Pre-Algebra
Expressions and equations
Order of operations
20 practice questions
0 video lessons
Theory + worked examples
Order of Operations
California Pre-Algebra • Standard 6.EE.2c • Expressions & Equations
Order of Operations is a topic in Expressions & Equations in the California Common Core State Standards. It is aligned to Standard 6.EE.2c, which requires students to apply the order of operations to evaluate numerical expressions.
The order of operations (PEMDAS) fixes the sequence for evaluating an expression.
Theory
The order of operations tells you the sequence to simplify an expression:
- Parentheses
- Exponents
- Multiply and Divide, left to right
- Add and Subtract, left to right
Multiply/divide and add/subtract are done left to right, not one before the other.
PEMDAS.
A worked example.
The order:
\[\text{P}\to\text{E}\to\text{MD}\to\text{AS}\]
Left to right within each level.
How to apply the order of operations
- Do everything in parentheses first.
- Evaluate exponents.
- Multiply and divide, left to right.
- Add and subtract, left to right.
Example 1 — Multiply first
Simplify \(2+3\cdot4\).
Solution
Multiply before adding.
| \(2+12\) | \(=\) | \(14\) |
Example 2 — Parentheses
Simplify \((2+3)\cdot4\).
Solution
Parentheses first.
| \(5\cdot4\) | \(=\) | \(20\) |
Example 3 — Exponents
Simplify \(2+3\cdot4^2\).
Solution
Exponent, then multiply, then add.
| \(2+3\cdot16\) | \(=\) | \(2+48=50\) |
Example 4 — Left to right
Simplify \(20\div4\cdot2\).
Solution
Divide and multiply left to right.
| \(5\cdot2\) | \(=\) | \(10\) |
Common pitfalls
Multiply before adding: \(2+3\cdot4=14\), not \(20\).
Multiply/divide are equal rank — go left to right.
Exponents come before multiplication.
Frequently asked questions
What does PEMDAS stand for?
Parentheses, Exponents, Multiply/Divide, Add/Subtract.
Do I multiply or divide first?
Left to right — they are equal rank.
Simplify \(2+3\cdot4\).
\(14\).
What comes first?
Parentheses.
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Equivalent expressions and properties of operations
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