Understanding Order of Operations
Order of operations is like following a recipe! Just like you need to follow steps in order when baking cookies, we need to follow special rules when solving math problems with more than one operation.
The Special Rules
When we see a problem like 5 + 3 × 2, we need to know which operation to do first!
Remember the Order of Operations Rules
If parentheses are nested, solve from inside out.
Expressions with Parentheses: Parentheses First
Parentheses show that these operations need to be done first. If there are nested parentheses, solve from inside out: first the inner \(( \ )\), then the outer ones. After parentheses, continue with the regular order: \(\times\) and \(\div\) before \(+\) and \(-\), all from left to right.
Same numbers — different answers:
Without parentheses:
\(5 + 3 \times 2\)
Multiplication first: \(3 \times 2 = 6\)
Then addition: \(5 + 6 = 11\)
Answer: \(11\)
With parentheses:
\((5 + 3) \times 2\)
Parentheses first: \(5 + 3 = 8\)
Then multiplication: \(8 \times 2 = 16\)
Answer: \(16\)