Evaluating the Expression $\frac{99}{100} \times 99$

This solution details the calculation steps to find the value of the mathematical expression $\frac{99}{100} \times 99$. The goal is to simplify the expression and present it as a mixed number.

Step-by-Step Calculation

1. Start with the given expression:

   $ \frac{99}{100} \times 99 $

2. Rewrite the fraction $\frac{99}{100}$ to make the calculation easier. Notice that $\frac{99}{100}$ is equal to $1 - \frac{1}{100}$.

   $ \left(1 - \frac{1}{100}\right) \times 99 $

3. Distribute the $99$ to both terms inside the parentheses:

   $ (1 \times 99) - \left(\frac{1}{100} \times 99\right) $

4. Simplify the terms:

   $ 99 - \frac{99}{100} $

5. To subtract the fraction, express $99$ as an equivalent fraction with a denominator of $100$.

   $ 99 = \frac{99 \times 100}{100} = \frac{9900}{100} $

6. Perform the subtraction:

   $ \frac{9900}{100} - \frac{99}{100} = \frac{9900 - 99}{100} $

7. Calculate the numerator:

   $ 9900 - 99 = 9801 $

   The result is the improper fraction $\frac{9801}{100}$.

8. Convert the improper fraction $\frac{9801}{100}$ to a mixed number. Divide $9801$ by $100$.

   $9801 \div 100 = 98$ with a remainder of $1$.

   Therefore, the mixed number is $98 \frac{1}{100}$.

Final Answer Value

The value of $\frac{99}{100} \times 99$ is $98 \frac{1}{100}$.