1. **State the problem:** We need to check if $\frac{1}{2} + \frac{3}{10} = \frac{4}{10}$ is true. 2. **Recall the rule for adding fractions:** To add fractions, they must have the same denominator. If they don't, find a common denominator. 3. **Find a common denominator for $\frac{1}{2}$ and $\frac{3}{10}$:** The denominators are 2 and 10. The least common denominator (LCD) is 10. 4. **Convert $\frac{1}{2}$ to a fraction with denominator 10:** $$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$ 5. **Add the fractions:** $$\frac{5}{10} + \frac{3}{10} = \frac{5 + 3}{10} = \frac{8}{10}$$ 6. **Simplify the result if possible:** $$\frac{8}{10} = \frac{\cancel{2} \times 4}{\cancel{2} \times 5} = \frac{4}{5}$$ 7. **Compare with the given sum $\frac{4}{10}$:** $\frac{4}{5}$ is not equal to $\frac{4}{10}$. Therefore, the statement $\frac{1}{2} + \frac{3}{10} = \frac{4}{10}$ is false. **Final answer:** $$\frac{1}{2} + \frac{3}{10} = \frac{4}{5} \neq \frac{4}{10}$$