\( 1 \frac{5}{14} \) or \( \frac{10}{7} ? \)

Both representations refer to the same value! The mixed number \( 1 \frac{5}{14} \) can be converted to an improper fraction by multiplying the whole number (1) by the denominator (14) and adding the numerator (5). This results in \( \frac{14 + 5}{14} = \frac{19}{14} \). On the other hand, \( \frac{10}{7} \) is already an improper fraction. To compare, we can convert \( \frac{19}{14} \) to a common denominator with \( \frac{10}{7} \). The least common multiple of 14 and 7 is 14. So \( \frac{10}{7} \) becomes \( \frac{20}{14} \). Now you see \( \frac{19}{14} < \frac{20}{14} \), demonstrating that \( 1 \frac{5}{14} \) is less than \( \frac{10}{7} \).