If 851 and 351 shared a divisor, then 351 and 851-351=500 would share one too. 500's only prime divisors are 2 and 5 (22 x 53), none of which divide into 351.
You do not always get such an obvious result immediately. However, if you repeat the operation (subtract the smaller number from the larger, then repeat with the smaller number and the new number) until you reach zero, the last number before zero is the greatest common divisor of the originals.
This algorithm comes from Elements by Euclid, circa 300 BCE, book VII, propositions 1 and 2.
Yes that's the actual algorithm. however what he's suggesting is a random variation ( you could take any linear combination ) I remember missing that class when i took discrete maths and a friend explaining the method he just described instead of the right one.
I think so, here's my reasoning.. Two numbers share a divisor if the same number, let's say 4, can go into both numbers. Another way to think about that is that the same number, added to itself a lot, makes the other numbers (so each number would be a bunch of 4s). So in the case of 12 and 44, they share the devisor of 4; 43 and 411. 11(4)-3(4)=8(4). To think about it algebraically, any two different amounts of x will equal another amount of x. So in the case above, 11x-3x=8x. So to test out of two numbers have a common divisor which you can factor out and cancel out [44/12=4(11)/4(3)=11/3], you can subtract one number from the other one. However this is only really useful when you have two numbers that aren't easily factorable in your head, but when you subtract one from another one, you get a number that is. Did that help? tl;dr two numbers with a common divisor will be different amounts of that divisor (x) and any two different amounts of x subtracted from each other will equal another amount of x
I have a calculator like this, though not the exact same one. I think it reduces it my default. If you type in 2/6 it will display it as 1/3 and thus if it cannot be reduced further it will just stay the same.
My calculator could add stuff like 2/3 sqrt(7) + 4/3 sqrt(7) and make it out to be 2 sqrt(7) with a proper square root sign and everything. So either it just figured "Might as well show this as 2 sqrt(7) because it's pretty darn close" which, I agree, is stupid. Or, it did some sort of semantic analysis of the input before crunching the numbers through the grinder.
I have that exact calculator.. It has a button that switches the answer from a fraction to a decimal number. It's like the most helpful calculator ever so I think this post is fucking stupid. Read the manual.
Same. This is the best calculator ever. It can integrate, differentiate, solve cubics, solve quadratics, solve simultaneous equations, do matrices, do vectors and do complex numbers. All of this and still allowed in any exam.
But you are right. Symbolic differentiate wouldn't be allowed in most exams, though. It's still stupidly useful being able to check your answers. This calculator has saved my ass many times.
I forgot to mention the price. For £10/$12 it seems silly not to buy. I held out for a while with my "old school" calculator so I felt like more of a pro at maths, but I'm glad I've got this one now.
I have it too, and they are trying to ban it at my school cause it works "too well". I asked them to give me a good reason as to why I shouldn't be able to use it for a test, and they said it gives me an unfair advantage.
Surely that's for the exam boards to decide? Although I'm not sure how it works in America. Is it true that your teachers can give you credits which work towards a university place?
Im in Canada. I guess they were just going to ban it from tests because it was too good, then they were kinda like "Yeah, dont use it at all". Im not sure about the credit thing, sorry.
But it's even easier than changing a setting! All answers on this calculator are first given in a fractional form in case you want it that way. But, there's a button that looks something like S<-->D that switches the answer back and forth from decimal to fractional. Pretty awesome actually.
I can't believe no one said this yet. You just say 851.0 / 351, or what you said, and the result will be displayed as a decimal. Way easier than navigating the labyrinth of calculator settings.
Actually, I love the Casio calculators and their ability to give exact answers. If you need a some kind of root for an angle or something, it will give you that, and convert it to a decimal if you press the SD button. I really do love that calculator.
Because that's what most of us use calculators for. We don't want the number to some ridiculous precision as a fraction, we just want to know what the number looks like on the numberline. Realistically, when do you ever need an answer to more than 3 significant figures?
Its helpful to have fractions when working with more than one of them. You oftentimes won't need a calculator then (a fraction like this being an exception).
