Why is it important to follow the order of operations? what are some possiable out comes when the order of operations is ignored?

While simple math problems, such as 1 + 1, can be solved in a single operation, some math problems include several operations.  Each of these problems can be written in a variety of ways.  For instance, 5 + 3(8+4) might be written as 3(4+8) + 5.  The order of operations allows math problems with a variety of operations to be calculated correctly, no matter what order the information is given in.  If the order of operations was ignored, the answer to a math problem would be based solely on whatever method was used to calculate it, such as left to right.  This would mean that two people might arrive at very different answers to the same math problem.

Although I believe the current notations for remembering the order of operations are sufficient, I suppose one could come up with any number of phrases that might prove more memorable to them.  For instance, a dog lover might prefer “Pet Every Mangy Dog And Smile."  The point of such phrases is to help one remember, so whatever is most memorable is best for that person.

I will use the problem mentioned earlier as an example.

5 + 3(8 + 4).
5 + 3(12)  First, I would calculated the portion in parenthesis.
5 + 36   Since no exponents exist within this problem, I would complete the multiplication next.  If the problem had division, it would have been done at this step.
41    Now I do the addition and come up with the final answer. If the problem had subtraction, it would have been done at this step.

Hope this helps.

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb