Let's go through each part of this question step-by-step.

Part (a)

The problem asks us to convert $1 \frac{6}{7}$ into an improper fraction.

1. To convert a mixed number to an improper fraction, we use the formula: $\text{Improper fraction} = (\text{whole number} \times \text{denominator}) + \text{numerator}$

2. For $1 \frac{6}{7}$:

   • Whole number = 1
   • Numerator = 6
   • Denominator = 7

3. Calculating the improper fraction: $(1 \times 7) + 6 = 7 + 6 = 13$ So, $1 \frac{6}{7}$ as an improper fraction is $\frac{13}{7}$.

Part (b)

The question now asks us to calculate $5 \div \frac{13}{7}$ and express the answer in its simplest form.

1. Dividing by a fraction is the same as multiplying by its reciprocal. Thus: $5 \div \frac{13}{7} = 5 \times \frac{7}{13}$

2. Now, multiply: $5 \times \frac{7}{13} = \frac{35}{13}$

3. The fraction $\frac{35}{13}$ is already in its simplest form, as there are no common factors between 35 and 13.

Final Answers

• (a) $\frac{13}{7}$
• (b) $\frac{35}{13}$

Would you like more details on any of these steps, or do you have any questions?

Here are 5 related questions for further practice:

1. How do you convert a mixed number to an improper fraction in general?
2. How do you simplify a division problem involving fractions?
3. What is the reciprocal of a fraction, and how is it used in division?
4. Can you convert $\frac{35}{13}$ into a mixed number?
5. Why is it important to simplify fractions?

Tip: When dividing by a fraction, always remember to multiply by its reciprocal. This makes the calculation much simpler.