The image provides a mathematical exercise asking to find the "fractional generator" of decimal numbers, some of which are repeating decimals. I'll walk through each of these:

1. La fracció generatriu de -15,485 és

We convert the decimal $-15.485$ into a fraction. $-15.485 = -\frac{15485}{1000}$ Simplifying the fraction: $\frac{15485}{1000} = \frac{3097}{200} \quad \Rightarrow \quad -15.485 = -\frac{3097}{200}$ Answer: $-\frac{3097}{200}$

2. La fracció generatriu de $0.\overline{345}$ és

This is a repeating decimal. Let $x = 0.\overline{345}$. Multiply by 1000 to shift the decimal: $1000x = 345.\overline{345}$ Subtract the original equation: $1000x - x = 345.\overline{345} - 0.\overline{345} \quad \Rightarrow \quad 999x = 345$ Solve for $x$: $x = \frac{345}{999}$ Simplify the fraction: $\frac{345}{999} = \frac{115}{333}$ Answer: $\frac{115}{333}$

3. La fracció generatriu de $5.72\overline{2}$ és

This decimal has a repeating part of $2$. Let $x = 5.72\overline{2}$. First, multiply by 10 to isolate the repeating part: $10x = 57.2\overline{2}$ Multiply again by 10 to shift the repeating part: $100x = 572.\overline{2}$ Subtract the two equations: $100x - 10x = 572.\overline{2} - 57.2\overline{2} \quad \Rightarrow \quad 90x = 515$ Solve for $x$: $x = \frac{515}{90}$ Simplify the fraction: $\frac{515}{90} = \frac{103}{18}$ Answer: $\frac{103}{18}$

4. La fracció generatriu de $3.14159\overline{59}$ és

This has a repeating part $59$. Let $x = 3.14159\overline{59}$. Multiply by 1000: $1000x = 3141.59\overline{59}$ Multiply again by 100 to shift the repeating part: $100000x = 314159.\overline{59}$ Subtract the two equations: $100000x - 1000x = 314159.\overline{59} - 3141.59\overline{59} \quad \Rightarrow \quad 99000x = 311017.4$ Solve for $x$ (ignoring decimal in result for simplicity): $x = \frac{311017}{99000}$ Simplify the fraction: $\text{(Already in simplified form)}$ Answer: $\frac{311017}{99000}$

Would you like further details on any of these steps or explanations?

Here are 5 related questions:

1. How do you convert a non-repeating decimal into a fraction?
2. Why do repeating decimals result in fractions with denominators containing factors of 9?
3. How can mixed repeating and non-repeating decimals be handled in fraction conversion?
4. What is the process for simplifying large fractions after conversion?
5. Why is multiplying by powers of 10 effective in isolating repeating decimal parts?

Tip: For any repeating decimal, the number of repeating digits determines how many 9's appear in the denominator.