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Why did you perform the operation between the 2 and the parenthesis before the division? They have the same mathematical precedence, and left-to-right processing says divide first.

The left to right argument is a superficial misapplication of directionality in English to orders of operation in math. The properties of multiplication and division take precedence over mere left to right notation. Beyond this, to clearly demonstrate intent of operations, one uses parentheses. Here is the only circumstance under which 288 obtains: (48÷2)(9+3). It is only the placement of the parentheses that says, "two is the divisor of 48, not a multiplicand of the sum of 9 and 3. In 48÷2(9+3), the use of parentheses makes 2 and the sum of 9 and 3 to be multiplicands and subject to properties between multiplicands. The only correct answer is that which is also consistent with properties of multiplication and division, that is, 2.

Please note that in the symbol ÷, the dot on the top represents the dividend (in this problem the 48) and the dot below, the divisor (in this problem, everything else to the right and before the equality sign). There is commutativity between multiplicands but not between a dividend and a divisor. So 2(9+3) is the same thing as (9+3)2 but 4÷2 is not the same thing as 2÷4.

In this problem as written, 48÷2(9+3), there is one dividend (48) and two multiplicands, 2 and (9+3). The operation between like terms, the multiplicands, is carried out first. Thus, the multiplication between 2 and the sum of 9 and 3. Or, because of the distributive property, 2(9+3) could have been written as (18+6). So the problem as written, 48÷2(9+3), could also be written as 48÷(18+6).

If the problem had contained more than two multiplicands, the answer would be even more obvious. For example, 48÷2(2+2)(5-2)= 48÷2*4*3, the multiplication between all the multiplicands must take place first because of laws of association (a(bc) = (ab)c) and commutation (abc = cba) that exist between multiplicands but not between a dividend and a single divisor. Thus, the 48 will always be divided by the product of 2 and 4 and 3.

If I, as the one writing the problem had meant for the 2 to be the divisor of 48, I would have had to indicate this by the use of parentheses so that 2 would not appear to be a multiplicand of 4 and 3. If I failed to do this, I couldn't maintain that the correct answer is 288 because of a "left to right" approach. "The quotient of 48 divided by 2 then multiplied by 12" is not the same left to right reading as "The quotient of 48 divided by the product of 2 and 4 and 3."

In the instance of this problem, 48÷2(9+3), the operation between the multiplicands must be completed first otherwise commutation around the operand, allowed for in multiplication, would result in two different divisors, 2 or 12, which would result in two different answers, 288 = [(48÷2)(12)] or 8 = [(48÷12)(2)].

Remember this also:

PEMDAS. Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

48÷2(9+3) =

Parentheses: 48÷2(12) =
Powers: 48÷2(12) =
Multiplication: 48÷24 =
Division: 2