Let's determine the relationship between the numbers of girls and boys for each grade to find their proportions and see if any pairs of grades have the same proportion.
Consider the given table:
```
Grade | Girls | Boys
------|-------|-----
6 | 9 | 12
7 | 12 | 18
8 | 15 | 20
9 | 25 | 36
```
Now, let's calculate the proportion of girls to boys for each grade:
1. Grade 6:
[tex]\[
\text{Proportion} = \frac{\text{Number of girls in Grade 6}}{\text{Number of boys in Grade 6}} = \frac{9}{12} = 0.75
\][/tex]
2. Grade 7:
[tex]\[
\text{Proportion} = \frac{\text{Number of girls in Grade 7}}{\text{Number of boys in Grade 7}} = \frac{12}{18} \approx 0.6667
\][/tex]
3. Grade 8:
[tex]\[
\text{Proportion} = \frac{\text{Number of girls in Grade 8}}{\text{Number of boys in Grade 8}} = \frac{15}{20} = 0.75
\][/tex]
4. Grade 9:
[tex]\[
\text{Proportion} = \frac{\text{Number of girls in Grade 9}}{\text{Number of boys in Grade 9}} \approx \frac{25}{36} \approx 0.6944
\][/tex]
After calculating these proportions, we have:
- Grade 6: 0.75
- Grade 7: 0.6667
- Grade 8: 0.75
- Grade 9: 0.6944
We see that Grades 6 and 8 have the same proportion (0.75).
Thus, the two grades that have a proportional relationship between the numbers of girls and boys are:
[tex]\[
\boxed{\text{6 and 8}}
\][/tex]
