1. **State the problem:** Calculate the sum of the fractions $$\frac{1}{2} + \frac{1}{4} + \frac{1}{14}$$. 2. **Formula and rules:** To add fractions, find a common denominator, then add the numerators. 3. **Find the least common denominator (LCD):** The denominators are 2, 4, and 14. - Prime factors: 2 = 2 - 4 = 2^2 - 14 = 2 \times 7 The LCD is $$2^2 \times 7 = 28$$. 4. **Convert each fraction to have denominator 28:** $$\frac{1}{2} = \frac{1 \times 14}{2 \times 14} = \frac{14}{28}$$ $$\frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28}$$ $$\frac{1}{14} = \frac{1 \times 2}{14 \times 2} = \frac{2}{28}$$ 5. **Add the fractions:** $$\frac{14}{28} + \frac{7}{28} + \frac{2}{28} = \frac{14 + 7 + 2}{28} = \frac{23}{28}$$ 6. **Final answer:** $$\frac{23}{28}$$ is the sum.