images copyright HannaBarbera
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 = ?
