• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Lascap Fractions. 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

Extracts from this document...

Introduction

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.

image06.png

Generating a Statement for the Numerator:

To generate an equation for the numerator of the fraction, the fraction data must be organized and graphed. The table below shows the relationship between the row number and numerator being relative to an exponential function as the sequence goes on. N(n+1)-Nn

...read more.

Middle

6th:

N(5+1)-N(5)=N(5)-N(4)+1

N(6)-15=15-10+1

N(6)=15+6

N(6)= 21

7th:

N(6-1)-N(6)=N(6)-N(5)+1

N(7)-21=21-15+1

N(7)=42-15+1

N(7)= 28

This is only a supplement to the equation found in the graph above (N=0.5n2+0.5n). This pattern only tests the validity of the equation derived from the table because of both methods concluding to the same value.

Generating a Statement for the Denominator:

To examine the denominators in Lascap's Fractions, the values for the 6th row and their corresponding elements were put onto a table, and ultimately a graph. Showing a pattern, it was concluded that the denominator could be found with a general equation of D=r2-nr+r0.

...read more.

Conclusion

: D=22-(5)(2)+15=11

6th: D=22-(6)(2)+21=13

After knowing how to determine both denominator and numerators, the Lacsap's Fraction triangle could be filled out to the 7th row. image09.png

General Statement Overall:

After determining equations for both numerator and denominator and following patterns, all Lacsap's Fractions could be found with a general statement of:

En(r)= image00.png

=image01.png

Although proven for each separate category of numerator and denominator, the general statement can be concluded valid with these tests.

Finding X row:

5th row 4th Fraction: E5(4)=image02.png

=image03.png

8th row 3rd Fraction: E8(4)=image04.png

=image05.png

Limits and Conditions:

Other than the Nth row having to be greater than 0, there is no limit to this equation as it can find any fraction within Lacsap's Fraction Triangle.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Lacsap's Fractions : Internal Assessment

    = ... E6 (5) = Using the calculations above, the sixth row comes out as shown below Knowing that "1" was discarded while doing the calculations, the "1" must be added back into the row at the beginning and the end. The entire row is shown below: The seventh row is also found by doing the same as above: E7 (1)

  2. Continued Fractions

    1.618033989 1.618033989 0.0000000000 31 1.618033989 1.618033989 0.0000000000 32 1.618033989 1.618033989 0.0000000000 33 1.618033989 1.618033989 0.0000000000 34 1.618033989 1.618033989 0.0000000000 35 1.618033989 1.618033989 0.0000000000 According to the graphs, as the value of increases, will continuously fluctuate but start to stabilize when =8.

  1. This essay will examine theoretical and experimental probability in relation to the Korean card ...

    Starting with October, probability of winning with this hand is split into two different ways. First one is when player 2 has one card that has ? and second one is when player 2 does not have card with ?.

  2. MATH Lacsap's Fractions IA

    Using the values from Table 1: we will use the third row (x=3) meaning the numerator is 6 (y=6). In the quadratic formula, c is disregarded. 6 = a(3)2 + b(3) + 0 6 = 9a + 3b b = b = 2-3a Using x=4 and y=10, we substitute the value b=2-3a into the following equation: 10 = a (4)

  1. LACSAP Fractions. The aim of this portfolio is to discover an equation which ...

    4 × = 10 From this, we can observe that to find the numerator using the row number, we must multiply the row number by a certain constant plus more than the previous row. The equation derived from this information would be: EQUATION n (+)

  2. Lacsaps fractions are an arrangement of numbers that are symmetrically repeating based on a ...

    Hence I will let. Where k is the multiple needed to make row number equal the numerator (N). I will calculate k and present it in a table along with the numerator and the row number. To calculate k for the 2nd row: The rest will be presented in a table.

  1. Lascap's Fractions. I was able to derive a general statement for both the ...

    Then click STAT, select CALC, then select ?5:QuadReg? 1. Click 2ND, input L1, then comma, input L2 1. Then comma again, click VARS, then select Y-VARS, select ?1:Function?? 1. Then select ?1:Y1? 1. The answer is: Let x be the row number and y the numerator SIMPLIFYING SIMPLIFYING Therefore the general statement representing the numerator in each row is:

  2. LACSAP FRACTIONS - I will begin my investigation by continuing the pattern and finding ...

    value when n is equal to 6 N = 0.5n2 + 0.5n = 0.5(6)2 + 0.5(6) = 0.5(36) + 3 = 18 + 3 N = 21 Find numerator value when n is equal to 7 N = 0.5n2 + 0.5n = 0.5(7)2 + 0.5(7)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work