1. The problem is to simplify the fraction $\frac{3}{6}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD). 3. Find the GCD of 3 and 6. The factors of 3 are 1 and 3. The factors of 6 are 1, 2, 3, and 6. The greatest common factor is 3. 4. Divide both numerator and denominator by 3: $$\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$$ 5. So, the simplified form of $\frac{3}{6}$ is $\frac{1}{2}$. 6. This means $\frac{3}{6}$ and $\frac{1}{2}$ represent the same value, but $\frac{1}{2}$ is in simplest terms.