To simplify the given expression, we can rewrite it as:

9/1 * 2/1 + 9/2 * 3/1 + 9/3 * 4/1 + 9/4 * 5/1 + ... + 9/98 * 99/1 + 9/99 * 100/1

Now, we can see that each term has a common factor of 1 in the denominator and the next term's numerator. We can cancel out these common factors to simplify the expression further:

(9 * 2/1) + (9 * 3/1) + (9 * 4/1) + (9 * 5/1) + ... + (9 * 99/1) + (9 * 100/1)

= 18 + 27 + 36 + 45 + ... + 891 + 900

Now, we can see that each term is an arithmetic sequence with a common difference of 9. We can use the formula for the sum of an arithmetic sequence to find the sum of all the terms:

Sum = (n/2)(first term + last term)

Here, the first term is 18 and the last term is 900. The number of terms, n, can be found by subtracting the first term from the last term and dividing by the common difference, 9:

n = (900 - 18)/9 + 1 = 100

Substituting these values into the formula, we get:

Sum = (100/2)(18 + 900) = 50(918) = 45900

Therefore, the simplified expression is equal to 45900.