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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.
When evaluating an expression,
proceed in this order:
1. parentheses are done first
2. exponents are done next
3. multiplication and division are done as they are
encountered from left to right.
4. addition and subtraction are done as they are
encountered from left to right. |
The proper application of "order of
operations" is needed when working with
such mathematical topics as evaluating formulas, solving equations, evaluating
algebraic expressions, and simplifying monomials and polynomials.
There is a phrase that may help you to remember this order:
PEMDAS
Parenthesis,
Exponents, (Multiplication/Division),
(Add/Subtract)
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Please
Excuse (My
Dear) (Aunt
Sally).
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The reason (multiplication & division - MD) and (add & subtract - AS) are
"grouped" in sets of parentheses is that when those operations are next to each other you do the math from left to right. You do not
always do multiplication or addition first. It may be the case where
division will be done BEFORE multiplication or subtraction will be done BEFORE
addition.
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Be very careful when listening to Aunt
Sally!!! |
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If you forget to take MD
and AS in order as you come to them from left to right, Aunt
Sally's advice is toast! |
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Example: |
8 - 6 + 2
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2 + 2
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Subtraction is
done first !
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4
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Example: |
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When there are two or more parenthesis, or grouping symbols, perform the inner most
grouping symbol first. |
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2 + 3[ 5 + (4 -
1)2]
2 + 3[ 5 + (3)2]
inner most parentheses
are
done first
2 + 3[ 5 + 9]
then work your way out
2 + 3[ 14]
2 + 42
44
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Example: |
Simplify: 2 + 6 (3+1)2
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It may be helpful
to build a PEMDAS table. Check off the operation after it has been
performed. For operations that are not part of the problem,
place a hyphen.
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| P |
E |
M |
D |
A |
S |
| x |
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| P |
E |
M |
D |
A |
S |
| x |
x |
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| P |
E |
M |
D |
A |
S |
| x |
x |
x |
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| P |
E |
M |
D |
A |
S |
| x |
x |
x |
- |
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| P |
E |
M |
D |
A |
S |
| x |
x |
x |
- |
x |
- |
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Draw a PEMDAS table.
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2 + 6 (3+1)2
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Simplify any parenthesis first, starting with the inner most group, and check off the "P" box.
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2 + 6 (4)2 |
Simplify any powers ( exponents) and check off the "E" box.
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| 2 + 6 (16) |
Perform the multiplication and
division in order from left to right and check off the "M"
& "D" boxes.
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| 2 + 96 |
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. |
| 98 |
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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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