1. **State the problem:** Compare the fractions $\frac{2}{5}$ and $\frac{3}{10}$ using $<$, $>$, or $=$. 2. **Formula and rules:** To compare fractions, convert them to have a common denominator or convert to decimals. 3. **Find a common denominator:** The denominators are 5 and 10. The least common denominator (LCD) is 10. 4. **Convert $\frac{2}{5}$ to denominator 10:** $$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$ 5. **Compare the fractions:** Now compare $\frac{4}{10}$ and $\frac{3}{10}$. 6. Since $4 > 3$, we have: $$\frac{4}{10} > \frac{3}{10}$$ 7. Therefore: $$\frac{2}{5} > \frac{3}{10}$$ **Final answer:** $\frac{2}{5} > \frac{3}{10}$