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Order of Operations

Order of Operations. PEMDAS. Operations. "Operations"  means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like . Warning: Calculate them in the wrong order, and you will get a wrong answer !.

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Order of Operations

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  1. Order of Operations PEMDAS

  2. Operations "Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ... Warning: Calculate them in the wrong order, and you will get a wrong answer ! 7 + (6 × 52 + 3) ... what part should you calculate first?  Start at the left and go to the right? Or go from right to left?

  3. Order of Operations Do things in Parentheses First. Example:  6 × (5 + 3)=6 × 8=48 6 × (5 + 3)=30 + 3=33 (wrong)

  4. Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:  5 × 22=5 × 4=20 5 × 22=102=100 (wrong)

  5. Multiply or Divide before you Add or Subtract. Example:  2 + 5 × 3=2 + 15=17 2 + 5 × 3=7 × 3=21 (wrong)

  6. Otherwise just go left to right. Example: 30 ÷ 5 × 3=6 × 3=18 30 ÷ 5 × 3=30 ÷ 15=2 (wrong)

  7. How Do I Remember It All ... ? PEMDAS !

  8. Divide and Multiply rank equally (and go left to right). Add and Subtract rank equally (and go left to right)

  9. After you have done "P" and "E", just go from left to right doing any "M" or "D" as you find them. Then go from left to right doing any "A" or "S" as you find them.

  10. Examples

  11. Example: How do you work out 3 + 6 × 2 ? Multiplication before Addition: First 6 × 2 = 12, then 3 + 12 = 15

  12. Example: How do you work out (3 + 6) × 2 ? Parentheses first: First(3 + 6) = 9, then 9 × 2 = 18

  13. Example: How do you work out 12 / 6 × 3 / 2 ? Multiplication and Division rank equally, so just go left to right: First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3

  14. Oh, yes, and what about 7 + (6 × 52 + 3) ?

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