When I was at Dupont, I was paid to be very clear about everything. If there was a way to misunderstand something I wrote ... it would be done! So I practiced very hard to be clear.
Math that's written down should be the same way. And if everyone's math were absolutely clear, there would be no need to study this. But it's not always like that ... so over the years we've agreed that certain operations are done in a certain order so that everyone in the world will get the same answer.
So think of this as the way to protect yourself :-) Remember these simple rules and you can't be faulted for the answer you got.
Even if you use the calculator to do the math, you need to remember these rules ....
Let's look at this example: 10 - 3 + 4
If you do the adding first, you get as the next step 10 - 7 which gives you 3. Wrong answer
And remember - it's wrong just because everyone says so ... this is something you just have to remember.
The correct way is to do the operations in order from left to right. 10 - 3 + 4
We do the left-most operation ('-') first, so the next step is 7 + 4 which gives us the answer 11
Got it? When all you have left is adding and subtracting, do them from left to right - just the order you read a book!
Do that, and everyone else who gets a different answer is wrong!
Til next time ....
Note that the only time this matters is when a subtraction operation is present. If all the operations are addition, you can do them in any order (this is what the commutative property tells us!)