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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.

Work out 1 3/4 ÷ 1/5. Give your answer as a fraction in its simplest form.

Learn how to solve the fraction problem 1 3/4 ÷ 1/5 with a clear step-by-step solution. Convert mixed numbers to improper fractions and divide fractions by multiplying by the reciprocal. Suitable for students in Grades 5-7.

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