Let's denote the total number of people in the cinema hall as "x."

We are given the following information:

1. 22\(\frac{1}{2}\)% are children, which can be written as 0.225x (since 22.5% = 0.225 as a decimal).

2. 47\(\frac{1}{2}\)% are men, which can be written as 0.475x (since 47.5% = 0.475 as a decimal).

3. 84 are women.

Now, we can use the fact that the total number of people in the hall is the sum of children, men, and women:

\(x = 0.225x + 0.475x + 84\).

Combine the terms with "x":

\(x = 0.7x + 84\).

Subtract 0.7x from both sides:

\(0.3x = 84\).

Now, divide both sides by 0.3:

\(x = \frac{84}{0.3} = 280\).

So, there are a total of 280 people in the cinema hall.

Now, to find the number of men (47\(\frac{1}{2}\)% of the total):

Number of men = 0.475x = 0.475 280 = 133.