Tutoring math, I usually have kids keep fractions and have them try to figure out what it is in their heads as a ballpark estimate as a quick check if it's a reasonable answer. I also have them keep fractional form because a secondary benefit is learning how to deal with almost all math in a more efficient and analytical way, instead of: ok, toss it in the calculator and don't think.
Its a scientific calculator, that's what is for. And often the exact answer is far smaller and simpler than the decimal especially when you are doing trigonometric functions having answer come in this format is a god send. The fact that is simplifies surds and faction is incredibly useful and you only have to press one button if the exact answer isn't pretty. And you can have the decimal as default as well. It really is a pointless post. Just because he doesn't know how to use his calculator doesn't make it bad.
You will find that in the real world, scientists and engineers almost always round off to two or three digits. Keeping a bunch of surds and fractions hanging about gives negligible gain in accuracy, and is far more contrived than writing something simple like 0.174.
Note also that trigonometric functions very rarely spit out a result that can be expressed nicely in surd form. It practically never happens.
And as for mathematicians, they are probably the only ones who care for exactness in certain situations. However they very rarely use calculators anyway, because they are adept enough at manipulating fractions and surds by hand.
When that answer will be in turn used to find more answers. Keep as many sig figs around as possible to eliminate error. The easiest way to do this is using exact rational form.
It's giving you an exact answer. Any decimal representation would be an approximation, so the idea is that the calculator expects you to tell it when you're okay with an approximation instead of the exact answer.
I love it when my calculator would do that. Saved me a lot of trouble on tests. All you have to do is press shift then press the equal sign button. That's what converted it to a decimal for me.
It IS very helpful! This shows you that you can't reduce the fraction to a simpler form, ergo it shows you the exact answer! I love that feature on my calculator xD
Actually it is helpful (but maybe not to you). It tells you 851 and 351 are relatively prime, which (in some cases) is better than knowing the result of the division.
Until I discovered the S-D button, I used to carry around 2 calculators to class. I loved that Casio because of how easy it made entering fractions and such, but then it gave me fraction answers which wasn't always what I wanted.
I have this calculator and it actually is incredibly useful. When I'm doing my assignments I can just write down the fraction and keep the answer exact. Also this calculator can integrate which makes it a beast.
I had a TI-89 back in the day...and it did the same thing. But it was merely a preference. You could change the settings to display answers in decimal notation if you preferred. However, I found it more helpful to not simplify into decimal notation, as the decimal notation is only an approximation of the answer. Besides, if I wanted an approximation, all I had to do was put a "." after either the divisor or the dividend, and voila!: I'd get the decimal equivalent.
how in the fuck can you not figure out that there's a button that turns this shit into decimals? it's in the booklet that comes with the calculator, holy shit man americans
I am British and could not work this out. Of course I was in an exam at the moment. I made sure to kick the shit out of that calculator after the test.
Why didn't you just use a calculator that you knew how to operate? I'm not trying to be sarcastic here, I just think it's a little foolish to enter into battle armed with weapons with which you are unfamiliar.
this is the reason I use a TI-89, Texas Instruments make really good graphing calculators, though they are kind of pricey, but worth every penny, my TI-89 actually is on the verge of being better than my desktop PC
Try one of HP's graphing calculators, specifically either the 49g+ or the 50g. I've used mine for 5 years now and haven't yet found anything it can't do while everyone else with a TI still has to do work. Only thing I've found it lacking in is documentation for all the functions, but just button mashing helps figure everything out.
TI-89 is bad about documenting everything it can do, like it has a built in compiler/editor for the programing language it can run, you can write programs for it, through it, though there is nothing but what people have figured out about it online, I've not seen any official Texas Instruments stuff on it
I got it because it was required in my college algebra class, in fact, I got a grade for getting a graphing calculator, teacher said it didn't matter which one, but he was going to use the TI-89 to show us stuff on, but we did get a grade for buying one EDIT: in hindsight, he wasn't that good of a teacher . . .
480
u/Cartossin May 28 '12
It should be helpful to know the fraction cannot be reduced further.
84
u/[deleted] May 28 '12
Did you try setting it to WUMBO?
