Final answer:
There are 30 dogs in the kennel, 12 of which are brown, leaving 18 dogs that are not brown. The fraction representing non-brown dogs is 18 out of 30, or simplified, 3/5.
Step-by-step explanation:
If there are 30 dogs staying in the boarding kennels and 12 of the dogs are brown, we can calculate the fraction of the dogs that are not brown. First, we need to find out how many dogs are not brown by subtracting the number of brown dogs from the total number of dogs:
30 dogs (total) - 12 dogs (brown) = 18 dogs (not brown)
Now, to find the fraction of dogs that are not brown, we'll use the number of non-brown dogs and divide it by the total number of dogs:
Fraction of non-brown dogs = 18 dogs (not brown) / 30 dogs (total)
To simplify the fraction, we divide both the numerator (18) and the denominator (30) by their greatest common divisor, which is 6:
Fraction of non-brown dogs = (18/6) / (30/6) = 3/5
Therefore, the fraction of the dogs that are not brown is 3/5, which can also be expressed as 0.6 when converted to decimal form.