The 8th grade has $\frac{650}{520+650} = \frac{650}{1170} = \frac{65}{117}$ of the total students. To simplify this fraction further, we notice that $65 = 5 \cdot 13$. Since $117$ is not divisible by $5$, we test if it's divisible by $13$ and find that $117 = 9 \cdot 13$. Thus to have fair representation, the 8th grade should have $\frac{65}{117} \times 18 = \frac{5}{9} \times 18 = \boxed{10}$ of the $18$ representatives.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The 7th and 8th grades have enrollments of 520 and 650 respectively. The two grades have a total of 18 representatives on the Student Council. How many representatives should the 8th grade have if there is to be a fair representation of the two grades?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
10
The 7th and 8th grades have enrollments of 520 and 650 respectively. The two grades have a total of 18 representatives on the Student Council. How many representatives should the 8th grade have if there is to be a fair representation of the two grades?
test