Math is a language, and order of operations is simply grammar to that language. Some times the order of operations makes logical sense, like performing parentheses and exponents first. But some operations, like adding/subtracting, multiplying/dividing see to be able to work regardless if the order. I mean, we do get an answer every time right? Jist different answers. So, how do we know what the "right" answer is? Well, as I said before, we use order of operations in the same way we use gramercy to dictate specific rules in language to help meaning in written word come across without confusing the intent.

Every mathematical operations. Can be analogies tk a real world scenario. A formula that reads, 2+5x3 can give an answer of 17 or 21 depending on whether the order of operations occurs or not.

The way to see what's happennign is to analyze what the problem is saying. This problem is saying, im adding two apples to 5 bags worth or apple, each holding 3 apples. Or 2 apples to 3 bags of apples, each containing 5 apples. That's the principle of of multiplicity. In this analogy we see the answer is 17 and that it makes sense.

Addition and subtraction are a lower ordered operation because they deal with single dimensional operations. Single number of apples vs. Multiplication. And division which deal with higher dimensional math, grouping or fractions. You can't add two single apples to packs of apples containing multiple apples and magically end up with more than what you actually have.

This break in logic is what is happenni g when you add or subtract before multiplying or dividing.