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

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

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

►11stst PARENTHESES or BRACKETSPARENTHESES or BRACKETS Grouping symbols are always done from Grouping symbols are always done from

the innermost set outward.the innermost set outward.

►11stst PARENTHESES or BRACKETSPARENTHESES or BRACKETS Grouping symbols are always done from Grouping symbols are always done from

the innermost set outward.the innermost set outward.

►22ndnd EXPONENTS EXPONENTS Remember applying an exponent is Remember applying an exponent is

different than just multiplying. EX: 2different than just multiplying. EX: 233 means 2 x 2 x 2 = 8means 2 x 2 x 2 = 8

►11stst PARENTHESES or BRACKETSPARENTHESES or BRACKETS Grouping symbols are always done from Grouping symbols are always done from

the innermost set outward.the innermost set outward.

►22ndnd EXPONENTS EXPONENTS Remember applying an exponent is Remember applying an exponent is

different than just multiplying. EX: 2different than just multiplying. EX: 233 means 2 x 2 x 2 = 8means 2 x 2 x 2 = 8

►33rdrd MULTIPLY or DIVIDE MULTIPLY or DIVIDE These operations are done in the order These operations are done in the order

they appear from left to right.  They are they appear from left to right.  They are done together because they have the done together because they have the SAME IMPORTANCE.SAME IMPORTANCE.

► 11stst PARENTHESES or BRACKETSPARENTHESES or BRACKETS Grouping symbols are always done from the Grouping symbols are always done from the

innermost set outward.innermost set outward.

► 22ndnd EXPONENTS EXPONENTS Remember applying an exponent is different Remember applying an exponent is different

than just multiplying. EX: 2than just multiplying. EX: 233 means 2 x 2 x 2 = 8 means 2 x 2 x 2 = 8

► 33rdrd MULTIPLY or DIVIDE MULTIPLY or DIVIDE These operations are done in the order they These operations are done in the order they

appear from left to right.  They are done together appear from left to right.  They are done together because they have the SAME IMPORTANCE.because they have the SAME IMPORTANCE.

► 44thth ADD or SUBTRACT ADD or SUBTRACT Here again we have two operations of the SAME Here again we have two operations of the SAME

IMPORTANCE.   These are done in the order that IMPORTANCE.   These are done in the order that they appear from left to right.they appear from left to right.

► 11stst PARENTHESES or BRACKETSPARENTHESES or BRACKETS Grouping symbols are always done from the Grouping symbols are always done from the

innermost set outward.innermost set outward.

► 22ndnd EXPONENTS EXPONENTS Remember applying an exponent is different Remember applying an exponent is different

than just multiplying. EX: 2than just multiplying. EX: 233 means 2 x 2 x 2 = 8 means 2 x 2 x 2 = 8

► 33rdrd MULTIPLY or DIVIDE MULTIPLY or DIVIDE These operations are done in the order they These operations are done in the order they

appear from left to right.  They are done together appear from left to right.  They are done together because they have the SAME IMPORTANCE.because they have the SAME IMPORTANCE.

► 44thth ADD or SUBTRACT ADD or SUBTRACT Here again we have two operations of the SAME Here again we have two operations of the SAME

IMPORTANCE.   These are done in the order that IMPORTANCE.   These are done in the order that they appear from left to right.they appear from left to right.

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

Try these on your own.Try these on your own.

►3 + 9 x 8 - 63 + 9 x 8 - 622 = ? = ?►16 + (416 + (422 - 2 x 3) - 2 x 3)22- 9 = ?- 9 = ?►16 - 8 + 3 - 2  + 4 = ?16 - 8 + 3 - 2  + 4 = ?►24 / 6 x 2 x 2 / 4 = ?24 / 6 x 2 x 2 / 4 = ?