### Instruction: Find \[\dfrac{3}{\,\,\frac{6}{11}\,\,}.\].### Response: To find the value of this fraction, I need to divide 3 by 6/11.
But dividing by a fraction is the same as multiplying by its reciprocal, so I can rewrite this as 3 times 11/6.
To multiply fractions, I just multiply the numerators and the denominators separately, so I get 3 times 11 over 6 times 1, or 33/6.
Now, I can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3.
So I get 11/2 as the simplified fraction.
Alternatively, I can also write this as a mixed number by dividing 11 by 2 and finding the quotient and the remainder.
The quotient is 5 and the remainder is 1, so I get 5 and a half as the mixed number.
Either way, the fraction 3 over 6/11 is equivalent to 11/2 or 5.5.