The aim if this IA is to investigate Lacsap’s Fractions 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 ‘and the column number represents the ‘r’ value. Eg. Row 3, colomn 2 = 3C2 = 2.
I noticed that all the numerators of the fractions in Lascap’s fraction (3,6,10,15) are also found in Pascal’s triangle. So I tried to see if I would get the denominator of the fractions by using the row as ‘n’ and the colomn (or element) as ‘r’. This did not work out because Lascap’s triangle does not have a row with only one element like Pascal’s does. To solve this I just added 1 to each row number. This gives me the formula[pic].
Now that we have found an equation to solve to numerator of the fractions, we now have to try and work out how to solve the denominator. As we already know the numerator, we can presume that there is some sort of relationship between this and the denominator.
I noticed that the difference between the numerator and denominator increased by one with each row I went down (1,2,3,4)
Because the denominators in one row are different from each other (row 3 = 7, 6, 7), it can be presumed that the unknown ‘r’ which stands for the elements/column will be part of the general statement.
Because the first and last element in each row is 1 (or 1/1) and no general statement is needed to find these, they can be ignored and erased from the triangle for now.
Row number (n) Difference between numerator and denominator in the 1st element (see   above)  1 /  2 1  3 2  4...
...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 to find the...
...Lacsap’sFractions
Laurie Scott
SLMath 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...
...
MathSL 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...
...INTRODUCTION
Lacsap’s triangleThe set of numbers in concern are basically an inverse of the Pascal’s triangle. These terms themselves are fractions which follow different series themselves. There is a specific function that can accurately predict the fractional numbers accurately. Using the graph plots we can calculate this function and predict the numbers accurately. The whole process for finding the adequate function would involve the use of different smaller...
...
Yao
Cia
Hua
Mathematics
SLLACSAP’SFraction‐
Portfolio
Type
I
LACSAP’SFractions  MathSL Type I
Name: Yao Cia Hua
Date: March 22nd, 2012
Teacher: Mr. Mark Bethune
School: Sinarmas World Academy
1
Yao
Cia
Hua
Mathematics...
...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...
...Jonghyun Choe
March 25 2011
Math IB SL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 1
1 1
Row 2...
...MathSL I.A:
Lacsap'sFractions
Introduction
In my internal assessment, type 1, I was given Lacsap'sFractions 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'sFractions
To find the numerator of the sixth row I looked at the difference between each of the...
685 Words 
4 Pages
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