rabbittss wrote:
eric76 wrote:
rabbittss wrote:
Math was my best subject until we got to the Order of Operations. Like many Grammar Rules, I never have found a teacher willing to explain to me WHY it's done that way, and so I don't see any reason to do it that way.
There has to be an order of operations so that everyone working the problem will, if doing it correctly, get the right answer. If there was no established order of operations we would have chaos.
In addition to that, it seems quite natural for multiplication and division to take precedence over addition and subtraction.
If we write 1+x/y (think of writing it with x over y with a horizontal line between them), the x/y is clearly grouped together. To add 1 to x and then divide by two breaks that clear grouping. Similarly, for 1+xy, the xy feels like a single thing even if it is the product of a multiplication. So we multiply the x by y first and then add 1 to it.
You still didn't really explain WHY it's done that way, you just said "It seems quite natural", and just speaking personally, I disagree. I learned to add and subtract first, so I don't see why they shouldn't also still be first. I mean I'm not blaming you, I've had college proffesors who know differential equations like the back of their hand yet they still can't explain to me WHY certain things are the way they are.
That is why it's done that way.
Also, it mirrors language much closer. If you say "I would like four apples and five oranges", the grocery clerk gives you four apples and he gives you five oranges. He doesn't try to give you (four apples + five) oranges. He gives you (four apples) + (five oranges). Similarly four 'x' plus five 'y' means four of 'x' and five of 'y', not (4 of 'x' plus 5) of y. That would be silly and very confusing.
Actually, if addition was first, then 4x+5y would be 4*(x+5)*y. If we spoke like that in language, than four apples and five oranges would be four (apples + 5) oranges which makes no more sense than just doing the operations strictly left to right.
If we did it one way in language and another way in math, then that would really confuse people.