Let's have a look...
You have learned how to write and simplify numbers written in exponential notation, such as \( 7^{3} \). This notation has several uses throughout mathematics, and it often appears in mathematical expressions. For example:
\( 9 + 6 \cdot 3^{2} \div 3 \)
The expression \( 9 + 6 \cdot 3^{2} \div 3 \) has four operations to consider: addition, multiplication, an exponent, and division. Which operation should you perform first?
When facing an expression that has more than one operation, you should use the order of operations to determine which operation to start with. The order of operations is a collection of rules that formalizes the order in which you perform the arithmetic operations on numbers. It is shown below.
- Parentheses
- Exponents
- Multiplication and Division from left to right, in the order they appear.
- Addition and Subtraction from left to right, in the order they appear.
Many people use the mnemonic phrase PEMDAS to help them remember the order of operations. Each letter of PEMDAS stands for the first letter of an operation.
The PEMDAS graphic is defined by the following labels:
- P = Parentheses
- E= Exponents
- MD = Multiplication and Division
- AS = Addition and Subtraction]
For Example
Simplify \( 9 + 6 \cdot 3^{2} \div 3 \).
To simplify this expression, follow the order of operations.
Parentheses |
This expression does not contain parentheses, so you can skip this step. |
Exponents This expression contains the exponential notation \( 3^{2} \). |
Simplify \( 3^{2} \), and keep everything else the same. \( 9 + 6 \cdot \require{color}\colorbox{yellow}{$ 3^{2} $} \div 3 \) \( 9 + 6 \cdot \require{color}\colorbox{yellow}{$ 9 $} \div 3 \) |
Multiplication and Division from left to right. Multiplication and division operations are performed from left to right, in the order they appear. |
This expression has multiplication followed by division. \( 9 + \require{color}\colorbox{yellow}{$ 6 \cdot 9 $} \div 3 \) \( 9 + \require{color}\colorbox{yellow}{$ 54 $} \require{color}\colorbox{lime}{$ \div 3 $} \) \( 9 + \require{color}\colorbox{lime}{$ 18 $} \) |
Addition and Subtraction from left to right. Similar to multiplication and division, you perform addition and subtraction operations as they appear from left to right. |
This expression contains only addition. \( \require{color}\colorbox{yellow}{$ 9 + 18 $} \) \( \require{color}\colorbox{yellow}{$ 27 $} \) |
The final simplification of \( 9 + 6 \cdot 3^{2} \div 3 \) is 27. |
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Give it a shot!
How well can you determine which operation to perform first? Use the activity below to practice. Read each expression and determine which operation you should perform first. Then click the expression to check your answer.
