https://file.aiquickdraw.com/mathbot/file/1727891700099r1x6uue4.jpg

Let's solve the division problem in the image:

### Problem:
\[
\frac{1}{5} \div 1 \frac{3}{4}
\]

#### Step 1: Convert the mixed number to an improper fraction.
The mixed number \( 1 \frac{3}{4} \) can be rewritten as an improper fraction:
\[
1 \frac{3}{4} = \frac{7}{4}
\]

#### Step 2: Rewrite the division as multiplication by the reciprocal.
Division by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression as:
\[
\frac{1}{5} \div \frac{7}{4} = \frac{1}{5} \times \frac{4}{7}
\]

#### Step 3: Multiply the fractions.
To multiply the fractions, multiply the numerators together and the denominators together:
\[
\frac{1}{5} \times \frac{4}{7} = \frac{1 \times 4}{5 \times 7} = \frac{4}{35}
\]

#### Step 4: Simplify the result.
The fraction \( \frac{4}{35} \) is already in its simplest form, as 4 and 35 have no common factors other than 1.

### Final Answer:
\[
\frac{4}{35}
\]

Let me know if you need further details or explanations!

Here are some related questions:
1. How do you convert mixed numbers to improper fractions?
2. What is the rule for dividing fractions?
3. How do you simplify fractions?
4. Can you explain why division by a fraction is equivalent to multiplying by the reciprocal?
5. What other methods can be used to check the result?

**Tip:** Always simplify your final answer if possible by checking for common factors in the numerator and denominator.

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

Learn how to solve the fraction division problem 1/5 ÷ 1 3/4, including converting mixed numbers to improper fractions and applying the rule of multiplying by the reciprocal. This step-by-step solution is suitable for Grades 6-8.

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