Lacsap's fractions
Yao 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 mainly on finding the relationship between the number of row n and the numerator N and also the relationship between the element of a row r and the denominator D . Through this, a general statement base for En (r) on N and D are suppose to be stated and explained. For this task various technologies, such as Geogebra, MathType and calculator, are needed in order to produce a more organized piece of work and clearer graphs and diagrams.
Finding The Numerator In The Sixth Row:
In order to find the sixth row of this of this triangle, a pattern must firstly be found.
As it is seen from the diagram on the above, the pattern shows that, by adding 1 to each of the difference between the 2 previous numerators, this will equate the numerator of the next row.
For example: (using the first 2 numerators)
Difference: 3 – 1 = 2
The following numerator: 2 + 1 = 3
2
Yao Cia Hua Mathematics SL LACSAP’S Fraction-‐ Portfolio Type I
There is also another way of looking at these patterns. If the difference between the
2 previous numerators is already known, the following numerator can be found by summing the difference and the value of the current numerator, finally adding 1 .
For example: (using the first 2 numerators)
Difference: 3 - 1 = 2
Current numerator: 3
The following numerator:
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 mainly on finding the relationship between the number of row n and the numerator N and also the relationship between the element of a row r and the denominator D . Through this, a general statement base for En (r) on N and D are suppose to be stated and explained. For this task various technologies, such as Geogebra, MathType and calculator, are needed in order to produce a more organized piece of work and clearer graphs and diagrams.
Finding The Numerator In The Sixth Row:
In order to find the sixth row of this of this triangle, a pattern must firstly be found.
As it is seen from the diagram on the above, the pattern shows that, by adding 1 to each of the difference between the 2 previous numerators, this will equate the numerator of the next row.
For example: (using the first 2 numerators)
Difference: 3 – 1 = 2
The following numerator: 2 + 1 = 3
2
Yao Cia Hua Mathematics SL LACSAP’S Fraction-‐ Portfolio Type I
There is also another way of looking at these patterns. If the difference between the
2 previous numerators is already known, the following numerator can be found by summing the difference and the value of the current numerator, finally adding 1 .
For example: (using the first 2 numerators)
Difference: 3 - 1 = 2
Current numerator: 3
The following numerator: