Why do we need the Order of Operations?
The order of operations is a convention. The beauty of mathematics is that often, there are many ways of getting to one correct answer. However, when there is a series of operations in a problem, the order in which you evaluate those operations will generate unique answers. Thus, without having a convention, a set way of doing things, there would be chaos.
Consider the following problem: 15 - 4 x 3
If we do Multiplication first Subtraction first
15 - 4 x 3 15 - 4 x 3
15 -12 11 x 3
3 33
So, if we didn't have a set way to do the math, we would not be able to have an answer to the math problem.
Consider the following problem: 15 - 4 x 3
If we do Multiplication first Subtraction first
15 - 4 x 3 15 - 4 x 3
15 -12 11 x 3
3 33
So, if we didn't have a set way to do the math, we would not be able to have an answer to the math problem.