48÷2(9+3) = ?

[Cluck]

Really though, if you want an actual interesting mathematical problem to discuss, consider the infinite ball and jug problem.

At 2 minutes to midnight, balls labeled 1 through 10 are put in a jug. At 1 minute to midnight, the ball with the label 1 is removed, and ten more balls - labelled 11 through 20 - are put in. Every time the time to midnight halves, the process is repeated, with the least ball being removed, and the 10 next balls being added.

The question then, is how many balls are in the jug after midnight?



Presume that there is no difficulty in performing the task of adding and removing the balls arbitrarily fast, otherwise the problem is degenerate.

The answer to this depends on how easily extra balls can escape from the jug. Since the jug is a normal jug, it has a finite capacity for balls, thus the amount of balls in it after midnight is either equal to the amount that can fit into the jug before it's full as any extra balls added at that point simply roll out of the jug. Alternatively if the balls keep being entered into a jug that they can't easily escape from, the answer is no balls, as all that is left at that point is fragments as the volume of balls inside eventually passes the volume of the jug.

[WarDaft]

You don't have to code the problem, so there's no overflow error.

You get to midnight quite easily simply by doing things twice as fast each time - you never have to do things infinitely fast, and you always have enough time to finish before the next iteration.

[iorcedurmother]

Every step has a finite non-0 amount of time to be completed, and we presume that the balls can be added and removed arbitrarily fast, so the task does finish by midnight.

So, if there are infinitely many, what's the least ball still in the jug?

Yea, finite non 0 amounts of time will go on infinitely continuing to be halved until midnight.

[Deleted]

You can clearly see the * between 2 (

So? Do you imply calculators ARE truthtellers? Do you imply my statement is invalid?

[Pieterman]

Really though, if you want an actual interesting mathematical problem to discuss, consider the infinite ball and jug problem.

At 2 minutes to midnight, balls labeled 1 through 10 are put in a jug. At 1 minute to midnight, the ball with the label 1 is removed, and ten more balls - labelled 11 through 20 - are put in. Every time the time to midnight halves, the process is repeated, with the least ball being removed, and the 10 next balls being added.

The question then, is how many balls are in the jug after midnight?



Presume that there is no difficulty in performing the task of adding and removing the balls arbitrarily fast, otherwise the problem is degenerate.

Not the most interesting mathematical problem if you ask me. By only halving any given number (in the case, the time left) you cannot reach zero, therefore cannot reach midnight. Unless putting balls in the jar takes no time, you won't be quick enough to put balls in the jar, therefore going past midnight.

[Fauxpaws]

All of those give the same answer which is wrong for given equation.

Actually, it's correct.

The answer is 2, and only 2.

2(9+3) is one expression and must be solved first before finishing the equation.

Simplified it's 48/24, which equals 2.

[iorcedurmother]

Infinite iteration, overflow error when using 20 unsigned integers to hold the value of the balls. You'll never get to midnight because the time will be halved infinitly, being closer to midnight each halve. And because math people hate me when I use infinity

Sumation to x, x is a limit to infinity... (10 + 10 - 1)
Excuse my notation I don't do math well.

Edit on topic: The calculators think differently because their coded differently. The discrepancy between the two could have been a fix to ensure that a parenthesis expression would be treated as one, or it could be an error that they tried to correct in their last version... If you're unsure just always add the multiplication and note that it's for clarification and evaluate it like that. . . In real life you have context for numbers so you can derive how you want things to be done.

Yea, thus is just a matter of common sense though I wouldn't even consider it a math problem, but I guess the guy who posted it has no idea what he's talking about

[WarDaft]

Yea, finite non 0 amounts of time will go on infinitely continuing to be halved until midnight.

The sum of an infinite decreasing geometric series is finite, despite having infinitely many terms, the task is completed at midnight.

No balls are added except the ones you add, no balls are removed except the ones you remove.

And space within the jug is not a concern, or the problem is again degenerate, being dependent upon things not specified in the original question. Everything you need to know to answer the question was specified. You can safely assume that if there is something which was not specified, but could limit the outcome, that it was specified in a way such that it does not actually limit the outcome.

[Mister K]

Its simple

48/2(9+3)

We take the brackets first 9+3 is 12. Now we take the division which is 48/2 and the result is 24. Now we don't have Indices or anymore brackets so next in line is division once again. We take 24 and divide it by 12 which is 2.

The second equation:

48/2x(9+3)

Always work out the brackets first due to BIDMAS. So we have

9+3 = 12 Then see if there is division which there is. So 48/2 is 24. Now we have multiplication so we take the 12 and 24 and multiply it 24x12 which is 288.

BIDMAS (brackets, indices, division, multiplication, addition, subtraction) Thats the order it goes in. Are there any brackets? If so work out the numbers in brackets first. No? Is there Indices? If not look for division if so work that first before anything else...

I dot understand all the fuss...First answer is 2 and the second 288....

[Omarian]

So? Do you imply calculators ARE truthtellers? Do you imply my statement is invalid?

Nope, I'm just saying " You can clearly see the * between 2 ( ".
You're someone who tries to add stuff which isn't there, right?
Not responding to my last post about the image shows that you're just acting foolish.

[Sim]

Actually, it's correct.

The answer is 2, and only 2.

2(9+3) is one expression and must be solved first before finishing the equation.

Simplified it's 48/24, which equals 2.

No, it is not

Because that would mean its 48 / ( 2( 9+ 3) ), which it clearly is not. Once you solve the brackets they go away.

I quote it again

Example 3: Evaluate 9 - 5 ÷ (8 - 3) x 2 + 6 using the order of operations.

Solution:
Step 1: 9 - 5 ÷ (8 - 3) x 2 + 6 = 9 - 5 ÷ 5 x 2 + 6 Parentheses
Step 2: 9 - 5 ÷ 5 x 2 + 6 = 9 - 1 x 2 + 6 Division
Step 3: 9 - 1 x 2 + 6 = 9 - 2 + 6 Multiplication
Step 4: 9 - 2 + 6 = 7 + 6 Subtraction
Step 5: 7 + 6 = 13 Addition



48 / 2(9+3)

48 / 2 * 12

24 * 12

288

Simple.

To anyone who says you need to "clear" parentheses. No. Just No. Their purpose is to designate that what is within them needs to be completed first. Once that math is complete, they serve no purpose; therefore, they are removed

/topic

[Simca]

Yeah, enough. We gave it a chance.

However, there's no actual discussion here (that is relevant to the topic). People are just posting their own interpretations of the problem ad nauseum which is not useful or constructive.

An interesting discussion could have been had on the value of implicit mathematics and shorthand usage in modern calculators and the decisions that led the companies to include such a feature, but I don't think anyone is interested in that besides me. There are several other potential discussions to be had here as well, but again, all we're seeing is the same posts over and over.

Locked.