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Let's go through the questions visible in the image and provide solutions:

### 1. Convert each number to a decimal:
- \( \frac{1}{3} \) = 0.333...
- \( \frac{4}{7} \) ≈ 0.571 (rounded to 3 decimal places)

### 2. Write three fractions equivalent to \( \frac{-50}{-17} \) using only the numbers \( -50, -17, 17, 50 \):
- \( \frac{-50}{-17} \) is positive, so it simplifies to \( \frac{50}{17} \), which is already in simplest form. 
Three equivalent fractions can be obtained by multiplying both the numerator and denominator by the same number:
   - \( \frac{50}{17} \times \frac{2}{2} = \frac{100}{34} \)
   - \( \frac{50}{17} \times \frac{3}{3} = \frac{150}{51} \)
   - \( \frac{50}{17} \times \frac{-1}{-1} = \frac{-50}{-17} = \frac{50}{17} \) (unchanged)

This is a rational number because both the numerator and denominator are integers, and the denominator is not zero.

### 3. Find each quotient:
- \( 42 \div (-7) = -6 \)
- \( \frac{-27}{5} = -5.4 \)
- \( -56 \div 8 = -7 \)
- \( \frac{35}{3} \approx 11.67 \) (rounded to 2 decimal places)

### 4. Use Repeated Reasoning (Table of Fractions and Decimals):
The table shows the following fractions: \( \frac{1}{3}, \frac{2}{3}, \frac{3}{3} \).
- \( \frac{1}{3} \) = 0.333...
- \( \frac{2}{3} \) = 0.666...
- \( \frac{3}{3} = 1 \)

#### A. Pattern:
Each fraction is a multiple of \( \frac{1}{3} \), and as the numerator increases by 1, the decimal value also increases by about 0.333... each time.

#### B. Does the pattern continue? Why or why not?
Yes, this pattern continues because the fraction \( \frac{n}{3} \) (for integer \( n \)) results in decimal representations that increase in steps of approximately 0.333 for each successive numerator.

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Would you like more details on any part of this, or do you have any questions?

### 5 Relative Questions:
1. How would you convert \( \frac{7}{8} \) into a decimal?
2. What happens if you multiply both the numerator and denominator of \( \frac{1}{3} \) by 4?
3. Can you think of another set of equivalent fractions for \( \frac{50}{17} \)?
4. What is the decimal of \( \frac{-35}{6} \)?
5. Why is dividing by zero undefined?

### Tip:
When converting fractions to decimals, you can use long division or a calculator to ensure precision in the result.

Solve the following mathematical problems including converting fractions to decimals, finding equivalent fractions, and determining patterns in fractions.

Explore how to convert fractions to decimals, find equivalent fractions, and understand patterns in fractions with detailed solutions. This problem set covers key concepts such as converting \( \frac{1}{3} \), \( \frac{4}{7} \), and understanding repeated reasoning in fraction patterns.

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