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Chapter 1 · Numbers · page 4 of 68

Order of operations

levelPre-algebra
standard6.EE.A.1
practiceOrder of operations

When an expression has several operations, there is one agreed order so everyone gets the same answer. Grouping symbols first, then exponents, then multiplication and division together from left to right, then addition and subtraction together from left to right.

How to use it

  1. Do what is inside grouping symbols first, innermost first.
  2. Then exponents.
  3. Then × and ÷, left to right. Neither waits for the other.
  4. Then + and −, left to right. Neither waits for the other.

Example

3−4×2=3−8=−53 - 4 \times 2 = 3 - 8 = -5
(3−4)×2=(−1)×2=−2(3 - 4) \times 2 = (-1) \times 2 = -2
5+32×2=5+9×2=235 + 3^2 \times 2 = 5 + 9 \times 2 = 23

Where it goes wrong

  • Reading left to right regardless of operation. 3 − 4 × 2 is not (3 − 4) × 2.
  • Doing all multiplication before all division. They are the same rank; go left to right.
  • Treating 3² as 3 × 2. It is 3 × 3.

Related

ExponentsGrouping symbolsThe sign belongs to the term
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