1. Order Of Operations

2. 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.

3. 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.

4. Example 1: evaluate without grouping symbols
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.

5. Example 2: Expressions with powers
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.

6. Example 3: Expressions with grouping symbols
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

7. Example 3: Expressions with fraction bars
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.

8. Example 3: Evaluating Variable Expressions
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 x=2, y=3, and n=4
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:
Subtract
Exponents (powers) 62 = (6)(6) = 36
Subtract
The order of operations must be followed each time you rewrite the expression.
Add