Spontaneous Musings

This is actually a problem with the folks who made up the problem!

There is an 'order' of arthimetic operations, but unless the person who set up the problem is thoroughly versed in that convention and did the setup perfectly, and the person on the other end (ie you or I) both knows and agrees with their order, the answers all of us will get from the problem will be garbage.

(7+7)/(7+7)*(7-7) is also unfortunately a possible interpretation of the problem as presented. The correct answer to that problem is
(14)/(14)*(0)= 0

Why is this such a mess? Because of the awkward format today's calculators use. I and many others warned those who wanted this format to be standard 30 odd years ago of the nightmares it would create when going beyond the simplest math problems. But it was to no avail because they could type in correctly written algebra problems without thinking. You can't do that with arithmetic problems instead of algebra!

Put simply never try entering a complex arithmetic problem without breaking it down into multiplications and divisions first, because otherwise it will never come out right.
7+(7/7)+(7*7)-7= 7+(1)+(49)-7= 8+42= 50

Edited Date: 2014-06-28 02:20 pm (UTC)

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elisi

I was going to comment and just say 'BRACKETS!' Thank you for going into far more detail. (Maths is straightforward, but only when the rules are followed.)

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shipperx.livejournal.com

Same. Even reading it I interpreted it differently than shadowkat. But reading Shadowkats version I could see it that way too which had me looking at the equation again, realizing that without brackets there are multiple ways to do it.

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Or clearly expressed.

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I never got why they did not teach the newer calculators, where you can enter a string of operations, that multiplication and division come before addition and subtraction.
It is something the kids learn in basic school, but then they get confused in 8th grade when their calculators don't do it automatically.

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Actually the problem here is the opposite. For a lot of people, with dyslexia (like Shadowkat and I) or not, getting partial answers is key to being able to work the problem with confidence. I'd guess if S'kat enters the whole thing on her calculator without hitting the '=' button till the end, it will give her 50 as it should. The problem is she needs those partial answers all along to allow her to see she hasn't made an entry mistake. Modern calculators are set up for perfect entry, not folks who may have problems along those lines. The key to understanding the math, as always, is understanding what happens when. The calculators take that away from her, so she can't recreate the steps and assure herself she's done it correctly.

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EXACTLY! Thank you. I suffer from a specific form of dyslexia - or discalcia, where numbers confuse me and sequencing does. Also left to right, I automatically flip. So this math problem is designed to provide me with the wrong answer. Demonstrates that whomever created it and the modern calculator that I'm using, doesn't realize everyone processes information differently.

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I'd guess if S'kat enters the whole thing on her calculator without hitting the '=' button till the end, it will give her 50 as it should.

No, it wont. At least mine (TI30X) will give you 56 as a result, because it just makes the operations in the order they are written in. Not in the one required by the rank of the operation.

Math itself is pretty clear on these issues and I think it would be fairly easy to program them correctly.

I know the dyslexia problem. It's a life long companion for me too. I have to say, I like the newer calculators though, because even if they don't get this rule, they show you what you have typed so it is way easier to spot errors. With all the mistypings I did on the old models that could do just one operation at a time and where you could not see what you had entered, I was a complete mess.

Edited Date: 2014-06-28 08:05 pm (UTC)

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My algebraic calculator a TI-36 (which I rarely use) gives 50. Very disturbing that you have one that gives the wrong answer!

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Now that I think about it there was a discussion in Scientific American magazine, I think, about 20 years ago about some algebraic calculators which would give bad answers like this on chained operations. I guess that problem has not been eliminated completely.

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Just tried it on my calculator - it won't wait for the next, or for me to enter an = sign. I plug in 7+7 and I get 14, before I even can press / by 7.
In order for it to work, I have to do this:

7/7 =1
7x7=49
1+7+49-7 =50

And I have to press "clear" really hard between calculations. But it's also a dirt cheap basic calculator provided by the government. Not a fancy one.

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The old ones from about 15 years ago all do that. If you know it, you can always insert brackets to make up for it and it is not much of a problem.

The true algebraic ones usually have the rule implemented.

ETA: And I think even the newer normal ones for school do. I checked with a current TI36 (but not pro) from a tutoring kid and it does it perfectly fine.

Edited Date: 2014-06-29 12:31 pm (UTC)

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The new cheap one's don't - because the one I recently got through work comes up with 56, unless I separate out the calculations. Granted, I rarely if ever have to do complicated algebraic equations. And if I do - it's in excel.

I rarely use the calculator for them.

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Yep, I usually use matlab for algebra. My calculator can't do it. You can enter a string of calculations but you can't calculate with letters.

I kind of would like to have one of those cool algebraic graphical calculators, but they are not exactly cheap considering that every cell phone has more power than they do these days.

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Yeah, as my cousin stated - this problem was a really good test of calculators. Excel is your friend. Except Excel automatically rounds up, which drives my co-workers crazy.

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Excel is good for most stuff, but in some labs you are not allowed to use it because weirdly enough it's results are not always reproducable. If you transfer files between computers, the data can change depending on settings.

For some uses in the pharmaceutical industry it's explicitly forbidden to keep the records in excel for this reason.

You can make it round correctly, but its a bit of procedure for such a simple thing.

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I've discovered that as well. In my industry it's fine - procurement of railroad environmental engineering, construction and consulting services. But I've had to double check it on the rounding and had to turn off the rounding feature. Often the consultants that I negotiate with - don't do this, which means their figures are always slightly off.

That's why I think it's important to understand the calculations that EXCEL is completing so you can do it separately if required. Between you, catcuswatcher, and my cousin, I finally understood why 50 was the correct answer. Thanks for that by the way.

