1. **State the problem:** We need to find the quotient of $3 \div \frac{1}{12}$ and then check the answer by multiplication. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$3 \div \frac{1}{12} = 3 \times \frac{12}{1}$$ 3. **Perform the multiplication:** $$3 \times \frac{12}{1} = \frac{3 \times 12}{1} = \frac{36}{1} = 36$$ 4. **Check by multiplication:** Multiply the quotient by the divisor to see if we get the dividend. $$36 \times \frac{1}{12} = \frac{36}{1} \times \frac{1}{12} = \frac{36 \times 1}{1 \times 12} = \frac{36}{12} = 3$$ Since the product is the original dividend, the quotient is correct. **Final answer:** $$3 \div \frac{1}{12} = 36$$