48÷2(9+3) = ??

mtn wrote:

92CelicaHalfTrac wrote:

mtn wrote: <<Math major 288. As it has been mentioned above, multiplication and division are the same thing and are interchangeable. You do them in the order that they appear. 48÷2(9+3) =48÷2(12) =(48÷2)(12) <------- Whichever one comes first, remember. =(24)(12) =288 Now, for a little more fun: What is 9 3 + 48 2 ÷ *?

=(48÷2)(12) Why can you do that instead of =48÷(2(12))? Am i wrong in saying that the way the original equation was written you could interpret it as the following? 48 -------- = X 2(9+3) Solve for X. Or... look at it as "2" was factored out of (9+3)?

It is simply a poorly written equation, but you have to do order of operations. Remember (as has been mentioned above) that multiplication and division happen in the order they appear in the problem. So if you do 48÷(2(12)), you are not doing them in the order they appear.

So basically, you are saying that parantheses are = to "x" in every possible way?

Not being argumentative, just trying to understand, since this is backwards from all the math i was taught up through 2nd and 3rd year of college. I was always taught that order of operations said you had to resolve the parantheses before anything else, and that in this case 2(12) was not resolved yet.

I have already had this argument on two other forums, so I'll leave somebody else's answer here that I agree with:

Make all of the digits variables with the equation equal to X. Simplify the equation, and solve for the answer. You get 288 every time. If you don't like the way an equation is stated, change it!

HiTempguy wrote: I have already had this argument on two other forums, so I'll leave somebody else's answer here that I agree with: Make all of the digits variables with the equation equal to X. Simplify the equation, and solve for the answer. You get 288 every time. If you don't like the way an equation is stated, change it!

48 / 2(9 + 3) = ?

48 / x(9 + 3) = 2
48/12x = 2
48 = 24x
x = 2 check

48 / 2(x + 3) = 2
48 / (2x + 6) = 2
4x + 12 = 48
4x = 36
x = 9 check

48 / 2(9+x) = 2
48 = 36 + 4x
12 = 4x
x = 3 check

why the hell is this still going on hahaha all these numbers and equations

no matter what, answer is always Miata

92CelicaHalfTrac wrote: So basically, you are saying that parantheses are = to "x" in every possible way? Not being argumentative, just trying to understand, since this is backwards from all the math i was taught up through 2nd and 3rd year of college. I was always taught that order of operations said you had to resolve the parantheses before anything else, and that in this case 2(12) was not resolved yet.

Yes, that is what I am saying. You do what is INSIDE the parentheses first; once that is done it is just another number.

The 2(12) is just 2*12.

for the 7th time ^ yes correct lol

92CelicaHalfTrac wrote: So basically, you are saying that parantheses are = to "x" in every possible way? Not being argumentative, just trying to understand, since this is backwards from all the math i was taught up through 2nd and 3rd year of college. I was always taught that order of operations said you had to resolve the parantheses before anything else, and that in this case 2(12) was not resolved yet.

Again, I'm not a math guy, so no big deal to me if I'm wrong. I don't see where there ever is a 2 (12)

If you do the order of operations, after you do the 9+3 you have to do 48/2 next. So when you get to that point, the 2 is already accounted for.

lol ^

ok, now i'm just laughing

The only thing I'm confused about is where the confusion is.

92CelicaHalfTrac wrote: Saw this on another forum, then was amazed at the near 50/50 split on the answers.

1. Parentheses trump.

[edit] Stupid automated list routine changes my 2 to a 1.

I don't know if someone else has made this argument yet, but the equation in question is 100% completely, unarguably, identical to writing "48 ÷ 2x = ?, where x=9+3." If you performed a substitution for x back into that equation you would be left with the one in the thread title, so that is how it should be treated. The answer is 2.

The brackets always act as an operator on the number they're "attached" to and that operation is performed right after the evaluation of the contents of the brackets. BEFORE anything else.

