1. The problem is to arrange the fractions $\frac{7}{12}$, $\frac{1}{2}$, and $\frac{2}{3}$ in ascending order, i.e., find $a < b < c$ where $a$, $b$, and $c$ are these fractions. 2. To compare fractions, we use the rule: convert them to a common denominator or convert to decimals. 3. Find the least common denominator (LCD) of 12, 2, and 3. The LCD is 12. 4. Convert each fraction to have denominator 12: - $\frac{7}{12}$ stays $\frac{7}{12}$ - $\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$ - $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ 5. Now compare numerators: 6, 7, and 8. 6. So in ascending order: $\frac{6}{12} < \frac{7}{12} < \frac{8}{12}$ which corresponds to $\frac{1}{2} < \frac{7}{12} < \frac{2}{3}$. Final answer: $\frac{1}{2} < \frac{7}{12} < \frac{2}{3}$