48÷2(9+3) = ???

[tonywonder]

i just figured it out guys and i have proof its too long to type so you will have to go here

http://mathwhiz.com/index/pemdasusage

[Conki]

Its tomorrow, just figured it out. The bear is white(ish).





I'm not using a 2 in this problem; I am showing that the logic for 288 is flawed. Basically, using PEMDAS with the original problem, we come up with
48÷2(9+3) = 48÷2(12) = 24(12) = 288.

But if we use that logic, we can get (new equation here):

48÷(9+3) = 48÷(12) = 48(12) = 576. So we get 48÷(12)=576.
Here is how it works: (9+3)=1(9+3). So lets go back to the equation,
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12).

Got it? Now, this proof is still flawed (remember, the entire problem is flawed), but it still "works" because you can't really do an un-flawed proof of the problem for 2 or 288.

Yeah it's clear now. And you are right. And I don't know what else to say about that:)

[Violet88]

you're ALL wrong!

[Not an asshole]

Its tomorrow, just figured it out. The bear is white(ish).

Where did the 2 go? And how did the division sign turn into multiplication (or the lack of it)?

48÷(9+3) = 48÷(12) = 48(12) = 576...
What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this:
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576

I'm not using a 2 in this problem; I am showing that the logic for 288 is flawed. Basically, using PEMDAS with the original problem, we come up with
48÷2(9+3) = 48÷2(12) = 24(12) = 288.

But if we use that logic, we can get (new equation here):

48÷(9+3) = 48÷(12) = 48(12) = 576. So we get 48÷(12)=576.
Here is how it works: (9+3)=1(9+3). So lets go back to the equation,
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12).

We lost the division sign because we did 48÷1. 48÷1=48, and we get 48(12).

Got it? Now, this proof is still flawed (remember, the entire problem is flawed), but it still "works" because you can't really do an un-flawed proof of the problem for 2 or 288.

[Conki]

BUT by this logic

48÷(9+3) = 48÷(12) = 48(12) = 576...
What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this:
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576

Where did the 2 go? And how did the division sign turn into multiplication (or the lack of it)?

He is still a mile away from his tent.

Sleep on it and try again tomorrow;)

[Not an asshole]

I'm a math major at an Ivy league school.

Okay, no I'm not. But I am a junior math major at one of the top 15 public schools in the country (if you put any stock into those bullshit rankings).

The question is incorrect. Anybody who would actually be asking/writing it for reasons other than to cause ruckus on the internet would never actually write it that way. Besides this, in most applications, you would notice that either 2 or 288 is way off.

Anyways, proof for 2:
Going 100% by PEMDAS, we get 288. This is what I believe to be correct, but to play devils advocate, I'll argue for 2.


I'm going to assume that you all have seen the proof for 288 (basically PEMDAS)
But the problem with this is this is that we are doing

48÷2(9+3) = 48÷2(12) = 24(12)=288

BUT by this logic

48÷(9+3) = 48÷(12) = 48(12) = 576...
What? 48÷(12) = 576? Yes, because by the logic we were using above, we get this:
48÷(9+3) = 48÷1(9+3) = 48÷1(12) = 48(12) = 576

By contradiction, we have proven that the answer is 2.

A man decided to go hunting. He set up his base, then started looking for a prey. He walked a mile south, but found nothing, so he decided to turn west. After another mile, still nothing to shoot at, he turned north. After walking another mile, much to his surprise, he got back to his base, and saw a bear looking at him from his tent. What color is the bear?

He is still a mile away from his tent.

[alane]

2

[reelizmpro]

No, the concept of implied multiplication is not universally accepted. Which is what how you are arriving at the answer of 2.

Which is why I bought up the reciprocal. You take the reciprocal by flipping the entire fraction not just one number. I'm trying to show that perhaps it should be accepted.

[Conki]

Because depending on the calculator it's programmed to go left to right sometimes ignoring brackets. This was discussed in the first few pages...people showing different calculators with the same thing typed in with different answers. Do it by hand. We know what we mean but the calculators may not.

I saw that and I know that. Calculators can be programmed and they come with different settings from the factory. This is why I said in one of my comments that it is important to consult the user's manual before using a product.
However, this still doesn't change the basic rules of algebra;)

[Conki]

I'm getting tired of this. I tutor college students in math that struggle with it. They are just as clueless as some of you guys here, but they at least don't argue about simple mathematical laws.