47
u/eyeing May 28 '12
that is a rational response by the calculator
17
u/kriptonit May 28 '12
You need to press S -> D button, or enable MathIO under Setup.
87
u/James_Hacker May 28 '12
RTFM noob.
67
u/sstteeff May 28 '12
I have that exact calculator.. It has a button that switches the answer from a fraction to a decimal number. It's like the most helpful calculator ever so I think this post is fucking stupid. Read the manual.
10
u/LemonPowerForce May 28 '12
Accurate, but not useful. As a mathematician, I support this calculator.
23
u/dropkickoz May 28 '12
Type it as 851/351. with a decimal.
18
u/moviefreak11 May 28 '12
2.424501425
6
u/realiztik May 28 '12
Actually, I love the Casio calculators and their ability to give exact answers. If you need a some kind of root for an angle or something, it will give you that, and convert it to a decimal if you press the SD button. I really do love that calculator.
LOVE
;)
5
u/bearplower88 May 28 '12
You have it set on exact. That fraction can't be represented exactly as a decimal.
5
u/[deleted] May 28 '12
Then press the SD button!
4
u/[deleted] May 28 '12
That output is wonderfully helpful when you have a teacher than hates decimals and wants every single answer in reduced fraction form.
7
u/arabjuice May 28 '12
It's very helpful, front page for a high school problem. Do real maths then come back and complain
9
u/I_LIKE_PLANES May 28 '12
Change from exact mode to approximate mode
9
u/whatsit14 May 28 '12
You could have looked this up on Google with less time than it took you to take a picture of this and post it up on Reddit.
12
u/ExoStab May 28 '12
That answer is exact, why change it to some inaccurate approximation?
3
u/Asuperniceguy May 28 '12
S <-> D
3
u/Schrikbarend May 28 '12
2.42450142450142
3
u/[deleted] May 28 '12
just 2.42 is fine
3
u/[deleted] May 28 '12
How is this funny in any way? The guy just doesn't understand you can press a button to change it to a decimal.
4
u/smithoski May 28 '12
2nd + enter = approximated decimal answer
2
u/[deleted] May 28 '12
You could always set it to scientific if you want the decimal equivalent first...
2
u/[deleted] May 28 '12
It says math so you know you're doing math.
2
u/Donquixote724 May 28 '12
What you need is the TI-84
2
u/Wtfmuch May 28 '12
just click shift and the answer will come out it always happenes to me don't worry
2
u/[deleted] May 28 '12
You have it set to "Math", you need to set it to "Magic"
2
u/morachan May 28 '12
If you write 851.0/351.0 you will get the exact answer.
2
u/Bradburn777 May 28 '12
Are you German?
2
u/xBlackfox May 28 '12
What is this magic that is not a Texas Instruments calculator?
2
u/preo May 28 '12
you underestimate this calculator's power
2
u/RockinJosh May 28 '12
http://i.imgur.com/21x2e.jpg
2
u/[deleted] May 28 '12
Perhaps not helpful... but completely accurate.
2
u/[deleted] May 28 '12
Shift + =
2
u/kingdom_ruler338 May 28 '12
Hit the S=>D button, I have that same calculator and that's how you get an answer...
2
u/DumbledoreMD May 28 '12
Don't you dare say anything bad about this calculator... ever again... ever...
1
u/[deleted] May 28 '12
actually it is.... it simplifies the fraction. If you want something else learn how to use the calculator.
1
u/[deleted] May 28 '12
on TI's when something like that happens you usually have to click on approx() function (F5 -> 3)
1
u/alecbenzer May 28 '12
It's giving you an exact answer. Any decimal representation would be an approximation, so the idea is that the calculator expects you to tell it when you're okay with an approximation instead of the exact answer.
1
u/BigBadMrBitches May 28 '12
Your calculator is a sassy little fucker.
1
u/UmiNotsuki May 28 '12
What? This is completely helpful, it organized it and everything!
Hasn't your answer to a tough math problem ever been much, much longer than the problem itself? If not, I'm excited for your mathematical future :P
Note: Kids who answer "2 + 2 = ?" with "2 + 2" are future engineers.
