The thing is, it shouldn't matter. The / represents division, but division of the 2, not of everything behind the 2. The actual symbol is irrelevant, what matters is what the symbol represents, in this case the division of 2 (or the multiplication of 1/2). And I would say for your equation above: 48 -------------------------- 2(9+3) That should be written as 48/(2(9+3)) It's not a question of whether I like it or not, it's a question of mathematical notation, of which nobody likes, it just is. And I do not see why we shouldn't use machines, after all while the machine itself is obviously not human, it was designed and programmed by humans, to work in accordance to the laws of mathematics, so really there should be no difference between a human calculating sums and a machine calculating sums, in fact one could argue a human calculating sums is actually imitating a machine, not the other way round.
Understood. And I'm of the opinion this discussion shouldn't be happening in either case because with or without *, the multiplication is the same.
The extra set of parenthesis is unnecessary. 1+1=2 or (((((1+1)))))=(((((((((((2)))))))))))) Both are correct. (48)/(2(9+3)) can be written: (48) -------- (2(9+3)) or simply, 48 ------- 2(9+3) & 48/2(9+3)
Apples and oranges. Division is not associative. Changing parenthesis can change the problem so it is not allowed. This was discussed pages ago.
Changing parenthesis could change a problem. Removing extra parenthesis would not. You keep doing it your way, and I will keep doing it my way.
the extra set of parenthesis are necessary and 48 ------- 2(9+3) is not how this problem is written, it is written (literally) 48 divided by 2 multiplied by 12. Read it from left to right like a book, like the rules tell you to instead of making up your own interpretations.
If you didn't have the parentheses the equation would read: 48/29+3 That doesn't work. The parentheses imply a multiplication sign: so it reads 48/2x(9+3) written in a straight line like that, you are to divide/mulitply from left to right. So the answer is 288. I know I'm late to the debate - but that was fun...
The extra set of parentheses is what allows for 48 to be divided by 2(9+3). 48/2(9+3) This equation is 48 divided 2, times (9+3). 48/(2(9+3)) This equation is 48 divided by 2(9+3). There is no your way and my way. There is the correct order of operations and that's all.
48 divided by 2 multiplied by 12 48/2(9+3) Can you write out this equation the same way you just did?
I agree...That was a weird point. I'd only distrust machines/programs when I don't know how to use it and when I don't understand it.
How can you say they are all the same when two of them give you 288 and two give you 2? You have the common misconception that the distributive property takes precedence over all other math operations, which isn't the case. Ex: To get 2 with this 48 ------------ 2(9+3) you would need to notate it in this manner 48/2*(1/(9+3)) = 48/2*(1/12) = 2. Last time I checked 1/12 does not equal 9+3. Hope that helps.
Your way is only good for a piece of paper. Let's pretend the way your doing it is correct. Why can't you say/write out the equation below? 48 ------------ 2(12)
48/(2(9+3)) 48 divided by a denominator of 2 times 12 48/2(9+3) 48 divided by a denominator 2 times 12 The numerator is still 48 in both cases. The denominator is the same in both cases. If the numerator were twelve times forty-eight and the denominator was two then the answer would be 288.
Reminds of this thread where you struggled with another grade school math problem. Just stop already. The rules for parsing an arithmetic expression are straight forward. "48/2(9+3)" is equivalent to "48/2*(9+3)" which is equivalent to "48/2*12". Two operators left -- divide and multiply -- and the well established rule everyone should have learned in elementary school is you evaluate operations of identical precedence left to right.
