Why is an order of operations required?

Question

Why is an order of operations required?

Answer 1

Because if it weren't things would get very confusing. Everyone doing the problem would get a different answer.

4 + 3 * 2 = could have 2 different answers (10 or 12) (The correct answer being 10) depending on what order you address it in.

Answer 2

We need to agree on an order of operation so that we will all find the same answer when given the same question.

The normal rules are:
if there are levels of brackets, then begin with the most inside brackets.
do exponents first; then multiplications and division, then additions and subtractions.


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Some computer programs will do operations in a different order, so you better know what the order is before trusting the answer. For example, APL will do levels of brackets first, then operators beginning with the right-most:


3 * 4 + 7 / 4 - 3 * (-2 * 4)
3 * 4 + 7 / 4 - 3 * (-8)
3 * 4 + 7 / 4 - (-24)
3 * 4 + 7 / 28
3 * 4 + 0.25
3 * 4.25
12.75

If you do not know the order of operation, you'll use the 'normal' order and get 37.75 instead.

Or, more importantly, you will enter an equation thinking that the program does it a certain way but the program does it according to different rules and you keep getting the wrong answer.

There are also some that will do operators from the right (especially old 'calculator' types).

Better understand what the calculator (or computer program) does before trusting it completely.

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It gets to be more fun in higher math when you hit non-Abelian groups where A*B is not equal to B*A.

Hours of fun...

Answer 3

Because if you write numbers and symbols all over willy-nilly, you get a bunch of different answers. 3(4+7) = 33, right? but if you multiply the 3 and 4 (12) THEN add the 7, you get 19. You need those rules, man.