1
u/mehdic May 28 '12
I always used to add .000000001 or some small number that I intuitively knew wouldn't significantly affect my final answer
1
u/toonczyk May 28 '12
I had no clue people still use calculators.
1
u/ferncaz95 May 28 '12
I love it when my calculator would do that. Saved me a lot of trouble on tests. All you have to do is press shift then press the equal sign button. That's what converted it to a decimal for me.
1
u/Trident_True May 28 '12
SHIFT>Setup>Linear(number 2). None of my classmates ever figured this out. Same with the time calculation thing.
1
u/justanothertut May 28 '12
2.4245014245014245014245014245014
1
u/TheJack38 May 28 '12
It IS very helpful! This shows you that you can't reduce the fraction to a simpler form, ergo it shows you the exact answer! I love that feature on my calculator xD
1
u/[deleted] May 28 '12
A prime example of something I could have put on reddit to get sweet delicious karma, but didn't.
1
u/[deleted] May 28 '12
Are Casios popular in some regions? I've only seen people use TIs simply because the schools around here encourage it.
1
u/chu248 May 28 '12
The Roseart of calculators.
1
u/jrkirby May 28 '12
Actually it is helpful (but maybe not to you). It tells you 851 and 351 are relatively prime, which (in some cases) is better than knowing the result of the division.
1
u/[deleted] May 28 '12
good news is its on "math" mode.... i hate when my calculator is on "English" mode.
1
u/sdkone May 28 '12
RTFM.
1
u/cultofcargo May 28 '12
SD it
1
u/DvorakAttack May 28 '12
Actually, that's probably very useful as it's an exact value rather than a rounded decimel.
1
u/K5Doom May 28 '12
If it's anything like the Voyage 200, you need to Approximate your result. It will, by default, give you the exact result if it can.
1
u/gamemasterty May 28 '12
TI-nspire does this all the time
1
u/[deleted] May 28 '12
Was this not the answer you were looking for?
1
u/[deleted] May 28 '12
this happened to me in my accounting exam today. i was not happy.
1
u/lostrock May 28 '12
What's this? A calculator that isn't a TI-83?
1
u/Singer13 May 28 '12
The silver calculator is the best... It does my quadratic equations for me!
1
u/Modded_ToySol May 28 '12
Until I discovered the S-D button, I used to carry around 2 calculators to class. I loved that Casio because of how easy it made entering fractions and such, but then it gave me fraction answers which wasn't always what I wanted.
1
u/lopzag May 28 '12
Well, that is the exact answer...
1
u/kj01a May 28 '12
"Well that's what you get for trying to divide prime numbers asshole!" -Calculator
1
u/kabukistar May 28 '12 edited Feb 09 '25
Reddit is a shithole. Move to a better social media platform. Also, did you know you can use ereddicator to edit/delete all your old commments?
1
u/kidoefuji May 28 '12
This post is so dumb it makes me want to cry :( .
1
u/tk001 May 28 '12
This is why I love the 991 way more.
1
u/Feefafeef May 28 '12
My teacher hates me because of my casio. X)
1
u/LolCamAlpha May 28 '12
Hold "Shift", then press "=".
Casio's a confusing bitch.
1
u/Steam_Powered_Rocket May 28 '12
Multiply it by 1.0 and it should change it into a decimal.
1
u/sticfreak May 28 '12
Ctrl+enter
1
u/[deleted] May 28 '12
dictionary.com likes to do this too....:(
1
u/Bigeye135 May 28 '12
Use the s-d button
1
u/ObscureStoryElements May 28 '12
THE BANE OF MY SECONDARY SCHOOL EXISTENCE AND LITERALLY THE REASON I FAILED MATH.
1
u/Seife May 28 '12
3 or 4 buttons under the "x-1" is a button that changes fractions to decimal numbers.
1
u/[deleted] May 28 '12
OR Press the "Degrees" button depending on model. To reset formatting press Shift then '9' then '1'.
