1. The problem asks us to write equivalent fractions for $\frac{1}{10}$ and $\frac{1}{2}$ using the least common denominator (LCD). 2. To find the LCD, we find the least common multiple (LCM) of the denominators 10 and 2. 3. The multiples of 10 are 10, 20, 30, 40, ... 4. The multiples of 2 are 2, 4, 6, 8, 10, 12, ... 5. The smallest common multiple is 10, so the LCD is 10. 6. Now, convert each fraction to have denominator 10. 7. $\frac{1}{10}$ already has denominator 10, so it stays $\frac{1}{10}$. 8. For $\frac{1}{2}$, multiply numerator and denominator by 5 to get denominator 10: $$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$ 9. Therefore, the equivalent fractions with the least common denominator are: $$\frac{1}{10} = \frac{1}{10}$$ $$\frac{1}{2} = \frac{5}{10}$$