Let's work through the given problem step-by-step.

Problem:

Work out $1 \frac{3}{4} \div \frac{1}{5}$
Give your answer as a fraction in its simplest form.

Step 1: Convert the Mixed Number to an Improper Fraction

The mixed number is $1 \frac{3}{4}$. To convert it into an improper fraction: $1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$

Step 2: Set Up the Division

The expression becomes: $\frac{7}{4} \div \frac{1}{5}$

Step 3: Convert Division to Multiplication by the Reciprocal

To divide by a fraction, multiply by its reciprocal: $\frac{7}{4} \times \frac{5}{1} = \frac{7 \times 5}{4 \times 1} = \frac{35}{4}$

Step 4: Simplify if Necessary

The fraction $\frac{35}{4}$ is already in its simplest form.

Final Answer

The answer is: $\frac{35}{4}$

Do you have any questions, or would you like more details on a particular step?

Related Questions:

1. How do you convert mixed numbers to improper fractions?
2. What is the process for dividing fractions?
3. Can division of fractions be applied to real-world problems?
4. What is a reciprocal, and how is it used in fraction operations?
5. How do you simplify a complex fraction?

Tip: When dividing fractions, always remember to multiply by the reciprocal of the divisor.