Answer: The fraction of the pets that are dogs with long hairs is \(\dfrac{1}{4}.\)
Step-by-step explanation: Given that \(\dfrac{3}{8}\) of the pets in the pet show are dogs and \(\dfrac{2}{3}\) of the dogs have long hair.
We are to find the fraction of the pets that are dogs with long hairs.
Let x represents the total number of pets in the pet show.
So, the number of dogs in the pet show is
\(n_d=\dfrac{3}{8}\times x=\dfrac{3x}{8}.\)
Therefore, the number of dogs with long hairs in the pet show is
\(n_{dh}=\dfrac{2}{3}\times\dfrac{3x}{8}=\dfrac{1}{4}x.\)
Thus, the fraction of the pets that are dogs with long hairs is \(\dfrac{1}{4}.\)
