To compare the ratios \( \frac{5}{9} \) and \( \frac{3}{6} \), we can first simplify \( \frac{3}{6} \):
\[ \frac{3}{6} = \frac{1}{2} \]
Next, we can check the ratio \( \frac{5}{9} \) in decimal form:
\[ \frac{5}{9} \approx 0.555... \]
Now we compare \( 0.555... \) to \( 0.5 \) (which is the decimal representation of \( \frac{1}{2} \)).
Now, let's analyze the provided tables to confirm the ratios:
For \( 5:9 \):
- When \( 5 \) is compared to \( 9 \), it's a ratio of \( \frac{5}{9} \).
- If we multiply \( 5 \) and \( 9 \) by the same number, their ratios remain equivalent:
- \( 10:18 = \frac{10}{18} = \frac{5}{9} \)
- \( 15:27 = \frac{15}{27} = \frac{5}{9} \)
- \( 20:36 = \frac{20}{36} = \frac{5}{9} \)
- \( 25:45 = \frac{25}{45} = \frac{5}{9} \)
For \( 3:6 \):
- When \( 3 \) is compared to \( 6 \), it simplifies to \( \frac{1}{2} \).
- Similarly, the other ratios will yield the same result:
- \( 6:12 = \frac{6}{12} = \frac{1}{2} \)
- \( 9:18 = \frac{9}{18} = \frac{1}{2} \)
- \( 12:24 = \frac{12}{24} = \frac{1}{2} \)
- \( 15:30 = \frac{15}{30} = \frac{1}{2} \)
Given that \( \frac{5}{9} \approx 0.555... \) is greater than \( \frac{1}{2} \), we can conclude:
\[ \frac{5}{9} > \frac{3}{6} \]
Thus, the ratio \( 5:9 \) is greater than \( 3:6 \).