I'd like to delve deeper to clarify this concept. If we're talking PURELY numbers, PURELY mathematics, there IS NO order of operations. The math just *IS*.

For example, 1+2+3 = 6 doesn't happen left to right, right to left, or whatever order at all. 1+2+3 *IS* 6 and it *IS* 12-6 and it *IS* 18/3. All of these terms are just different ways of representing the number 6. They are equivalent, one in the same. Another way to think of it is that ALL the operations are done *at the same time*.

However, human beings aren't instant and we lose track of things all the time. Therefore, we devised the order of operations as an INTERPRETATION of how we observe the math actually works.

But I do want to clarify, this order of operations isn't just an "agreed upon standard" arbitrarily. It's following observed rules. The reason why multiplication comes before addition is because it is already a form of repeated addition.

7 + 3 x 4 is the same as 7+(4+4+4).

If we try it purely left to right, it doesn't make sense.

7+3x4 is not the same as 10x4 because the 3 is *modifying* the 4.

The 3 and the 4 are not separate terms. They are telling us that 4 happens 3 times (or that 3 happens 4 times). The 7 is just another term being added to the evaluation of 3 times 4. So we MUST evaluate 3x4 first.

Here's an illustration:

7 apples + 3 baskets of 4 apples. You don't add 7 apples to 3 baskets. You'd get what, 10 apple/baskets? That doesn't make sense. You add the baskets first (12 apples total), then add the extra 7 apples for a total of 19 apples.