1. **State the problem:** We have a number line with points 0, ?, 1/2, and 1, and an arrow moving left by 1/7. We want to express the movement and positions using a common denominator and find the unknown fraction represented by ?. 2. **Find a common denominator:** The fractions involved are 1/2 and 1/7. The least common denominator (LCD) is 14. 3. **Rewrite the fractions with denominator 14:** $$\frac{1}{2} = \frac{7}{14}$$ $$\frac{1}{7} = \frac{2}{14}$$ 4. **Express the movement:** The command says start at ?/14 and move 2/14 to the left (since 1/7 = 2/14). 5. **Set up the equation:** Starting at ?/14 and moving left by 2/14 means: $$\frac{?}{14} - \frac{2}{14} = \frac{7}{14}$$ 6. **Solve for ?:** $$\frac{?}{14} = \frac{7}{14} + \frac{2}{14}$$ $$\frac{?}{14} = \frac{9}{14}$$ 7. **Final answer:** $$? = 9$$ So, the unknown fraction is $\frac{9}{14}$.