Let's analyze and solve the given mathematical expression in the image:

$\frac{100 \cdot 1}{1 \cdot 2} \times \frac{99 \cdot 2}{2}$

First, simplify each fraction separately:

1. The first fraction is $\frac{100 \cdot 1}{1 \cdot 2}$: $\frac{100 \cdot 1}{1 \cdot 2} = \frac{100}{2} = 50$

2. The second fraction is $\frac{99 \cdot 2}{2}$: $\frac{99 \cdot 2}{2} = 99$

Now, multiply the simplified results:

$50 \times 99$

Perform the multiplication:

$50 \times 99 = 4950$

So, the final result is:

$\boxed{4950}$

Do you want more details or have any questions? Here are five more questions you might be interested in:

1. How do you simplify fractions involving multiplication?
2. What is the general approach to solving complex fractions?
3. How do you multiply large numbers effectively?
4. Can you explain how to handle division within fractions?
5. How does factorization help in simplifying mathematical expressions?

Tip: When simplifying fractions, always look for common factors in the numerator and the denominator to reduce the fraction to its simplest form.