<p>It’s disputable because both 2 and 288 are possible answers… </p>
<p>It all depends if you subscribe to the idea of implied multiplication or not. Some people do, some don’t. All calculators aren’t even made with the same configuration regarding it.</p>
<p>I’d say 288 is the “most correct” answer, simply because that’s the way most people learn how to do it, but that doesn’t make 2 incorrect. </p>
<p>You’re obviously flunking sixth grade stuff.</p>
<p>
</a></p>
<p>Nice photoshop.</p>
<p>
</p>
<p>Not if you input it just as it is written here.</p>
<p>
</p>
<p>No.</p>
<p>
</p>
<p>Calculators that evaluate it as 2 either have a setting that lets them assume that is what you meant or else aren’t really worth their weight in air. This is a simple expression with one single answer. If a calculator gives you 2, the assumption it is making is that you meant to type in a slightly different expression. If course, this is why you always have to be careful and just put in parentheses where they should go. Just out of curiosity, what model of calculator are you running that gives you the answer of 2 for this? I need to know what not to buy.</p>
<p>
</p>
<p>Yes it does. 2 is incorrect. If I was teaching your math class and you put down 2, I would mark it wrong as it shows a distinct lack of understanding of the order of operations, which are some of the basic rules of arithmetic.</p>
<p>There is only one correct answer to the question being asked, but it is possible to interpret the question being asked differently. One way gives 2 as the answer and the other gives 288. </p>
<p>Implied multiplication vs explicit multiplication is a discussion that has been discussed so many times before. Are you saying all people, books, and calculators that choose implied multiplication > explicit multiplication, are wrong?</p>
<p>After reading about this on the physicsforums, it appears the answer depends on whether you go into the problem assuming the implicit multiplication order of operations or the standard order of operations. </p>
<p>Keep in mind that the rule: “multiply/divide going from left to right” does not come from any naturally derived proof, but rather it’s an arbitrary rule put in place to keep arithmetic operations simplified. Likewise, the implicit multiplication rule is also an arbitrary rule put in place to help simplify algebraic operations. </p>
<p>So the correct answer depends on what you assume to be the correct rule to follow. Since the problem is written arithmetically and not algebraically, I think we should approach it from the arithmetic standard order of operations, which of course gives me the opposite answer I originally proposed.</p>
<p>I’m glad this question came up, it’s not a problem I had ever even considered before.</p>
<p>From Texas Instruments:</p>
<p>[</p>
<p>Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators. - Knowledge Base by Texas Instruments - US and Canada](<a href=“Self-service Knowledge Base | Texas Instruments”>Self-service Knowledge Base | Texas Instruments)
Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2<em>X), while other products may evaluate the same expression as 1/2</em>X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper. </p>
<p>This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage 200 and the TI-Nspire Handheld in TI-84 Plus Mode. Implied and explicit multiplication is given the same priority.</p>
<p>
</p>
<p>Just because something can be interpreted two ways doesn’t make both ways correct. I might say that I think 2 can be larger than 3 because 2 cars are larger than 3 basketballs, but that doesn’t make it correct. The question, as asked, has only one correct interpretation.</p>
<p>
</p>
<p>If they fail to document that implied multiplication is given the higher priority, then yes, it is wrong. If it is documented then you just need to take note of the fact and distribute your parentheses accordingly. You need to be aware of what you are using.</p>
<p>The most common TI calculators (83/84, 89 and 92) all do not do implied multiplication and would evaluate it the “correct” way. The same goes for Matlab, Mathematica, Maple, and any programming language. The only way that implied multiplication is given preference is if the machine is specifically told to do it that way.</p>
<p>
</p>
<p>Generally, the way you should assume it is done is according to the standard order of operation unless you are explicitly told otherwise. Generally, an author of a book will have something near the beginning explaining his assumptions and notations, and most calculators will not give implicit multiplication precedence these days, and if they do, they will likely tell you. Most if not all of the TI models that were cited above for implicit precedence are discontinued, I believe.</p>
<p>One possible answer is that there is no correct answer. Why? Because the argument commits the fallacy of ambiguity and no correct answer can be derived from a fallacious argument.</p>
<p>Hmm…there is some thought that division took precedence (slightly over multiplication) even though the “multiply/divide left to right” infers that division and multiplication is on the same level.</p>
<p>Therefore, some may consider 48 divided by everything else.</p>
<p>Also if that (9+3) was a (X+3) then 2(X+3) with no spacing will be looked at first.</p>
<p>48/2(X+3).</p>
<p>I don’t care what is in the standards of operation. Even a PHD in Math from MIT will focus on the 2(X+3) with no spacing as its own term.</p>
<p>The problem is the “/” sign is used instead of a fraction. Because of this we don’t know whether the 2 is multiplied to the parenthesis, or if 48/2 is multiplied to the parenthesis.
