when is it possible to find a rational number between two given rational numbers? ( 1 point)

1 answer

It is always possible to find a rational number between any two given rational numbers, as long as the two numbers are distinct. If you have two rational numbers, \( a \) and \( b \), where \( a < b \), you can find a rational number between them by taking their average:

\[ \frac{a + b}{2} \]

This number will be rational and will lie between \( a \) and \( b \). For example, if \( a = \frac{1}{3} \) and \( b = \frac{2}{3} \), then

\[ \frac{\frac{1}{3} + \frac{2}{3}}{2} = \frac{1}{2} \]

is a rational number between \( \frac{1}{3} \) and \( \frac{2}{3} \).