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Type I - Lacsap's Fractions


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The task itself gives an example as the following:

E5(2) = 15/9

The example means that 15/9 is the 2nd element (i.e. the second fraction from left to the right) in the 5th row. You may ask why the 2nd element is not 15/11 but 15/9. Because we don't take into account 1 and 1 at each ends of a row and this is the primary reason why we write (r+1)th element.

Another example would be E4(3) = 10/7. In this case, we look at the 4th row and the 3rd element (without including 1s at each end), and it corresponds to 10/7.

I hope it helps. =)

@KateKesler: This is an old post that I've made. I think it answers your question.

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Arent we suposed to take into account the 1s that are the sides ?

yes

I don´t know how to find the denominators of the 6th and 7th row, the ones that are in the middle :bawling: and i have to give this thing tomorrow

hey, sorry, you could've quoted my post so I get a notification and can reply much earlier. it's basically the same thing as the previous ones..but try to work out the denominator not row by row but diagonal by diagonal, it would be much easier then.

Desy Glau, Oh God, you have tons of patience to go through that over and over. thumbs up mate... :read:

lol, thanks.. I'm just sad those people who've finished the task don't go back here to help others.

we just got this portfolio at my school... its very difficult. we have figured out the numerator, but not the denominator, if anyone understands how to find it, please help!

it's actually simple once you see the pattern! read through this thread from the beginning, I'm sure I've posted all the necessary clues to find the denominator. if you still don't get it then ask again but be specific as I can't reexplain everything all over.

Hey

Just wanted to thank you for all the help. Got a great mark on this portfolio because of ur concise explanantions

Tip to everyone who still has to do it: Follow Desy's suggestion on pg.2 i think: it will definitely help you find the denominator

and GOOD LUCK!

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Hey guys, I think i have figured it out , but i got a ridicolous equation for the denominator, which works, but it still is ridicolous......Does anyone think that a ridicolous (meaning its quite long) yet correct (since it gives me the exact values for each) equation will be graded well?

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I'm very happy to see all the help given while I'm not around!! :D +1 to everyone who have given great advice!

Hi all. I'm confused about the 1's on the sides. When I use the formula when n=5 and r=0 hould I be getting 15/15? Or does the formula not work for 1's because the numerator and denominator are unknown?

do not worry about the 1's when trying to formulate the general statement. after you've got the complete general statement, you'll see that it actually gives a fraction that can be cancelled and become 1. the formula must work with the 1's.

I have a quick question for anyone. I am trying to type up the sixth and seventh rows in Microsoft Word but I don't quite know how to. I have mathtype if that is needed. Can anyone help me?

Thanks!!

you can just use the equation feature in Ms.Word if you know how to, instead of MathType.

are you familiar with tabs? if so, it'll be easier to use them. otherwise use table like St Silver suggested!

I am kinda stuck on where to go from here on the Lascap's fraction's math portfolio..

Any help on the sequence? I think it is x/(n + 1 – x) but I'm not sure.

what do you mean by "any help?"??? lots have been given already... please read the whole thread, it should help. otherwise please spend more time and focus on reading and read carefully... if you still don't understand then ask, but please ask specific questions (like on certain parts). I will not answer questions like "can anyone explain how to do this IA?" because the answers have been stated in this thread. more specific questions like "how to formulate the general statement after noticing the pattern?" or "how to do the graph?" or "what are the limitations?" are likely to get more answers.

and what is x? I've seen some other people using x too. please DON'T use x. use n and r.

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Hey guys, I think i have figured it out , but i got a ridicolous equation for the denominator, which works, but it still is ridicolous......Does anyone think that a ridicolous (meaning its quite long) yet correct (since it gives me the exact values for each) equation will be graded well?

lol how long is it? if you can, please simplify the equation. it'll be best to simplify anything that is simplifiable (if that's even a word...). mine is a quadratic involving two variables. if you get it right but it's not in the simplest form yet, the reader/examiner might not be as happy as seeing a correct general statement in the simplest form... well if the rest of your paper is great, I think they will still give you the mark. but if the rest of your paper is a bit...errr...then you might get only 1 out of 2 marks in criterion F. and maybe some other criteria.

