1. Order of Operations Giant Elephants May Attack
When a numerical or algebraic expression contains
more than one operation symbol, the order of
operations tells which operation to perform first.
Order of Operations
Perform operations inside grouping
symbols.
First:
Giant
Elephants
May
Attack
Second:
Evaluate powers.
Third:
Perform multiplication and division
from left to right.
Perform addition and subtraction from
left to right.
Fourth:

2. Giant Elephants May Attack Grouping symbols Exponents Multiply/ Divide
Grouping symbols include parentheses ( ), brackets [ ], braces { }, fraction bar /, absolute value | |, and square root . If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.
Grouping symbols
Exponents
Multiply/ Divide
left to right
Addition/subtraction
Giant
Elephants
May
Attack

3. Example 1: Translating from Algebra to Words
Simplify each expression.
There are no grouping
symbols or exponents.
A. 15 – 2 · 3 + 1
= 15 – 2 · 3 + 1
= 15 – 6 + 1
Multiply.
= = 10
Subtract and add from left to right.
B. 12 – ÷ 2
= 12 – ÷ 2
There are no grouping symbols.
= 12 – ÷ 2
Evaluate powers. The exponent applies only to the 3.
= 12 – 9 + 5
Divide.
Subtract and add from left to
right.
= = 8

4. Check It Out! Example 3
Simplify the expression.
–20 ÷ [–2(4 + 1)]
There are two sets of grouping
symbols.
= –20 ÷ [–2(4 + 1)]
Perform the operations in the
innermost set.
= –20 ÷ [–2(5)]
Perform the operation inside
the brackets.
= –20 ÷ –10
= 2
Divide.

5. Example 4: Simplifying Expressions with Other Grouping Symbols
The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing.
𝟐 −𝟒 +𝟐𝟐 𝟒 𝟐 −𝟗
= (𝟐 −𝟒 +𝟐𝟐) ( 𝟒 𝟐 −𝟗)
Multiply to simplify the numerator.
= −𝟖+𝟐𝟐 𝟒 𝟐 −𝟗
Evaluate the power in the denominator.
= −𝟖+𝟐𝟐 𝟏𝟔−𝟗
Add to simplify the numerator. Subtract to simplify the denominator.
= 𝟏𝟒 𝟕
= 2
Divide.

6. Example 5: Simplifying Expressions with Other Grouping Symbols
The absolute-value symbols act as grouping symbols.
3| ÷ 2|
= 3| ÷ 2|
Evaluate the power within the
absolute-value symbols.
= 3| ÷ 2|
Divide within the absolute-value symbols.
= 3|16 + 4|
= 3|20|
Add within the absolute-symbols.
= 3 · 20
Write the absolute value of 20.
= 60
Multiply.

7. Check It Out! Example 6
Simplify.
|4 – 7|2 ÷ –3
The absolute-value symbols act as grouping symbols.
= |4 – 7|2 ÷ –3
= |–3|2 ÷ –3
Subtract within the absolute-value symbols.
= 32 ÷ –3
Write the absolute value of –3.
= 9 ÷ –3
Square 3.
= –3
Divide.

8. Check It Out! Example 7
Simplify.
The radical symbol acts as a grouping symbol.
Subtract inside the radical.
= 3 · 7
Take the square root of 49.
= 21
Multiply.