If you'd written "48 ÷ 2 × (9+3) = ?", the question would be different because the bracketed part is not acting as an operator on the 2, and therefore isn't part of the denominator as it is written. It's a little ambiguous but that way you'd evaluate it with BEDMAS. But that's not how it's written. The decision to write it with an explicit multiplication sign (×) or not does change the equation.

BEDMAS is not slavishly applicable in all cases, and this is one of them. You run into that situation a lot more in higher math (university-level calculus, etc.) but this is a good illustration of it.

The answer is 2. End of story.

fast_eddie_72 wrote: The only thing I'm confused about is where the confusion is.

exactly haha

Jay wrote: The brackets always act as an operator on the number they're "attached" to and that operation is performed right after the evaluation of the contents of the brackets.

You might be right, but now I gotta break out the google machine.

haha I know, I mean I asked a math teacher himself and got the answer, so I already explained myself

I've decided if you want 2 as your answer you would need parentheses around the 2 times 9 plus 3.

48÷(2(9+3)) = 2

^ this

Jay wrote: I don't know if someone else has used this logic yet, but the equation in question is 100% completely, unarguably, identical to writing "48 ÷ 2x = ?, where x=9+3." If you performed a substitution for x back into that equation you would be left with the one in the thread title, so that is how it should be treated. The answer is 2. The brackets always act as an operator on the number they're "attached" to and that operation is performed right after the evaluation of the contents of the brackets.

Sorry, but this is incorrect. The brackets do in fact act as an operator; but the operation is not always performed right after the evaluation of the contents.

Jay said: I don't know if someone else has used this logic yet, but the equation in question is 100% completely, unarguably, identical to writing "48 ÷ 2x = ?, where x=9+3." If you performed a substitution for x back into that equation you would be left with the one in the thread title, so that is how it should be treated. The answer is 2.

This is again, incorrect. Yes, the equation is "48 ÷ 2x". But "2x" is also the same as "2*x". So we have "48 ÷ 2 * x". 288.

I looked for a bit and can't find any rule that says the brackets have to work on the number they are attached to. All I can find is confirmation that I got the order of operations right. With the information I can find, it's still what I said before. There might be a rule about that, but I can't find it. The brackets are just multiplication, near as I can tell, and at that point we're just wroking left to right.

Tell you what, Jay, I’ll trade you the weight of a bowling ball on the eighth moon of Jupiter for my lunch, for the weight of a feather on the second moon of Neptune from your lunch.

48/2x = 2

Cross multiply and divide, you get 12.

48/2x = 288

Cross multiply and divide, you get 0.0833333333333333333

brackets? [ not ( then you got { which I forget the name

I’ll trade you 1000 picoliters of my milk for 4 gills of yours.

mtn wrote: Sorry, but this is incorrect. The brackets do in fact act as an operator; but the operation is not always performed right after the evaluation of the contents.

No it isn't. In the way it's written there, the operator acts first. Always. There is absolutely no logical situation in which you'd split (equation) ... 2x ... (equation) into (equation ... 2)(x ... equation).

mtn wrote: This is again, incorrect. Yes, the equation is "48 ÷ 2x". But "2x" is also the same as "2*x". So we have "48 ÷ 2 * x". 288.

No, it's not the same! 2x is clearly one unit in the denominator. You CANNOT claim 48/2x = (48/2)x. Writing "48 ÷ 2 × x" may or may not include x in the denominator, I'd say it's a bit ambiguous. That looks to me more like (48/2)x. If I had that question on a test I'd go argue with the prof until he clarified it.

xy is NOT always the same as x × y or x * y. As soon as you add in an instruction sign (×), you have to take into account the context of the equation! Otherwise you change things.

Ben, i'm going to e donkey punch you in the nuts

48 ÷ 2x is NOT the same as 48 ÷ 2 x "x".

Bring it Nick!!!!!!