### Instruction: Simplify $\frac{15}{6}.$.### Response: To simplify a fraction, I want to divide both the numerator and denominator by a common factor.
I can see that both 15 and 6 are divisible by 3, so I can divide them by 3 to get $\frac{15}{6} = \frac{5}{2}.$
This is the simplest form of the fraction, since 5 and 2 have no common factors other than 1.
Alternatively, I could have converted the fraction to a mixed number by dividing 15 by 6 and writing the remainder as a fraction.
This would give me $\frac{15}{6} = 2 \frac{1}{2}.$
This is another way of simplifying the fraction, but I prefer to keep it as an improper fraction for algebraic purposes.