To compare the fractions \( \frac{8}{12} \) and \( \frac{1}{2} \), we can first simplify \( \frac{8}{12} \):
\[ \frac{8}{12} = \frac{2}{3} \]
Now we need to compare \( \frac{2}{3} \) and \( \frac{1}{2} \).
To compare the two fractions, we can find a common denominator. The least common multiple of 3 and 2 is 6. We can convert both fractions:
\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \] \[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \]
Now we can compare:
\[ \frac{4}{6} > \frac{3}{6} \]
Thus, \( \frac{2}{3} > \frac{1}{2} \).
Therefore, \( \frac{8}{12} \) is greater than \( \frac{1}{2} \).
The statement that \( \frac{8}{12} \) (or \( \frac{2}{3} \)) is greater than but less than \( \frac{1}{2} \) is incorrect. In fact, \( \frac{8}{12} \) is greater than \( \frac{1}{2} \).