# Lacsap's fraction math portfolio

Lacsap's fraction

Ryohei Kimura

IB Math SL 1

Internal Assessment Type 1

Lacsap’ fraction

Lacsap is backward word of Pascal. Thus, the Pascal’s triangle can be applied in this fraction.

How to find numerator

In this project, the relationship between the row number, n, the numerator, and the denominator of the pattern shown below.

Figure 1: The given symmetrical pattern

(Biwako)

Figure 2: The Pascal’s triangle shows the pattern of

.It is clear that the numerator of the pattern in Figure 1 is equal to the 3rd element of Pascal’ triangle which is when r = 2. Thus, the numerator in Figure 1 can be shown as,

(n+1)C2

[Eq.1]

where n represents row numbers.

Sample Calculation

- When n=1

(1+1)C2

(2)C2

-When n=2

(2+1)C2

(3)C2

-When n=5

(5+1)C2

(6)C2

15

Caption: The row numbers above are randomly selected within a range of 0≤x≤5.

Therefore, the numerator of 6th row can be found by,

(6+1)C2

(7)C2

x = 21                                                   [Eq. 2]

and the numerator of 7th row also can be found by,

(7+1)C2

(8)C2

x = 28                                        [Eq. 3]

How to find denominator

Figure 3: The pattern showing the difference of denominator and numerator for each fraction. The ...