tag:blogger.com,1999:blog-7718462793516968883.post5944651796588703097..comments2024-06-21T03:26:36.002-04:00Comments on MadMath: PEMDAS: Terminate With Extreme PrejudiceDeltahttp://www.blogger.com/profile/00705402326320853684noreply@blogger.comBlogger27125tag:blogger.com,1999:blog-7718462793516968883.post-20975749422399700482023-12-11T22:03:56.147-05:002023-12-11T22:03:56.147-05:00and the author seems to miss a salient feature of ...and the author seems to miss a salient feature of the solidus, which probably wouldn't be missed using the vinculum - time-honored convention holds that it automatically brackets everything over and everything under it, in contradiction to the example given by the author:<br /><br /> 24 24 <br />----------- = 4 vs ------------ • 2 = 16<br /> 3 • 2 3 <br /><br />confirmed by these guidelines:<br /><br />https://journals.aps.org/authors/bracketing-mathematical-expressions-h9<br /><br />[...]<br />"Use enough bracketing to make the meaning clear and unambiguous. Be especially clear with fractions formed with the solidus (/). According to accepted convention, all factors appearing to the right of a solidus are to be construed as belonging in the denominator"<br />[...] (with examples)<br /><br />I've actually written to APS asking if their 2009 guidelines have been revised or notjack gabelhttps://www.blogger.com/profile/12864453622430075393noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-31841641457067633402018-02-16T10:03:11.148-05:002018-02-16T10:03:11.148-05:00Calvin (and most/all conventions) PEMDAS simplify ...Calvin (and most/all conventions) PEMDAS simplify expressions. Logic did lead the way when defining it. It gets rid of strange ideas like implicit multiplication has a higher precedence that explicit (wouldn't it be more "logical" to revese that?).<br /><br />There is no convention called "real world math usage", That's more like anarchy. Nobody would be sure what the other person meant.<br /><br />The same manufacture of very similar calculators will give different results for the identical input.<br /><br />What's complicated about 6/2*3 = 9 or even 6/2(1+2) = 9? I accept the latte is going to confuse illogical people that can't follow very simple rules.Martin Adamshttps://www.blogger.com/profile/11406889215946937383noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-44096986527259439942017-06-03T14:04:47.085-04:002017-06-03T14:04:47.085-04:00I don't think so. Consider computer programmin...I don't think so. Consider computer programming, entering expressions into a spreadsheet, etc.; we have no choice but to use the / symbol. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-60596041131696031152017-06-03T14:03:33.471-04:002017-06-03T14:03:33.471-04:00There's a lot there that I'm afraid I can&...There's a lot there that I'm afraid I can't agree with. To begin with, I think you're using the word "equation" when you mean "expression", etc. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-13610189011085920162017-05-02T11:44:42.937-04:002017-05-02T11:44:42.937-04:00If you use the / symbol in a written sum instead o...If you use the / symbol in a written sum instead of the ÷ symbol, you're going to cause just as many problems as PEMDAS itself.Anonymoushttps://www.blogger.com/profile/03778157559812368975noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-33407144933828506792016-02-07T02:54:27.429-05:002016-02-07T02:54:27.429-05:00Delta, glad you at least broke down the issues cre...Delta, glad you at least broke down the issues created by PEMDAS. The first thing I'd like to mention is about making this simple. (KISS rule) Logic should always take the lead. We live in a linear world and our minds think in a logical sequence.<br /><br />So your math equation typically will be just as it happens in time and space. The only time we see the use of zero is in a test created by a teacher. That is because we will only generate real numbers in real time.<br /><br />You also mentioned that parentheses even when absent are assumed due to the left to right logical order. So just like entering the numbers in an ordinary calculator every math equation is of 2 numbers so the first 2 numbers and it's process will make the two included in a set of parentheses. <br /><br />When they follow PEMDAS they add the Parentheses anywhere they think PEMDAS should start.<br /><br />This makes the simple task much more complicated and will give the wrong answer to the overall equation by making a number that would never have been there in the first place.<br /><br />Teachers should follow real world math usage as mathematical strings never really exist. Every computation has a meaning or definition to finally help the user get his answer.<br /><br />Math has purpose when used daily. When you put random numbers in the form of an equation it has no meaning and thus is meaningless and pure nonsense.<br /><br />Math is all about taking our data and putting it in order. If the data is baseless then why the waste of time.