9
2
2  222  8
3
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.
Last but not least!
‘Aunt Sally’ stands for:
Add and subtract
IN ORDER
from left to right.
Let’s try it!
10  2  3  4(5)
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 (that’s what Please means)
• As a multiplication sign (that’s what this is)
How can you tell which way it’s being used? (next…)
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
(6x4)
• Division
( 10 / 2 )
Parentheses as a multiplication symbol
Once we start algebra and use x to mean the unknown
number that we’re trying to find, we can’t 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 4  5
10  2  3  4(5)
S
Identify your
operations and them
perform them in the
correct order.
Multiply first – from
left to right. Then add
and subtract in order.
M
A
M
10  2  3  4(5)
10  6  20
4  20
24
4  2  23
2
A
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.
D
M E
4  2  2  32
4  2  29
4  1 9
4
13
9
15  (3  2)(1  2)
D
Identify your operations
and them perform them
in the correct order.
Parentheses first, then
multiply and divide, in
order, from left to right.
P
M
P
15  (3  2)(1  2)
15  (5) (3)
3(3)
9
The parentheses around the 5 in line 2 are optional.
3 2  2 5
M
Identify your
operations and them
perform them in the
correct order.
Multiply first and
then add.
A
M
3 2  2 5
6  10
16
(6  2)2  4  2
P
Identify your
operations
and them
perform them
in the correct
order.
Parentheses
first, then
exponents,
then multiply
and divide in
order.
E
D
M
( 6  2)  4  2
2
( 4 )  42
16
42
2
2
4
8
Order is important in court . .
and in math!
Please excuse my dear Aunt Sally.