1. The problem is to divide fractions and mixed numbers as given: $\frac{3}{10} \div \frac{1}{5}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ which means multiply the first fraction by the reciprocal of the second. 3. Applying this to the problem: $$\frac{3}{10} \div \frac{1}{5} = \frac{3}{10} \times \frac{5}{1}$$ 4. Multiply numerators and denominators: $$\frac{3 \times 5}{10 \times 1} = \frac{15}{10}$$ 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor 5: $$\frac{\cancel{15}^{3} }{\cancel{10}^{2}} = \frac{3}{2}$$ 6. The final answer is $$\frac{3}{2}$$ or 1.5 in decimal form.