Let's try something else now... I had this question on a physics test in middle school:

A man decided to go hunting. He set up his base, then started looking for a prey. He walked a mile south, but found nothing, so he decided to turn west. After another mile, still nothing to shoot at, he turned north. After walking another mile, much to his surprise, he got back to his base, and saw a bear looking at him from his tent. What color is the bear?

No googling allowed. First one that answers it gets 48÷2(9+3) internets.

[reelizmpro]

dude... The reciprocal of 2(9+3) is 1/(2(9+3)), it's obvious. If you don't have the '48/' in front of the '2(9+3)', it equals 24, that is obvious too. I don't see how these have anything to do with the fact that people believe they shouldn't follow simple math.

Why would I put '1/((5(1+2))/(8(2+3)))' into wolframaplha? That's not our equation. You just prioritized the multiplications using parentheses. In this case they get calculated first. Why did you put those parentheses around the multiplications? Because you wanted them to be calculated before the division. BECAUSE OTHERWISE THE MULTIPLICATIONS WOULDN'T BE CARRIED OUT BEFORE THE DIVISION. It's like you proved my point. Thanks a lot bro:)

Because depending on the calculator it's programmed to go left to right sometimes ignoring brackets. This was discussed in the first few pages...people showing different calculators with the same thing typed in with different answers. Do it by hand. We know what we mean but the calculators may not.

[lambo]

The definition of a reciprocal isn't universally accepted?

No, the concept of implied multiplication is not universally accepted. Which is what how you are arriving at the answer of 2.

[Conki]

Okay, try this instead. Wolframalpha thinks you're doing something else.

1/((5(1+2))/(8(2+3))) copy and paste that.

Btw, I like how you conveniently decided NOT to use the reciprocal calculator I posted previously and chose to do it the hard way with an online calculator that thinks you're doing something else because there aren't enough parentheses. C'mon now....

http://www.algebra.com/algebra/homework/Inverses/FIND-reciprocal-of-a-FRACTION.solver

Reciprocal of ((5(1+2)) / (8(2+3))) is simply ((8(2+3))/(5(1+2)))...just as the reciprocal of 2(9+3) is 1/(2(9+3)) . It's important to note that (9+3) is kept in the DENOMINATOR (2) opposed to the numerator (288)

dude... The reciprocal of 2(9+3) is 1/(2(9+3)), it's obvious. If you don't have the '48/' in front of the '2(9+3)', it equals 24, that is obvious too. I don't see how these have anything to do with the fact that people believe they shouldn't follow simple math.

Why would I put '1/((5(1+2))/(8(2+3)))' into wolframaplha? That's not our equation. You just prioritized the multiplications using parentheses. In this case they get calculated first. Why did you put those parentheses around the multiplications? Because you wanted them to be calculated before the division. BECAUSE OTHERWISE THE MULTIPLICATIONS WOULDN'T BE CARRIED OUT BEFORE THE DIVISION. It's like you proved my point. Thanks a lot bro:)

[reelizmpro]

I'm officially done with the original subject, because the answer is 288. It may make more sense to you to group the 2 together with the (9+3), but that doesn't make it mathematically correct. So here's the end of it for me.

Now let's look at the reciprocal problem.

Why did I move the 8 above the line? Because if you write 1/(5(1+2)/8(2+3)) down, it looks like this:

or 1/(5*(1+2)*(2 + 3)/8 )
from here you move the 8 up, because that is the denominator of the denominator.

Clear?:)

Okay, try this instead. Wolframalpha thinks you're doing something else.

1/((5(1+2))/(8(2+3))) copy and paste that.

Btw, I like how you conveniently decided NOT to use the reciprocal calculator I posted previously and chose to do it the hard way with an online calculator that thinks you're doing something else because there aren't enough parentheses. C'mon now....

http://www.algebra.com/algebra/homework/Inverses/FIND-reciprocal-of-a-FRACTION.solver

Reciprocal of ((5(1+2)) / (8(2+3))) is simply ((8(2+3))/(5(1+2)))...just as the reciprocal of 2(9+3) is 1/(2(9+3)) . It's important to note that (9+3) is kept in the DENOMINATOR (2) opposed to the numerator (288)

[Conki]

I'm officially done with the original subject, because the answer is 288. It may make more sense to you to group the 2 together with the (9+3), but that doesn't make it mathematically correct. So here's the end of it for me.

Now let's look at the reciprocal problem.

Why did I move the 8 above the line? Because if you write 1/(5(1+2)/8(2+3)) down, it looks like this:

or 1/(5*(1+2)*(2 + 3)/8 )
from here you move the 8 up, because that is the denominator of the denominator.

Clear?:)