To solve the expression \( \frac{9}{11} \div \frac{5}{11} \), we can rewrite the division of fractions as multiplication by the reciprocal:
\[ \frac{9}{11} \div \frac{5}{11} = \frac{9}{11} \times \frac{11}{5} \]
When we multiply these fractions, the \( 11 \) in the numerator and denominator cancels out:
\[ \frac{9 \times 11}{11 \times 5} = \frac{9}{5} \]
Now we have \( \frac{9}{5} \). To express this in the form \( a \frac{b}{c} \):
The fraction \( \frac{9}{5} \) can be represented as a mixed number. Since \( 9 \) divided by \( 5 \) is \( 1 \) remainder \( 4 \):
\[ \frac{9}{5} = 1 \frac{4}{5} \]
Thus, in this case, \( a = 1 \), \( b = 4 \), and \( c = 5 \).
Putting it all together, the values are:
\[ a = 1, b = 4, c = 5 \]
So the correct answer is:
a = 1, b = 4, c = 5.