So as it is written, the answer could be both 2 or 288.</p>
<p>One more thing to look at is depending which branch of math one is doing…</p>
<p>1/2N</p>
<p>Ask a statistician who is doing random sampling and they will say 1 divided by 2N.</p>
<p>I agree that the issue is with the / being interpreted as a fraction or division bar versus the division sign and not an error in the Order of Operations. As written, it should be interpreted as a replacement for the division sign, not a fraction bar. So the answer is 288.</p>
<p>
</p>
<p>You haven’t met many math majors of the PhD variety then. The rule of thumb (order of operations) is there for a reason. Unless otherwise specified, you follow them. Technically, evaluating it as (48)/[2(9+3)] would be an abuse of notation. Most math majors that I have ever known frown on that.</p>
<p>
Division is multiplication by the reciprocal so it’s meaningless to say one takes precedence.</p>
<p>In that form, the answer is unambiguously 288. There is no question of interpretation – without any other clarifications, we must choose the standard order of operations (which goes left to right in multiplication vs. division). Implied multiplication is not standard in this century. And guess which century we’re living in? This one!</p>
<p>This “viral” math problem is as dumb as the “.999… = 1?” problem from a few years ago.</p>
<p>So would 1/2N (no spaces) = (1/2) * N?</p>
<p>…probably so in the “book” but for that statistician doing sampling all day…it’s 1/(2N)</p>
<p>Which brings me to another topic that relates to this board…</p>
<p>Everything is not linear and by the book. I personally think engineers (including myself at a younger age) will think that to get from A-to-Z, you must go B-through-Y. That is not the case in real life. There is just about an argument for everything and probably a loophole for everything.</p>
<p>Here is the REAL answer to that problem.</p>
<p>It’s whatever that V.P. or regional director SAYS it is when computing those values for that report.</p>
<p>
</p>
<p>Without an otherwise established precedent, then yes, 1/2N = (1/2)N. Of course, if it is an established precedent, then people in that line of work know what it means. This thread had no precedent to override the order of operations (which are the global established precedent unless otherwise specified) and so the answer is 288, not 2.</p>
<p>There is a difference between doing things by the book to a fault and doing things properly. Doing things properly will always leave room for thinking outside the box if you let it. However, taking shortcuts, not following established precedent without documentation and just generally doing things improperly are how things like the Mars Climate Orbiter happen. One group uses Newtons, one uses Pounds-force and no one communicates and you lose a $650M spacecraft.</p>
<p>Yes, young engineers tend to overwork problems and overdesign products at first, but you are better off doing that than underworking or underdesigning. I would like to keep my planes in the air and my bridges in one piece.</p>
<p>There is a proper way of doing just about anything in science and engineering to prevent these kinds of mixups:
<ol>
<li><p>If you deviate from that convention, document it.</p></li>
<li><p>If there is no convention, use the established precedent and document it.</p></li>
<li><p>If you deviate from precedent, document it.</p></li>
</ol>
<p>
</p>
<p>I highly doubt most majors care.</p>
<p>I would definitely say the answer is 288 as written. However, the expression is clearly ambiguous, as say for example</p>
<p>x/yz would be interpreted as x/(yz) by the majority of the population. However, technically it should be interpreted as xz/y.</p>
<p>therefore ■■■■■■ win.</p>
<p>Fun discussion. I always add redundant parathesis when I’m providing instructions to my programmer so that he doesn’t change things to what he thinks I meant, i.e., assuming an implied convention in the order of preference!</p>
<p>Google, MATLAB, and WolframAlpha all say it’s 288.
If you contradicted them, you are incorrect. There are absolutely no exceptions.</p>