Let's solve the given expression:

We are asked to work out $1 \frac{3}{4} \div \frac{1}{5}$ and provide the answer as a fraction in its simplest form.

Step 1: Convert the mixed number to an improper fraction

The mixed number $1 \frac{3}{4}$ can be converted to an improper fraction. To do this: $1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}$

Step 2: Perform the division

We now need to divide $\frac{7}{4}$ by $\frac{1}{5}$. Dividing fractions involves multiplying by the reciprocal of the second fraction: $\frac{7}{4} \div \frac{1}{5} = \frac{7}{4} \times \frac{5}{1} = \frac{7 \times 5}{4 \times 1} = \frac{35}{4}$

Final Answer

The result of the division is $\frac{35}{4}$, which is already in its simplest form.

Would you like a detailed breakdown of any step?

Here are 5 follow-up questions related to the problem:

1. How do you convert mixed numbers to improper fractions?
2. Why do we multiply by the reciprocal when dividing fractions?
3. Can the fraction $\frac{35}{4}$ be expressed as a mixed number?
4. What are some common mistakes when dividing fractions?
5. How do you simplify complex fraction expressions?

Tip: When dividing fractions, always remember to flip (find the reciprocal of) the second fraction and then multiply.