An often misunderstood convention is that of order of operations. You are likely familiar with how it works, but here is why we use it and how it affects calculator usage.
Some facts to be remembered:
Order of operations is used when multiple opreations are combined in a single expression. Since addition and multiplication are both commutative individually, if the expression contains only one of these (remember that subtraction counts as addition and division is multiplication) then order of operations is not needed.
Example: The simplification of 5 + 2 − 3 + 4 is 8, not 0.
The need for order of operations is apparent in the expression 7 + 2 × 4. The issue is whether to first add 7 to 2, then multiply the result by 4 – or to add 7 to the result of 2 times 4. The shortcoming is due to the way we notate the expression. Read aloud, the desired order could be indicated with a pause. Instead of "Seven plus two times four" you would either say, "Seven … plus two times four" or "Seven plus two … times four". The pauses would not be needed if we reworded the expression as "The sum of 7 and the product of 2 and 4" or "The product of 4 and the sum of 7 and 2". Rewriting these without the need for order of operations or grouping symbols is possible by adopting prefix or postfix notation in place of the traditional infix.
This drastic change to the way we write expressions is not feasible. We could require grouping symbols in all expressions containing multiple operations, but it is cleaner to choose a default and only use grouping symbols to override the standard. A major problem occurs since we use written notation that is not available on the calculator. Horizontal fraction bars and similar grouping symbols do not appear in standard calculator entry, so when you see on paper, remember to enter (8+6)/(2−9) on the calculator.