In my internal assessment, type 1, I was given Lacsap's Fractions task. To do my calculations I used a TI84 graphic calculator. To type the I.A I used Apple's Pages, Microsoft Excel 2011 and Microsoft Word 2011.
Lacsap's Fractions
To find the numerator of the sixth row I looked at the difference between each of the numerators. 1 1
1 32 1
1 64 64 1
1 107 106 107 1

1 1511 159 159 1511 1
Row Numerator Difference between numerators nnn1
1 1 1
2 3 2
3 6 3
4 10 4
5 15 5
6 21 6
7 28 7
From this table one can notice that the difference between each numerator on each row is always d+1, where d represents the difference between the two previous rows. The equation representing this is: un=un1+(d+1), where un represents the numerator you are looking for, n is the row number and un1 is the numerator from the previous row. Therefore to find the numerator of the 6th row I did:
u6=15+5+1
u6=21
After that, I plotted a graph doing numerator vs. row:
The relationship between the numerator and the row is best described by the equation of the line:
y=0.5x2+0.5x
The equation is quadratic and can be used to determine any numerator at any row. In the equation, x stands for the row and y represents the numerator. To prove the equation right, I chose three random points:
A (2,3), B (3,6), C (4,10) and plugged it into the equation y=ax2+bx+c
3=a22+b2+c
6=a(32)+b3+c
10=a42+b4+c
3=4a+2b+c
6=9a+3b+c
10=16a+4b+c
3610=4219311641abc 36100.510.53.562.5683=abc
abc=0.50.50
Therefore the line equation for the numerator is 12n2+12n=u

The numerator (u) happens to always be bigger than the denominator (v) no matter what row (n) it is present on, therefore one can conclude that the n, v and r are all...
...Lacsap’sFractions
The aim if this IA is to investigate Lacsap’sFractions and to come up with a general statement for finding the terms.
When I noticed that Lacsap was Pascal spelt backwards I decided to look for a connection with Pascal’s triangle.
Pascal’s triangle is used to show the numbers of ‘n’ choose ‘r’(nCr). The row number represents the value of...
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Math SL PortfolioLacsap’sFractions 
Type 1: Investigation Portfolio
Greenwood High (An International School) 




Table of Contents:
Introduction……………………………………………………………………………………………………..……..…...Page 2
Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3
Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7
Finding...
...In Lacsap’sFractions, En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately, therefore to find the general statement, two different equations, one for the numerator and one for the denominator, must be found. Let M=numerator and let D=denominator so that En(r) = M/D.
To find the numerator for any number of Lacsap’sFractions, an equation must be made that uses the row number...
...Lacsap’sFractions
Laurie Scott
SL Math Internal Assessment
Mr. Winningham
9/5/12
Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern.
Pascal’s Triangle
n=0 1 
1 0 
2 3 
3...
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Yao
Cia
Hua
Mathematics
SL
LACSAP’SFraction‐
Portfolio
Type
I
LACSAP’SFractions  Math SL Type I
Name: Yao Cia Hua
Date: March 22nd, 2012
Teacher: Mr. Mark Bethune
School: Sinarmas World Academy
1
Yao
Cia
Hua
Mathematics
SL
...
...Exploration of Lacsap’sFractions
The following will be an investigation of Lacsap’sFractions, that is, a set of numbers that are presented in a symmetrical pattern. It is an interesting point that ‘Lacsap’ is ‘Pascal’ backwards, which hints that the triangle below will be similar to “Pascal’s Triangle”.
11111...
...Mathematical InvestigationLacsap’sFractions
The focus of this investigation is surrounding Lascap’s Fractions. They are a group of numbers set up in a certain pattern. A similar mathematical example to Lacsap’sFractions is Pascal’s Triangle. Pascal’s Triangle represents the coefficients of the binomial expansion of quadratic equations. It is arranged in such a way that the number...
...Lacsap’sFractions
IB Math 20 Portfolio
By: Lorenzo Ravani
Lacsap’sFractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’sfractions. The goal of this portfolio is to ﬁnd an equation that describes the pattern presented in Lacsap’sfraction. This equation must determine the numerator and the denominator for every...