Transcript Order of Operations

Order
of
Operations
Suppose we have the following:
3+48=
What operations are present here:
•Addition and Multiplication
What is your result?
Which answer is correct?
• As you can see we get different results by
performing the operations of multiplication
and division in different orders.
• Both can not be right -so which one is
correct?
35 or 56
Deciding what order...
• It seems we need some rules telling us
which operation we should perform
first.
• Whenever an expression contains more
than one operation . The operations
must be performed in a specific order.
What Order?
• Step 1 - Parentheses
• Perform all operations inside
groupings first. This includes
Parenthesis, Brackets and Braces.
()[]{}
If there are parenthesis inside brackets begin with the innermost
and work outward using steps 2-4.
Order of Operations cont..
• Step 2- Simplify any numerical
expressions containing
exponents.
• Step 3- Do multiplication and division
as they occur from left to right.
• Step 4- Do addition and subtraction
as they occur from left to right.
Please Excuse My Dear Aunt
Sally
Pink Elephants Must
Order Donuts And
Orange Sherbert
Why this order?
Consider the following…
An item is marked 3 for $12.
You want to know how
much you would pay for 2
of these items.
12  3  2 =
Do you divide or multiply first...
Consider the following:
If I give you four blue envelopes containing
$5 each and one red envelope with a $10 bill.
How much money do you have?
If I give you one yellow envelope containing $10
and four green envelopes containing $5 each.
How much money do you have?
Did you come up with the same answer?
How did you come up with your answers?
Why did you multiply first?
Or how about this...
30 + 2(205)(15-3)=
• You purchase a pair of
boots for $30 and two
shirts marked at $20 each
with a tag for $5 off on
each. You also return a
pair of boots originally
marked at $15 but
purchased them with a $3
discount…How much do
you owe?
Now that we know why…Lets try some...
• 12 + (6 + 4)=
• 12 + 10 =
simplify parentheses first
• 12 +10 = 22 perform addition
• 3(5+1)  32 + 8  4 = Perform operations in ( )
• 3(6)  32 + 8  4 =
• 18  9 + 2 =
• 9 + 2 = 11
Simplify exponents
Perform multiplication/division
Add or subtract as they occur
You try it...
30 + 4 ( 7  2)  5
2
30 + 4 ( 5)  5
30 + 4 (25)  5
30 + 100  5
30 + 20
50
2
Think about it..
• Explain the difference between
simplifying
• 6+9  3 & (6+9)  3
• When using the order of operations
under what conditions it it possible
to get more than one correct answer?
Lets try the calculator
• To determine whether or not
your calculator follows the
rules for order of operations
plug in ….
• 3+42
• The result is 11, if your
calculator shows 14 then it
does not follow and you will
have to adjust.
Quick review
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What is the correct order of operations?
Parentheses
Exponents
Multiplication/Division from left to right
Addition or Subtraction from left to right.
Web Pages
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Amby
Aplusmath
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