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When a numerical expression involves two or more operations, there is a specific order in which these operations must be performed.
PEMDAS
Parenthesis,
Exponents,(Multiplication/Division)
then
(Add/Subtract)
There is a phrase that helps students remember the order:
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Please
Excuse (My
Dear) (Aunt
Sally).
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The reason (multiplication & division) and (add & subtract) are grouped is when those operations are next to each other you do the math from
left to right. You do not necessarily do addition first if it is written next to subtraction.
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Example: |
8 - 6 + 2
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2 + 2
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Subtraction is first !
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4
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When there are two or more parenthesis, grouping symbols, you perform the inner most
grouping symbol first.
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Example: |
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2 + 3[ 5 + (4 -
1)2]
2 + 3[ 5 + (3)2]
2 + 3[ 5 + 9]
2 + 3[ 14]
2 + 42
44
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A method that has been very successful for
working with order of operations is the PEMDAS table.
Draw a PEMDAS (parenthesis, exponents, multiplication, division, add and subtract) box for every problem.
Check off the operation after it has been performed, or determined not part of the problem.
| P |
E |
M |
D |
A |
S |
| x |
|
|
|
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| P |
E |
M |
D |
A |
S |
| x |
x |
|
|
|
|
| P |
E |
M |
D |
A |
S |
| x |
x |
x |
|
|
|
| P |
E |
M |
D |
A |
S |
| x |
x |
x |
- |
|
|
| P |
E |
M |
D |
A |
S |
| x |
x |
x |
- |
x |
- |
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2 + 6 (3+1)2
2 + 6 (4)2
2 + 6 (16)
2 + 96
98 |
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This method is
very successful, especially when the problems get longer and more
involved! |
Summary of the Basic Steps :
| 1. |
Write the problem. |
| 2. |
Draw a PEMDAS table. |
| 3. |
Simplify any parenthesis first, starting with the inner most group, and check off the "P" box. |
| 4. |
Simplifly any powers ( exponents) and check off the "E" box. |
| 5. |
Perform the multiplication and
division in order from left to right and check off the "M"
& "D" boxes. |
| 6. |
Do the addition and subtraction last. Remember, if the operations are written next to each other work from left to right and check off the last two boxes.
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It is very important to understand that it does make a difference if the order is not performed correctly!!!!
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70 - 2(5+3)
70 - 2(8)
68(8)
544
incorrect  |
70 - 2(5+3)
70 - 2( 8)
70 - 16
54
correct  |
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(subtraction was done before
multiplication) |
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Order of Operations is not an isolated skill.
This skill applies to almost every topic in Math A.
Remember that "Aunt Sally" is used with evaluating formulas, solving equations, evaluating algebraic expressions, simplifying monomials & polynomials, etc..
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