1. The problem is to subtract the fraction $\frac{1}{3}$ from 1. 2. We can write 1 as a fraction with denominator 3: $1 = \frac{3}{3}$. 3. Now subtract the fractions: $$\frac{3}{3} - \frac{1}{3} = \frac{3 - 1}{3} = \frac{2}{3}.$$ 4. The result is $\frac{2}{3}$, which is the simplified form. 5. So, $1 - \frac{1}{3} = \frac{2}{3}$.