Order of Operations -

1
Order of Operations -

• rules for arithmetic and algebra that describe
  what sequence to follow to evaluate an expression
  involving more than one operation

2
The Rules

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

3
Order of Operations - WHY?
Imagine if two different people wanted to
evaluate the same expression two different ways...
1 does each step left to right
2 uses the order of operations
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.
4
Order of Operations - WHY?

• Can you imagine what it would be like if
  calculations were performed differently by
  various financial institutions?
• What if doctors prescribed different doses of
  medicine using the same formulas but achieving
  different results?

5
Order of Operations Example 1Evaluate without
grouping symbols

• This expression has no parentheses and no
  exponents.
• First solve any multiplication or division parts
  left to right.
• Then solve any addition or subtraction parts left
  to right.

Divide.
Multiply.
The order of operations must be followed each
time you rewrite the expression.
Add.
6
Order of Operations Example 2Expressions with
powers

• Firs,t solve exponents (powers).
• Second, solve multiplication or division parts
  left to right.
• Then, solve any addition or subtraction parts
  left to right.

Exponents (powers)
Multiply.
The order of operations must be followed each
time you rewrite the expression.
Subtract.
7
Order of Operations Example 3Evaluate with
grouping symbols

• 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.
Exponents (powers)
Multiply.
The order of operations must be followed each
time you rewrite the expression.
Divide.
8
Order of Operations Example 4Expressions with
fraction bars
Work above the fraction bar.
Exponents (powers)
Multiply.
48
16
Work below the fraction bar.
Simplify Divide.
Grouping symbols
Add.
9
Order of Operations Example 5Evaluate variable
expressions
Evaluate when x2, y3, and n4
1) Substitute in the values for the variables
Exponents (powers)
Add.
The order of operations must be followed each
time you rewrite the expression.
Subtract.
Exponents (powers)
Continue with the rest
Subtract.
Add.