PEMDAS is an acronym for the six mathematical operations of Parentheses, Exponentials, Multiplications and Divisions, Addition and Subtraction. When solving equations these are always treated in this order so as to minimise complication. In Britain, the term BODMAS or BIDMAS is used with ‘Orders’ or ‘Indices’ standing in for Exponentials and the division/ multiplication order reversed purely for sense reasons. The order of operations was settled on in order to prevent miscommunication, but PEMDAS can generate its own confusion; some students sometimes tend to apply the hierarchy as though all the operations in a problem are on the same "level", but often those operations are not "equal". Many times it helps to work problems from the inside out, rather than left-to-right, because often some parts of the problem are "deeper down" than other parts. A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). Thus should parentheses always be dealt with first before tackling any powers of digits, then any multiplications or divisions and then additions and then subtractions. When you have a several operations of the same rank, such as when you have to multiply and divide in the same sum without any given brackets, operate from left to right: For instance, 15 divided by three times four is as it comes (simplifying to five times four) and not 15 divided by 12. Going from left to right, you get to the division first. When a calculator is at hand, the answer is 20; the machine has been programmed with the Order of Operations hierarchy. For a simpler example, if the sum four plus two times three arises, one must multiply two by three then add the four according to PEDMAS.
