`4/5div4/5" of " 1/10xx1/10=?`

Options

A. `1/10`
B. `1/15`
C. `1`
D. `1/5`

Answer

To solve the expression \( \frac{4}{5} \div \frac{4}{5} \text{ of } \left( \frac{1}{10} \times \frac{1}{10} \right) \), we will follow the order of operations (BODMAS/BIDMAS rules).

### Step-by-step Solution:

1. **Identify the Parts of the Expression**:
The expression consists of division, multiplication, and the "of" operation which indicates multiplication.

\[ \frac{4}{5} \div \frac{4}{5} \text{ of } \left( \frac{1}{10} \times \frac{1}{10} \right) \]

2. **Calculate the "of" Part**:
First, we need to solve the "of" part, which is the multiplication of \( \frac{1}{10} \times \frac{1}{10} \).

\[ \frac{1}{10} \times \frac{1}{10} = \frac{1 \times 1}{10 \times 10} = \frac{1}{100} \]

3. **Rewrite the Expression**:
Now we can rewrite the expression with the result from the previous step:

\[ \frac{4}{5} \div \frac{4}{5} \times \frac{1}{100} \]

4. **Perform the Division**:
Next, we perform the division \( \frac{4}{5} \div \frac{4}{5} \).

\[ \frac{4}{5} \div \frac{4}{5} = 1 \]

5. **Multiply the Result**:
Now we multiply the result of the division by \( \frac{1}{100} \):

\[ 1 \times \frac{1}{100} = \frac{1}{100} \]

6. **Final Answer**:
Therefore, the final answer is:

\[ \frac{1}{100} \]