<br /><br />Just think how complicated a simple equation is being made by the use of PEMDAS,this is how ridiculous some people complicate the world. Anonymoushttps://www.blogger.com/profile/05221991729952301667noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-68774466862069131992015-10-27T23:22:20.069-04:002015-10-27T23:22:20.069-04:00Yet another useful rule from the proper order-of-o...Yet another useful rule from the proper order-of-operations table: consider the meaning of exotic symbols in the exponent. Radicals can be represented by fractions/divisions in an exponent. Division/fractions can be represented by a negative/subtraction in an exponent. In each case, one step down in the order-of-operations.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-10958834570184675422015-06-26T01:44:36.839-04:002015-06-26T01:44:36.839-04:00That doesn't make any sense.That doesn't make any sense.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-44479996255691412362015-06-24T20:12:56.074-04:002015-06-24T20:12:56.074-04:00GEMA works with in 99% of cases, but if you are do...GEMA works with in 99% of cases, but if you are doing math where computers are involved and accuracy is important then arbitrarily switching between division and multiplication can introduce rounding errors and it is actually a pretty dangerous pitfall.<br /><br />It's still important to teach that there is equal precedence between division and multiplication, but PEMDAS has importance as a method of standardization that GEMA doesn't.rabble rabble rabblehttps://www.blogger.com/profile/02446585144608542199noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-10990048839007672842014-08-19T13:29:34.696-04:002014-08-19T13:29:34.696-04:00Also: I just developed a new site for online pract...Also: I just developed a new site for online practice on basic skills, including a simple multiple-choice "what order would it be?" order-of-operations quiz. You might like to check it out, and feel free to point people to it if you think it would help:<br /><br /><a href="http://automatic-algebra.org" rel="nofollow">http://automatic-algebra.org</a>Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-8054864792000156772014-08-19T13:18:17.724-04:002014-08-19T13:18:17.724-04:00Thanks for the comment! Of course, I totally agree...Thanks for the comment! Of course, I totally agree -- and am continually amazed at people almost willing to be ignorant about the issue, and to teach it half-broken all the time. I think you're right that clearly stating there are FOUR phases is a clarifying approach. Thanks for your good works, good luck. :-)Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-38695300846244013042014-08-19T03:36:51.066-04:002014-08-19T03:36:51.066-04:00I love this blog post!!! I prefer GEMA for the sa...I love this blog post!!! I prefer GEMA for the same reason. Even people who apparently know about PEMDAS are somehow unaware of the precedence equality of the same Type of operators, Multiplication and Division, Addition and Subtraction. But the people I encounter MOST are those who have no knowledge whatsoever of the Order of Operations, or Precedence, and think that you just go left to right. I would like to know Who keeps teaching people that if there are no Parentheses there are no rules!! It's driving me so completely crazy on Facebook that I even created a group called The Defenders of the Order of Operations for all those who understand and explain how math works.Aaron Paul Ingebrigtsen (Plarndude)https://www.blogger.com/profile/09203127290169418771noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-49341613950916297082014-06-07T16:53:14.638-04:002014-06-07T16:53:14.638-04:00I'm 75 yrs., and I went to solve a problem on ...I'm 75 yrs., and I went to solve a problem on Google + defined as "simple maths" 9 - 5 + 5 x 0 + 3 = ?. Since it said simple. I assumed x meant multiply. Anyway I went with the assumption of (X - Y + Z) (0 + N) and obviously got it wrong. I looked up "bodmas" which I noticed in some of the answers... I may be dumb, and especially to younger people. I am not sure, but, maybe the Nation is really "Dumbing Down" as I have heard mentioned. I looked up bodmas, and I understand it, and can do it, but I will stick with the old ways on this one. If it was mentioned, as something like solving the problem in bodmas... I would have skipped it or looked it up prior... I think I got set up! Ron DavisAnonymoushttps://www.blogger.com/profile/11353067478600323034noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-83094471206566887482014-04-02T00:58:27.802-04:002014-04-02T00:58:27.802-04:00I'm going to subtly disagree: true, IF you fir...I'm going to subtly disagree: true, IF you first convert all subtractions to additions, THEN the order doesn't matter. But that's a mighty strong "if": you've washed all the subtractions out of the problem in an advance step, only additions remain, and of course adding is specially commutative. <br /><br />But how do you know what's being subtracted in the first place, before you make that translation? (This may seem obvious but I've absolutely seen students perplexed by it.) In "3-2+1", perhaps it could be either the 2 (read left-to-right) or the 3 (read right-to-left). Or slightly more sophisticated: in "(-2x)(-3)-(-4x)(-5)", what should be multiplied by the outermost negative, the first pair of factors, or the second, or all of them? Just knowing what's being subtracted in the first place is only answered by the rule of reading an expression left-to-right. <br /><br />Plus, it's just consistent with all the other operations and therefore should be one less thing for students to remember. Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-50767396717730324172014-04-02T00:40:48.550-04:002014-04-02T00:40:48.550-04:00Actually there is no particular reason to go left ...Actually there is no particular reason to go left to right with addition and subtraction. You can go right to left if you want as long as you remember that subtraction is simply addition of the negative. So 3-2+1 can be 1+1 = 2 (left to right) or 3 + (-2) + 1 = 3 + (-1) = 2 (right to left). The order you do the additions and subtractions is irrelevant as long as you think of the subtractions as additions of the negative.Willpilgrimhttps://www.blogger.com/profile/15444613767553264589noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-16419318579200302332014-03-13T22:32:05.248-04:002014-03-13T22:32:05.248-04:00Anti pemdas it sucks
Anti pemdas it sucks <br />Anonymoushttps://www.blogger.com/profile/14682188640708194704noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-84157997457597467772013-07-01T13:00:02.862-04:002013-07-01T13:00:02.862-04:00lol
lol<br />Anonymoushttps://www.blogger.com/profile/09068713295026977797noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-2978230225984850912013-04-08T12:28:28.905-04:002013-04-08T12:28:28.905-04:00don't forget to call out logarithms as part of...don't forget to call out logarithms as part of the clarification.<br /><br />I came here after seeing all the wrong answers people posted to the equation people kept sharing on Facebook, and incorrectly arguing PEMDASJanhttps://www.blogger.com/profile/15053994979413487478noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-84440991883043997062012-01-20T15:04:08.655-05:002012-01-20T15:04:08.655-05:00... which is to say that the operations inside the...... which is to say that the operations inside the grouping symbol, and those outside, have to be performed in separate steps.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-14080888933412573492012-01-20T12:46:58.179-05:002012-01-20T12:46:58.179-05:00Sue, thanks for the kind words! For what it's ...Sue, thanks for the kind words! For what it's worth, I actually make the distinction between the radical symbol itself (√) versus the overbar (<a href="http://en.wikipedia.org/wiki/Vinculum_%28symbol%29" rel="nofollow">vinculum</a>) as the grouping symbol -- which hopefully reinforces the fraction bar usage, and also the historical usage before parentheses came in vogue.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-38066084574983252432012-01-20T09:45:17.607-05:002012-01-20T09:45:17.607-05:00Nice! I've never included radicals, because I ...Nice! I've never included radicals, because I wasn't tying it as much to the big picture, and for order of operations, radicals are covered under grouping symbols. I like to make sure students understand how the fraction bar is a grouping symbol (one which calculators cannot emulate).<br /><br />I'm going to modify this a bit, and pass it around at my community college.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-72059493241272235342011-10-12T03:46:41.368-04:002011-10-12T03:46:41.368-04:00Hey, PhD -- Glad to know it helped, thanks for the...Hey, PhD -- Glad to know it helped, thanks for the kind words! :-) I do think that it makes a big difference seeing the correct ordering in this light.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-61412500100309035782011-10-08T16:44:33.031-04:002011-10-08T16:44:33.031-04:00Outstanding! I have to say I have taught college a...Outstanding! I have to say I have taught college algebra I & II and I undertook the task of teaching my wife math basics and I invariably got a question wrong because of my flawed understanding of the mnemonic. Thank you so much for your breakdown of the relationships. This should be published in books. So many textbooks do not spell out the correlation or the whole big idea of the more powerful operation being performed first. Wow!<br /><br />-Adjunct Instructor of Accounting, Finance, Math (sort of ashamed)PhD in Traininghttps://www.blogger.com/profile/02827582661469809828noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-26173747753014841862011-09-14T20:41:41.922-04:002011-09-14T20:41:41.922-04:00pemdas is good for the memorization of the rules b...pemdas is good for the memorization of the rules but it should be taught with the caveat that add&sub multi&divs are done left to right. ive been taught both the wrong and right way.mehttps://www.blogger.com/profile/10630555670004896141noreply@blogger.comtag:blogger.com,1999:blog-7718462793516968883.post-53321243129475534152011-02-15T13:43:04.265-05:002011-02-15T13:43:04.265-05:00New observation:
(7) Operations IN powers all fol...New observation:<br /><br />(7) Operations IN powers all follow an upshift-one-operation shortcut (i.e., the converse of rule #2 above). Examples: 3^(-2) has a negative in the exponent (i.e., the result of a subtraction), so this indicates what is effectively a division, that is, 3^(-2) = 1/3^2 = 1/9. Something like 16^(3/2) has a fraction in the exponent (i.e., the result of a division), so this indicates what is effectively a radical, that is, 16^(3/2) = sqrt(16)^3 = (4)^3 = 64.Deltahttps://www.blogger.com/profile/00705402326320853684noreply@blogger.com