Finding the Numerators and Denominators

1st Row

This investigation explores patterns in Lacsap’s Fractions, developing general rules which illustrate the rules for finding the numerators and denominators of these fractions. I will start with the following:

            I initially noticed the following:

Row Number

Numerator in Previous Row

Numerator in Current Row

Difference of Numerators

Row Number Equals Difference?

2

1

3

2

Yes

3

3

6

3

Yes

4

6

10

Finding the Numerators and Denominators

1st Row

This investigation explores patterns in Lacsap’s Fractions, developing general rules which illustrate the rules for finding the numerators and denominators of these fractions. I will start with the following:

            I initially noticed the following:

Row Number

Numerator in Previous Row

Numerator in Current Row

Difference of Numerators

Row Number Equals Difference?

2

1

3

2

Yes

3

3

6

3

Yes

4

6

10

4

Yes

5

10

15

5

Yes

 4

Yes

5

10

15

5

Yes