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Thank you! Otherwise I would have remained confused. Another person online answered 56, and said there are no brackets - he did it the same way I did it.

My second cousin on FB posted this link to "Order of Operations" = http://www.mathgoodies.com/lessons/vol7/order_operations.html

Just reading it gave me a headache. The rules are so arbitrary and don't make a heck of a lot sense.

I think the problem is most mathematicians think in concrete terms. My cousin for example (not the second-cousin), David, who is a nuclear physicist, can't really read novels - he just sees words on paper. But with math - he sees the equations in his head, they make sense. While you have to explain a mathematical equation to me, otherwise all it is is a bunch of meaningless symbols.

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beer-good-foamy.livejournal.com

Yeah, math is tricky that way. Do the calculations in the wrong order and you can end up anywhere...

One of my favourite stumpers:

Three salesmen share a hotel room costing $25/night. The next morning, they each hand the bellboy a $10 note. He runs down to the reception with the $30, gets $5 in change keeps $2 as a tip and hands $1 in change to each salesman.

So each salesman paid $9, times 3 = $27. Plus $2 for the bellboy, making a total of $29.

...Where did the thirtieth dollar go?

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dlgood.livejournal.com

There is no thirtieth dollar.

Each Salesman paid $9. $10 spent, with $1 returned as change) $25 of those dollars went to the hotel, and $2 went to the Bellboy.

The text of the last sentence makes it appear as if the 2 dollars should be added to the 27, when it is actually split out....

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beer-good-foamy.livejournal.com

I know, but it sounds like it makes sense... It's a deliberate mislead.

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Explains why mathematical word problems always confused me. ;-)

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frenchani.livejournal.com

There should be brackets!

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My thoughts exactly. I discussed this with a cousin on FB, who is a brilliant mathematician. He told me that it is basically a snobby math trick. If you know the "rules" you get it right and they assume of course everyone remembers the rules.

Then he goes on to explain, how according to the rules, you do what is in the brackets first, if there are no brackets, you do the multiplication and division first, then plug in to the formula adding from left to right.

See? This in a nutshell was why I hate math, and card games. LOL!

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In German we call it the "Punkt vor Strich" rule. It means dots before lines.
So multiplication (.) and division (:) need to be done first, if there are no brackets indicating otherwise. Calculators don't use the rule automatically, excel does.

ETA: Apparently in English the rule is called PEMDAS rule (The letters standing for Powers, exponentials, multioplication, division, addition substraction.

But the order should not matter for the pairs of the same rank (like multiplication and division)and even the calculators get that exponentials and powers are done before the rest (weirdly, since they don't get the devision, multiplication thing).

Edited Date: 2014-06-28 06:25 pm (UTC)

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Here's why I got confused:

If I do the multiplication and division first:

7x7= 49 /7 = 1, then 1+7+7 -7 = 8.

Which is not 50.

So what you should have said is multiply, get a total, divide, get a total, then plug those totals into the formula thus:

7 (+1)+(49)-7

Makes so much more sense.

Edited Date: 2014-06-28 10:08 pm (UTC)

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but 7x7 and 7/7 are linked with a + so it is clear that 49/7 can't be in there, no?

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Not unless I'm thinking of it in those terms. I wasn't. This gets into how differently people interpret and think about things.

So when people on FB said "do the multiplication and division" first then add and subtract from left to right, they made the assumption that I was thinking in the same terms they were. It was obvious to them - because that's how they were thinking.

But I read it as - oh you do the mulitiplication and division first, thus : 7x7/7, then you add and subtract from left to right.
I'm not thinking of a plus sign as a connector between the division sign. Also, once you tell me that the multiplication and division must be done first - you are changing the sequential order of the numerical sentence. So, I try to group it logically by how it was conveyed - which for me is, oh okay, multiply and divide this first, then add and subtract - that is after all what was said. What you didn't say: divide. Multiply. Plug in. Compute left to right. Which would have been clearer to someone who doesn't think of it the same way.

I do a lot of communicating for a living - where I have to explain things that are obvious to one group of people to a group who has never seen or doesn't know anything about it. The mistake is thinking what is obvious or logical to you is going to be for someone else. It never is.

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Yep, science can be a different language at points. Once you know the vocabulary it's clear as day and leaves very little room for interpretation. But in the beginning it just looks insane.

It's the same for me and programming languages. I always have a phase, where I'm going half mad,trying to get their logic.

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Law is similar - it's a whole different language, takes a while to get it down. I'm constantly interpreting it for people. Same with engineering, railroad or industry specific languages, and well net-speak. Not helped by the fact that words, phrases, numbers, and abbreviations have different meaning depending on which industry, field, or business you are working in.

For example?

ETA?

On the internet it means - edited to add. In business it means - Estimated Time of Arrival.

Or RFP? In business it means Request for Proposal. For some people - Red Frigging Print.

I've realized that when you are communicating with someone outside your field of expertise - you need to find a way to explain it in terms that make sense to them. It's not as easy to do as it sounds. It's to a degree what I've done for a living - explaining to the lay-man, what a lawyer, IT, engineer, or specialist are trying to say.
And of course most of these people think - "well it's obvious, everyone should get it. Or they should learn it. I shouldn't have to explain myself." Which results in miscommunication, and unnecessary tension. I think part of the problem - is it has become so obvious and so routine (they do it every day that it second nature to them), that it doesn't make sense that someone else doesn't see it or get it.

I'm training a guy at work, bright guy, who is a Russian immigrant and speaks English as a second language and came from a different industry and business. I have to realize that what is obvious to me, won't be to him. So I told him up front - there are no stupid questions. And I constantly remind myself to be patient. Not to make assumptions. It's hard.

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