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Grouping · exponents · operation precedence

ORDER OF OPERATIONS

An expression can contain several operations at once. The order of operations gives everyone the same interpretation: grouping first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Operation Priority

G
Grouping
Work inside grouping symbols first: ( ) [ ] { }
E
Exponents
Evaluate powers and roots next.
MD
Multiply / Divide
Equal precedence: move left to right.
AS
Add / Subtract
Equal precedence: move left to right.

Equal-Precedence Trap

Multiplication does not automatically come before division, and addition does not automatically come before subtraction. Within each pair, work from left to right.

Same Precedence, Left to Right

10 − 2 + 5
Add First · Wrong
10 − 7 = 3
Left to Right · Correct
8 + 5 = 13
Expression Lab

Operation Deconstructor

Click the next step
Multiply before you Add.
Another Mnemonic: GEMA

Grouping, Exponents, Multiplication/Division, Addition/Subtraction. The paired operations still have equal precedence and are handled left to right.

Implied Multiplication

A number written directly beside a grouping symbol indicates multiplication.
2(3) = 2 × 3 = 6

Reference & Check

Knowledge Check: Order of Operations1 / 3

In the expression "5 + (3² × 2)", which operation must you perform absolutely first?

Connect Forward

Order of operations tells us how to read an expression; properties tell us which rewrites preserve its value.

Next: Properties