Ray Olsen KO Knudson MS Las Vegas, Nv.

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Order Of Operations
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Order Of Operations
Rules for arithmetic and algebra expressions that
describe what sequence to follow to evaluate an
expression involving more than one operation.

• Step 1 First perform operations that are within
  grouping symbols such as parenthesis (), brackets
  , and braces , and as indicated by fraction
  bars.Parenthesis within parenthesis are called
  nested parenthesis (( )).
• Step 2 Evaluate Powers (exponents) or roots.
• Step 3 Perform multiplication or division
  operations in order by reading the problem from
  left to right.
• Step 4 Perform addition or subtraction
  operations in order by reading the problem from
  left to right.

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Order Of Operations
Method 2
Method 1
Performing operations using order of operations
Performing operations left to right only
Can you imagine what it would be like if
calculations were performed differently by
various financial institutions or what if doctors
prescribed different doses of medicine using the
same formulas and achieving different results?
The rules for order of operations exist so that
everyone can perform the same consistent
operations and achieve the same results. Method
2 is the correct method.
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Order of operations
Example 1 evaluate without grouping symbols
Follow the left to right rule First solve any
multiplication or division parts left to right.
Then solve any addition or subtraction parts left
to right.
Divide
A good habit to develop while learning order of
operations is to underline the parts of the
expression that you want to solve first. Then
rewrite the expression in order from left to
right and solve the underlined part(s).
Multiply
Add
The order of operations must be followed each
time you rewrite the expression.
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Order of Operations
Example 2 Expressions with powers
Follow the left to right rule First solve
exponent/(powers). Second solve multiplication or
division parts left to right. Then solve any
addition or subtraction parts left to right.
Exponents (powers)
A good habit to develop while learning order of
operations is to underline the parts of the
expression that you want to solve first. Then
rewrite the expression in order from left to
right and solve the underlined part(s).
Multiply
Subtract
The order of operations must be followed each
time you rewrite the expression.
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Order of Operations
Example 3 Expressions with grouping symbols
Follow the left to right rule First solve parts
inside grouping symbols according to the order of
operations. Solve any exponent/(Powers). Then
solve multiplication or division parts left to
right. Then solve any addition or subtraction
parts left to right.
Grouping symbols
Subtract
A good habit to develop while learning order of
operations is to underline the parts of the
expression that you want to solve first. Then
rewrite the expression in order from left to
right and solve the underlined part(s).
Exponents (powers)
Multiply
The order of operations must be followed each
time you rewrite the expression.
Divide
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A good habit to develop while learning order of
operations is to underline the parts of the
expression that you want to solve first. Then
rewrite the expression in order from left to
right and solve the underlined part(s).
Order of Operations
Example 3 Expressions with fraction bars
Exponents (powers)
Work above the fraction bar
Multiply
Work below the fraction bar
Grouping symbols
Subtract
Follow the left to right rule Follow the order
of operations by working to solve the problem
above the fraction bar. Then follow the order of
operations by working to solve the problem below
the fraction bar. Finally, recall that fractions
are also division problems simplify the
fraction.
Add
Simplify Divide
The order of operations must be followed each
time you rewrite the expression.
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A good habit to develop while learning order of
operations is to underline the parts of the
expression that you want to solve first. Then
rewrite the expression in order from left to
right and solve the underlined part(s).
Order of Operations
Example 3 Evaluating Variable Expressions
Evaluate when x2, y3, and n4
Substitute in the values for the variables
Grouping symbols
Exponents (powers) 33 (3)(3)(3) 27
Follow the left to right rule First solve parts
inside grouping symbols according to the order of
operations. Solve any exponent/(Powers). Then
solve multiplication or division parts left to
right. Then solve any addition or subtraction
parts left to right.
Add 2 27
Subtract 29 - 5
Exponents (powers) 62 (6)(6) 36
Subtract 24 - 16
The order of operations must be followed each
time you rewrite the expression.
Add