1. **State the problem:** Calculate the value of $3 \times \frac{1}{3}$.\n\n2. **Formula and rules:** Multiplying a whole number by a fraction involves multiplying the whole number by the numerator and then dividing by the denominator. The formula is: $$a \times \frac{b}{c} = \frac{a \times b}{c}$$\n\n3. **Apply the formula:** Here, $a=3$, $b=1$, and $c=3$. So, $$3 \times \frac{1}{3} = \frac{3 \times 1}{3}$$\n\n4. **Simplify:** $$\frac{3}{3} = 1$$\n\n5. **Conclusion:** Therefore, $3 \times \frac{1}{3} = 1$.