https://file.aiquickdraw.com/mathbot/file/17306437375878sz6ga1c.jpg

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.

a) Write 1 6/7 as an improper fraction in its simplest form.
b) Use your answer to part a) to work out 5 ÷ 1 6/7. Give your answer as a fraction in its simplest form.

Learn how to convert the mixed number 1 6/7 into an improper fraction and divide 5 by 1 6/7. This solution covers key fraction concepts, including improper fractions and dividing by a fraction, making it suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation