48÷2(9+3) = ??

[93forestpearl]

Some of you may have seen this elsewhere, but I'll post it anyways for some lulz.

Please solve and record your answer in the poll. Discuss if you wish.....


48÷2(9+3) = ??

[mike-tracy]

Order of operations.

1.Parentheses first (9+3) then
2. multiplication (2)*(12)
3. then division (of 48 by (24))

So... 2


But... My Ti-83 and Ti-30x say 288 so I guess that's the answer, lol

9+3=12, then 48/2=24 then 24*12 due to strict left to right order of operations. Tricky

Here's some more for lols (not my pics):

[speedmaxx]

36


So what do I win?


Lol

[93forestpearl]

I want to let this go a bit before I chime in. This turned into an 8 page argument on MNSubaru, and more than that on several other forums.



Here's a hint: Does implied multiplication have precedence or not?

[Apex3]

Smart people on this forum. There's a 28 page thread on bimmerforums about this, 2/3 said it was 2. Would have been a lot longer but it was locked.

I still say it's 288

But it is rather ambiguous.

And to get this out of the way(even though no one will listen), order of operations does NOT end up with 2, multiplication/division have equal importance, so from there you go from left to right. The only actual argument you can have for it being 2 is whether or not it's implied that the 2 is attached to what's in the parenthesis since there's no *, personally I think that's BS, but it's possible since I didn't really take much conceptual math.

On a side note, why am I procrastinating on my engineering homework by talking about math? wtf is wrong with me?

[93forestpearl]

^ I'm with you. Implied multiplication does not have precedence. Since 48÷2(9+3=48÷2*(9+3), there shouldn't be an issue. Due to the nature of typing equations on a single line, there can be a lot of ambiguity and some people assume precedence of inplied multiplication vs. explicit. There was a major rule was broken in writing this equation in that there should be absolutely no question as to how it should be interpreted.

Some professors and textbooks may say they give implicit multiplication precedence, but at the same time, they typically don't use single line notation so it is never an issue. Even if they did, breaking basic rules of math is bad form. Use brackets if you mean you need to be clear. Math professors often say that students make tons of mistakes by not using brackets early in a problem, and then carry those mistakes on throughout the solution.

Some people claim the distributive property, but they don't use that correctly either. If you are going to distribute, you have to distribute 48÷2, not just the 2, so you still end up with 288.


Lastly, on the calculator thing:

Some calculators do indeed perform this incorrectly, particularly graphing calculators from the previous millennium. TI led the charge in this regard. Their TI-80, 81, 82, and 85 calculators gave implied multiplication a higher precedence than explicit multiplication. TI reversed this decision in the late 1990s. Their TI-83, 84, 89, 92, and later calculators give the same precedence to implied and explicit multiplication.

[skid542]

On a side note, why am I procrastinating on my engineering homework by talking about math? wtf is wrong with me?

Quoted because I got a good laugh out of that. Nerd! *raises hand and admitts I'm entering this arguement and therefore fall under the nerd category by default.

And I know every few years we do this, but, how many engineers do we actually have on the board? This would be a great thread to find out.

I'll go first. Aerospace Engineering, B.S., 06', Virginia Tech



But, getting back to the question Dan raised - 288.

Anybody else remember that really old saying from 3rd grade? - Dirty Monkeys Smell Bad.

And I agree with the arguement regarding implied multiplication. The parenthesis take precedence as operation #1 but then the equation is solved left to right as there is no priority between the multiplication and division operations.

And yes, from someone who only does single line math operations (I love my diagonal vinculum) if there is question in order of operation then brackets are required. Clarity in mathematics is clutch any those that don't respect that issue shouldn't be doing critical math .

[Legacy777]

Easiest way to get this correct is rewrite it so it's not on a single line. It's much easier to visualize that 288 is correct.

[Binford]

Honestly, I'm impressed the answer I came up with was even an option! Sounds like I was wrong though! O well!

[Binford]

Also, whenever I need to do math, I type it into Google. Google says 288. Google cannot be wrong. It's that easy!

[PhyrraM]

My take:

If you can't tell that either 2 or 288 is WAY OFF, based on the intended application - you have bigger problems.

In my experience, if you don't reconcile the pure math with a bit of real world application you've spent too much time in a textbook.