Nothing places multiplication above division, but 2(9+3) is not the same as 2*(9+3). Alone, the answer is the same, but used in an equation, they are not the same thing.
Individually, the result is 24 either way, but when used in an equation, adding the “*” sign between the 2 and the parenthesis lowers the priority to the equivalent of the division process, which produces a different (and algebraically incorrect) answer.
Nonsense. The multiplication operator is implied in the first, but the math is exactly the same.
Please cite a source saying that an implied multiplication does not follow the rules of operator precedence.
“Nothing places multiplication above division, but 2(9+3) is not the same as 2*(9+3). Alone, the answer is the same, but used in an equation, they are not the same thing.”
They absolutely *are* the same.
By distributing first, you are multiplying before evaluating the operation(s) in the parens. This is incorrect.
In the original problem [ 48/2*(9+3) ] the parens are evaluated first, and leave a mult and div operation, which are evaluated from left to right.
48/2(9+3) =
48/2*12 =
24*12 =
288
2(9+3) IS the same 2*(9+3)... the problem is... you forgot to start from the LEFT.. “48÷2”
make a BIG difference, obviously..
Here’s what bothers me about the answers you guys have given:
It requires that the assumption be made that 48/2 is not the coefficient in front of the parenthetical expression.
Being represented in a left-to-right form, I have assumed a left-to-right parsing schema.
Using x for the value 48 would give x/2(9+3) as the equation.
Perhaps because I have been jaded by my computer science background, I read that as x/2 times the parenthetical sum.
In any event, It’s been a fun debate.