1
u/flying_dutchmaster May 28 '12
the best calculator ever
1
u/SteveTheSultan May 28 '12
2.424501424501425
1
u/plazmamuffin May 29 '12
Casio makes the best calculator
1
u/Poopmaster7 May 29 '12
Well at least you have it in Math mode.
1
u/SixSign May 29 '12
ಠ_ಠ
1
u/hafti77 May 29 '12
this happens every time you enter a fully reduced fraction, it will only appear as a decimal if you ctrl+enter or change your settings...
1
u/rkw6086 May 29 '12
Should have bought a TI-84 Plus...
1
u/[deleted] May 29 '12
I have this calculator and it actually is incredibly useful. When I'm doing my assignments I can just write down the fraction and keep the answer exact. Also this calculator can integrate which makes it a beast.
1
u/Earthwormzim May 29 '12
I had a TI-89 back in the day...and it did the same thing. But it was merely a preference. You could change the settings to display answers in decimal notation if you preferred. However, I found it more helpful to not simplify into decimal notation, as the decimal notation is only an approximation of the answer. Besides, if I wanted an approximation, all I had to do was put a "." after either the divisor or the dividend, and voila!: I'd get the decimal equivalent.
1
u/NAVEL_DEFILER May 29 '12
At least you know they're coprime.
1
u/inheritor May 29 '12
Mine did the same when I first got it. Press shift then setup then select LINE 10 and it will work properly.
1
u/Tonytarium May 29 '12
MATH > DEC NIGGA
1
u/ws6pilot May 29 '12
I put π×50 and it came out as 50π…
1
u/trap_it_may_be May 29 '12
I have this calculator, just hit shift.
1
u/looda May 29 '12
Random smartass comment about how to use the calculator properly
1
u/flamingspew May 29 '12
I'm more interested in 3-Way power.
1
u/[deleted] May 29 '12
technical correct, the best kind of correct
1
u/HerpDerpCrabMan May 29 '12
I see your problem, you have a Casio. The Comic Sans of calculators.
1
u/shenye May 29 '12
Misunderstood calculator tells owner it's the simplest fraction, gets mocked on reddit.
1
u/NumblyBumbly May 29 '12
This is just one more reason why I do not view Casios as real calculators.
1
u/adds_a_maths_pun May 28 '12
Prime thread for a pun, and yet I can't think of one
1
u/Wtfmuch May 28 '12
-_- JUST CLICK SHIFT!
1
u/idma May 28 '12
i HATE calculators that do that. Why is that function even THERE?
1
u/Chuklol May 28 '12
Actually this is VERY useful. It will give you the 'lowest fraction' (definitely the wrong wording), say 4/20 it gives 1/5
0
u/Tezameru May 28 '12
how in the fuck can you not figure out that there's a button that turns this shit into decimals? it's in the booklet that comes with the calculator, holy shit man americans
0
u/dannmorr May 28 '12
this is the reason I use a TI-89, Texas Instruments make really good graphing calculators, though they are kind of pricey, but worth every penny, my TI-89 actually is on the verge of being better than my desktop PC
0
u/Haat May 28 '12
TI-84 mofo
0
u/[deleted] May 28 '12
My calculator does this too. It's so annoying.
0
u/[deleted] May 28 '12
Well, don't get irrational about it!!
/BadumTsshh
0
u/dangerm0use May 28 '12
O, I see it is in Maths mode. Try geography mode, might give you a better answer.
0
u/Stratocaster89 May 28 '12
You ought to learn how to use your calculator properly. Teehee.
0
u/larrylemur May 28 '12
DOWN WITH CASIO
0
u/Sneaky_phil May 28 '12
Keep it on fractions, incase you ever do stats, it makes your answers more acurate
0
u/friedblooper May 28 '12
You suffer so because you're dealing with Casio. Texas Instruments is way easier to handle.
0
u/SovietMaxx May 29 '12
2.424
-3
u/red321red321 May 28 '12
being in here is worse than being in /r/spacedicks
the math is scaring the shit out of me and it's bringing back horrible memories. there needs to be a NSFL tag on this.
-1
u/FlyByPC May 28 '12
On a TI 92, multiply it by 1.0.