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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