Order of Operations

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Order of Operations
March 13/14 2006

• Pi Day
• Spirals
• Log Sheets
• E 63, E 65

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Order of Operations
Music You buy a used guitar for 50. You then
pay 10 for each of 5 guitar lessons. The total
cost can be found by evaluating the expression 50
10 ? 5. Is the total cost 100 or 300?
So that everyone gets the same result when
evaluating an expression, a set of rules called
the order of operations is always followed.
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P
Parenthesis
E
Exponents
M
Multiplication OR Division Left to right
D
A
Addition OR Subtraction Left to right
S
(Please Excuse My Dear Aunt Sally)
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Following Order of Operations
To find the guitar costs as described, evaluate
50 10 ? 5.
50 10 ? 5
50 10 ? 5
First multiply 10 and 5.
50
100
Then add 50 and 50.
ANSWER
The total cost is 100.
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Left-to-Right Rule When an expression has a
string of additions and subtractions or a string
of multiplications and divisions, you need to
perform the operations in order from left to
right.
Using the Left-to-Right Rule
12 7 3 6
12 7 3 6
5
Subtract 7 from 12.
5 3 6
Add 5 and 3.
8
2
Subtract 6 from 8.
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Left-to-Right Rule When an expression has a
string of additions and subtractions or a string
of multiplications and divisions, you need to
perform the operations in order from left to
right.
Using the Left-to-Right Rule
12 7 3 6
12 7 3 6
5
Subtract 7 from 12.
5 3 6
8
Add 5 and 3.
2
Subtract 6 from 8.
54 9 3
54 9 3
6
Divide 54 by 9.
2
Divide 6 by 3.
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Grouping Symbols Grouping symbols indicate
operations that should be performed first. The
most common grouping symbols are parentheses ( )
and brackets . A fraction bar is also a
grouping symbol.
Using Grouping Symbols
20
Add 13 and 7. Multiply 2 and 5.
10
Divide 20 by 10.
2
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Grouping Symbols Grouping symbols indicate
operations that should be performed first. The
most common grouping symbols are parentheses ( )
and brackets . A fraction bar is also a
grouping symbol.
Using Grouping Symbols
20
Add 13 and 7. Multiply 2 and 5.
10
Divide 20 by 10.
2
(4 1) 2 3
Add inside parentheses.
(4 1) 2 3
5 2
5 2 3
25
Evaluate the power.
75
Multiply 25 and 3.
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Lets try
Parentheses first inner-most
Exponents next
Multiplication next
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Subtraction next (its on the left)
Addition (its in the parenthesis)
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Examples
-7 27 20
-4 6 -3 -24 -3 -27
1 5(-3) 1 -15 -14
1 3 4 1 - 12 -11
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Evaluating a Variable Expression
Evaluate x 3y 3 when x 25 and y 2.
SOLUTION
x 3 y 3
(2 3)
x 3y 3
25
Substitute 25 for x and 2 for y.
25 3(2 3)
(8)
Evaluate the power.
25 3(8)
24
1
Multiply 8 and 3. Then subtract 24 from 25.
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Assignment

• In Class game
• Assignment A Stifling Situation