Is it just coincidence that "Lacsap" is "Pascal" spelt backwards, or does this have something to do with solving it?

interesting!! I've never noticed that :P

hmmm well I think it's related to the Pascal's triangle only as the pattern is symmetrical. that's the only common thing I see... but I'll look into it, I'll try to find out if we could use Combination instead.


I will rep (+1) anyone who gives helpful advice in this thread!

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Uhh, do we really need to get the general formula for the denominator? Which part did it actually say that?

Is it for the general statement of En®?

you definitely need to, unless you don't want to score well in this IA...

yeahh if you didn't find the general statement of the denominator, how could you find the general statement of En( r)?

Desy Glau, the thing is, mine will give you only the first n values of a sequence (half), then you just write the other half (because it finds all). Mine is a quadratic but it also involves a negative summation, thats why i think its wrong, cause maybe its over complicated.

:S try to find it with another method?

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There are two ways to figuring out the denominator:

1) The first way is just a pattern. Since it's not a formula or anything, it won't answer the task, but can help you find the 6th and 7th row:

The denominator of each row follows the same pattern as the numerator. It increases by 1, 2, 3, 4 and so on. Each "skew" column starts by adding 1 to the denominator, but you have to take into account that 1 in, for instance, row 3 actually is 6/6 and not 1, as the numerators are all supposed to be the same within the rows.

Now try to work out row 6 and 7.

2) Now that you've got more rows to base your general statement on you should try to figure out the difference between the denominator and the numerator. See any patterns? That's all I'm gonna say, because it is a MEGAclue. This is an alternative method to the one where you use linear regression to find an equation for each column, and then combine them. Everyone in my class is doing it that way, so I'm really worried that all our grades will be moderated...

Anyway, I've tried both methods and got the same result, yay :)

Edited by miamonique
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@ Desy Glau: should I include the method using technology as a means of checking my results? Or will this be "too much"?

Also, I read your comment on the scope and limitations. Is it enough to write about negative numbers, rational, irrational, real, zero, etc? I read something about how the scope and limitations are a way for students to prove their skills or something! :dontgetit:

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I think this is the easiest way:

1. Find the pattern in the difference between the NUMERATOR and the DENOMINATOR for ALL the elements listed.

2. You should see a pattern when you've made a table of the differences. Find a simple formula for the difference.

3. The general statement can be constructed this way

(formula for numerator) divided by (formula for numerator MINUS formula for difference between numerator and denominator)

These are quite detailed steps. We can't give you the entire solution, so you've got to TRY your the numbers you've been given. Look for patterns and do small twists to what you've already done.

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I'm sorry but if we are to explain everything from the beginning, we'd be self-repeating. So, as a starting point please consider the very first pages and the posts. Post #25, made by Desy, has helped many of us to find the denominator. Here's the link for it:

Good luck with your task!

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Hi, sorry. I am really having trouble with the second half of the assignment. The En® part. I don't understand when they ask for a general statement. Do they want a formula? If so, can anyone help guide me towards how to find that formula? I know how to get the numerator but the way i get the denominator is kind of tricky. HELP!!!

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Guys, I'm really clueless on how to make a general statement for the relationship between the row number and the numerator. I tried plotting and all but I don't know what to do with it.. Tips please. Thank u. :)

If you're using geogebra 4 you should mark the list of your coordinates and use Two Variable Regression with a 2'' polynomial.

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Hi, sorry. I am really having trouble with the second half of the assignment. The En® part. I don't understand when they ask for a general statement. Do they want a formula? If so, can anyone help guide me towards how to find that formula? I know how to get the numerator but the way i get the denominator is kind of tricky. HELP!!!

Yep, they want a formula in which if you change n and r, you'll get the value you need. For the denominator, have you tried stat plotting the rows against the denominators? That's one of the first steps I took to solving it.

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