IB Maths SL TYPE I Lacsap’s Fractions Portfolio Lacsap’s fraction Introduction: Lacsap’s fraction is a symmetrical triangle that has the following pattern in the first five rows The shape is similar to Pascal triangle. It has the same quantity of symmetrical triangle as Pascal triangle. And Lacsap is the inverse alphabet order of Pascal. These make me think about Pascal triangle and I made an assumption that elements in Lacsap triangle may have the same relationship as in Pascal triangle
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Pascal’s triangle. Another hint can also easily be noticed as Lacsap is exactly the backwards of Pascal. The goal of the investigation is to find the general statement En(r)‚ where En(r) is the (r+1)th element in the nth row‚ starting with r=0. An example of this would be . In order to develop the general statement for En(r)‚ patterns have to be found for the calculation of the numerator and the denominator. Figure 1: Lacsap’s fractions 1 1 1 3/2 1 1 6/4 6/4 1 1
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In Lacsap’s Fractions‚ when looking for a general pattern for the numerator‚ it can be noted that it does not increase linearly but exponentially. Numerators are 3‚6‚10‚ and 15‚ each preceding numerator added by one plus the row number. Using this general statement it can be concluded that the numerator in the 6th row is 21 (15+6)‚ and 28 for the 7th. Generating a Statement for the Numerator: To generate an equation for the numerator of the fraction‚ the fraction data must be organized and
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Exploration of Lacsap’s Fractions The following will be an investigation of Lacsap’s Fractions‚ 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”. 1 1 1 1 1 1 1 1 1 1 There are many patterns evident in this triangle‚ for instance I can see
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Lacsap’s Fractions IB Math 20 Portfolio By: Lorenzo Ravani Lacsap’s Fractions Lacsap is backward for Pascal. If we use Pascal’s triangle we can identify patterns in Lacsap’s fractions. The goal of this portfolio is to find an equation that describes the pattern presented in Lacsap’s fraction. This equation must determine the numerator and the denominator for every row possible. Numerator Elements of the Pascal’s triangle form multiple horizontal rows (n) and diagonal rows (r). The elements
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In Lacsap’s Fractions‚ 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’s Fractions‚ an equation must be made that uses the row number to find the numerator. Because the numerator changes depending on the row
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Fraction (mathematics) A fraction (from Latin: fractus‚ "broken") represents a part of a whole or‚ more generally‚ any number of equal parts. When spoken in everyday English‚ a fraction describes how many parts of a certain size there are‚ for example‚ one-half‚ eight-fifths‚ three-quarters. A common‚ vulgar‚ or simple fraction (examples: \tfrac{1}{2} and 17/3) consists of an integer numerator‚ displayed above a line (or before a slash)‚ and a non-zero integer denominator‚ displayed below (or after)
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Cia Hua Mathematics SL LACSAP’S Fraction-‐ Portfolio Type I LACSAP’S Fractions - 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 LACSAP’S Fraction-‐ Portfolio Type I Lacsap triangle is a reversed Pascal triangle. This task focuses
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In order to teach students the concept of equivalence when working with fractions with unlike denominators or finding equivalent fractions‚ there are some skills that the students must already possess. These are as follows: Students are able to both recognize and write fractions Students understand the ‘breakdown’ of a fraction where the top is the numerator and the bottom is the denominator Students must have some understanding of equivalence and what it means Students must be able to both
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Partial Fractions A way of "breaking apart" fractions with polynomials in them. What are Partial Fractions? We can do this directly: Like this (read Using Rational Expressions to learn more): 2 + 3 = 2·(x+1) + (x-2)·3 x-2 x+1 (x-2)(x+1) Which can then be simplified to: = 2x+2 + 3x-6 = 5x-4 x2+x-2x-2 x2-x-2 ... but how do we go in the opposite direction? That is what we discover here: How to find the "parts" that make the single fraction (the "partial fractions")
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