I am supposed to find the pattern of a triangle of fractions, and find the next two rows. However, I can't seem to find the pattern. Could you please help me out?

Row 1: 1 1
Row 2: 1 3/2 1
Row 3: 1 6/4 6/4 1
Row 4: 1 10/7 10/6 10/7 1
Row 5: 1 15/11 15/9 15/11 1
If you center out the numbers, it looks like a triangle.

first of all , write them down in nice column forms

Now look at the columns
the first column is obvious

2nd column:
look at the numerators.
1 3 6 10 15 ..
notice that the difference between them increases by 1 each time, so the next few are
1 3 6 10 15 21 28 ...
look at the numerators
2 4 7 11 ...
difference between 2 and 4 is 2, difference between 4 and 7 is 3, difference between 7 and 11 is 4 ...
can you see the pattern?

Can you finish it ?

To find the pattern in the given triangle of fractions, let's take a closer look at each row:

Row 1: 1 1
Row 2: 1 3/2 1
Row 3: 1 6/4 6/4 1
Row 4: 1 10/7 10/6 10/7 1
Row 5: 1 15/11 15/9 15/11 1

As you mentioned, if you look closely, it does resemble a triangle. Each row begins and ends with 1. Apart from the border elements, the numbers in each row seem to follow a specific pattern.

To identify the pattern, let's examine the numerators and denominators of the fractions:

Row 1: 1/1
Row 2: 3/2 = 1.5 (numerator increases by 2, denominator increases by 1)
Row 3: 6/4 = 1.5 (numerator increases by 3, denominator increases by 2)
Row 4: 10/7 ≈ 1.43 (numerator increases by 4, denominator increases by 3)
Row 5: 15/11 ≈ 1.36 (numerator increases by 5, denominator increases by 4)

From the observations above, we can deduce that the numerator increases by 1 for each subsequent row, while the denominator increases by 1 as well. This gives us the basic pattern.

To find the next two rows, we can extend this pattern:

Row 6:
Numerator = Previous row's numerator + 1
Denominator = Previous row's denominator + 1

Row 7:
Numerator = Previous row's numerator + 1
Denominator = Previous row's denominator + 1

Let's apply this pattern to find the next two rows:

Row 6:
Numerator = 15 + 1 = 16
Denominator = 11 + 1 = 12

So, Row 6 is: 1 16/12 16/12 1

Row 7:
Numerator = 16 + 1 = 17
Denominator = 12 + 1 = 13

So, Row 7 is: 1 17/13 17/13 1

Therefore, the next two rows in the triangle of fractions are:
Row 6: 1 16/12 16/12 1
Row 7: 1 17/13 17/13 1

By following the pattern, you can continue finding the elements of subsequent rows in the triangle.