The image shows the mathematical expression:

$\frac{2}{5} \div \frac{1}{10} - 2 \frac{1}{5} =$

Let's break down the expression step by step to solve it.

Step 1: Solve the division

$\frac{2}{5} \div \frac{1}{10} = \frac{2}{5} \times \frac{10}{1} = \frac{2 \times 10}{5 \times 1} = \frac{20}{5} = 4$

Step 2: Convert the mixed number to an improper fraction

The mixed number $2 \frac{1}{5}$ can be converted to an improper fraction: $2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}$

Step 3: Subtract the improper fraction

Now we subtract the result from the division: $4 - \frac{11}{5}$

To perform the subtraction, convert 4 to a fraction with a denominator of 5: $4 = \frac{20}{5}$

So the expression becomes: $\frac{20}{5} - \frac{11}{5} = \frac{20 - 11}{5} = \frac{9}{5}$

Step 4: Convert the result to a mixed number

$\frac{9}{5} = 1 \frac{4}{5}$

Final Answer

$\frac{2}{5} \div \frac{1}{10} - 2 \frac{1}{5} = 1 \frac{4}{5}$

Would you like more details or have any questions?

Here are five related questions to expand on this topic:

1. How do you convert a mixed number to an improper fraction and vice versa?
2. What are the rules for dividing fractions, and how does the reciprocal work?
3. How can you simplify fractions when performing addition or subtraction?
4. What are some common mistakes to avoid when dealing with mixed numbers and improper fractions?
5. How do you compare fractions to determine which is larger or smaller?

Tip: Always convert mixed numbers to improper fractions when performing operations like multiplication, division, addition, or subtraction to simplify the calculations.