See that is the problem. The second equation [48÷2*(9+3)] is exactly the same as the original equation. Why else would you multiply 2 by (9+3) if that multiplication symbol isn't in the equation? The multiplication symbol is implied, and division and multiplication have the same rank in the PEMDAS system, so therefore you start from the left and go right and do exacty what is there. 48 divided by 2 multiplied by the quantity 9 add to 3.
Equals 288.
What questions have I been missing? I'll do my best to answer them.
From wiki:
"The standard order of operations, or precedence, is expressed here:
terms inside brackets
exponents and roots
multiplication and division
addition and subtraction "
http://en.wikipedia.org/wiki/Order_of_operations
Multiplication and division have the same rank; therefore you do them in order.