Yes, I understand that at the end of the day they both equal 24. That's not what I'm arguing. My understanding of how those two parts thrown into the full equation changes how it works is what I'm arguing. I'm not saying I'm right or wrong, just explaining my side, which I'm sure has already been said hundreds of times in this thread. My overall argument is that the 2 is weighted towards the parenthesis and included in the equation, which is how I'd come into the thinking about the equation, and I understand it may be totally wrong, but that's how I've always gone into equations, although I can't say I've ever come across this specific type of scenario. Whenever I've had to "show my work" in school (years ago), I've always solved anything surrounding the parenthesis first, even the 2 in this scenario.
But again, the parenthesis is gone once you have solved what is inside of it. 4÷2*2 is exactly the same as 4÷2(2) (the solution is 4) because the parenthesis goes poof once only a single number is left.
The 'x' sign (aka "*") plays an important part in the formula. And that's where the discrepancy relies (interpretation of the counting sequence with brackets). You have not entered the "exact" formula as proposed by the OP into your engines, the original formula does not have the "x" or "*" sign in it. Like I said in my earlier post, with the "x" or "*" operator, the answer would be no doubt 288.
I see what you're saying but how about a problem like 49-3+(2+1)? What would you answer be? The 3 is in relation to the parenthesis in the same way the 2 is in 48÷2(9+3) except one is addition and the other is multiplication. 48÷2(9+3) is the same 48÷2*(9+3). Both multiplication and addition have distributive powers so I don't think their are exceptions between the 2.
Can we all just agree that the original formula is poorly illustrated? To play the devil's advocate, let's say: We all know that 2(x+y) = 2x+2y, so can we illustrate the original formula as 48÷2(9+3) = 48÷(2(9)+2(3)) = 48÷(18+6) = 48÷24 = 2 Can't say I am wrong, right?
Sorry, I don't get your point. The bracket has no effect at all in either of your formula above. The answers will always be 49 and 1. In a formula with operators of + and - only, the bracket effect is negligible.
This makes me a day by reading all this thread, guys, the equation is confused at the first place, 48÷2(9+3), you need to clarify whether it's 48÷2x(9+3) or 48÷2÷(9+3), or 48÷{2x(9+3)}, or 48÷{2÷(9+3)} If, 48÷2x(9+3)=24x12=288 If, 48÷2÷(9+3)=24÷12=2 If, 48÷{2x(9+3)}=48÷24=2 If, 48÷{2÷(9+3)}=48÷1/12=549.8281..
It's 288. People who are saying it as written as 48 2(9+3) are wrong. The way it is written it is 48 * (9+3) 2 It is a poorly written equation, however.
this makes sense if there were X's and Y's but there are not, the distributive properties of a number are different (less strict?) than a variable.
You are wrong, because once again, you are looking at the right half of the calculation before you address the left half, but there is no reason to do so, you have to go left to right.
You are wrong, because 48÷2(x+y) does not equal 48÷(2x+2y) it equals 24(x+y) or 24x+24y. The distributive property is simply a multiplication. Multiplication does not take precedence over division, so the division would take place first (since it is in front of the multiplication), and the result would be distributed through the parentheses. That is kind of the whole point of the thread. We can agree that the equation was not written in the best way though, and the proper use of parens would have made it clearer.
when you are integrating equations daily (in calculus), you tend to look at parenthesis and what is going on with that first. The algebra people love to bask in order of operations stuff. it has a grammar nazi feel to all this, "anyone who thinks its 2 needs to gtfo."
The technically "correct" answer is 288, BUT: It is far more intuitive to allow, say, 2(2) to denote (2*2) instead of merely 2*2. This agrees better with algebraic notation, as we would prefer to have 2(a)/2(a) = 2a/2a = 1 instead of 2(a)/2(a) = 2*a/2*a = a^2, or even functional notation, since if 2(x) is identified with the function f mapping x to 2x, we still have 2(x)/2(x) = 1 = f/f as required. Hardly the only poor notational convention in mathematics, although it does stand a pretty good chance of being the first!
