The ORDER of OPERATIONS


() ^ x   / +
   -
parentheses|  exponents | multiplication & division from left to right |  addition & subtraction from left to right
Please Excuse My Dear Aunt Sally.     (
a small saying to help you keep this all straight)



images copyright Hanna-Barbera

This whole topic began when four people were sitting at  a table trying to figure out the answer to this problem:

3 - 2 x 5 + 6 / 2 = ? 

Well Fred said,"It's obvious the answer is 5.5; you just work it from left to right and anyone will get that answer."

Then Wilma said, " No Fred you're wrong.  It is -1/2 because you must multiply the 2 x 5 first, then work from left to right."

Then Barney said, "No the answer is -5 because you must multiply the 2 times the 5, then add the 6, then divide that answer in half, then subtract that from 3."

Finally Betty said,"I don't know, I think the answer is -10, but I can't explain why."

What do YOU think the answer is?

It turns out that all four people were performing the individual math operations correctly, they were just doing them in different ORDERS.  

To solve this horrible problem of everyone doing the math correctly and everyone getting DIFFERENT ANSWERS, a special ORDER OF OPERATIONS was developed.

The math community agreed upon setting up some operations as MORE IMPORTANT and thus decided that they should always be done first.  Here is what they decided:

1'st PARENTHESES Grouping symbols are always done from the innermost set outward.
2'nd EXPONENTS Remember applying an exponent is different than just multiplying. EX: 2^3 means
2 x 2 x 2 = 8
3'rd MULTIPLY These operations are done in the order they appear from left to right.  They are done together because they have the SAME IMPORTANCE.
DIVIDE
4'th ADD Here again we have two operations of the SAME IMPORTANCE.   These are done in the order that they appear from left to right.
SUBTRACT

  The saying, Please Excuse My Dear Aunt Sally, is often used to help folks remember the proper order.   The first letter of each word here stands for a math operation.

Try these.  Move your mouse over the problem to see if your answer is correct.

3 + 9 x 8 - 6^2 = ?

16 + (4^2 - 2 x 3)^2 - 9 = ?

16 - 8 + 3 - 2  + 4 = ?

24 / 6 x 2 x 2 / 4 = ?

  

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