How to Use the Order of Operations (PEMDAS)

Problem

4 + 3 \times 2^2 - 6 \div 3

Answer

14

The order of operations removes doubt from an expression like this one. Work through the list in order: parentheses, exponents, multiplication and division, then addition and subtraction.

Step-by-step solution

Apply the exponent first.
$2^2 = 4$
Why: Exponents come before multiplication and division.
Replace the exponent, then multiply and divide from left to right.
$4 + 3 \times 4 - 6 \div 3 = 4 + 12 - 2$
Why: Multiplication and division rank the same, so work from left to right.
Add and subtract from left to right.
$4 + 12 - 2 = 16 - 2$
Why: Addition and subtraction rank the same, so work from left to right.
Write the final answer.
$16 - 2 = 14$
Why: The expression has one value when you follow the order of operations.

Common mistakes

Multiplying before the exponent: 3 x 2 = 6. Exponents come first.
Adding 4 + 3 before multiplying. Multiplication comes before addition.
Working right to left. Multiplication and division go left to right.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$5 + 2 \times 3$

Show answer

$11$
$3^2 + 4$

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$13$
$10 - 6 \div 2$

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$7$
$2 + 3 \times (8 - 5)$

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$11$
$(6 + 4) \div 2 + 1$

Show answer

$6$