Asked by DL
when is it possible to find a rational number between two given rational numbers? ( 1 point)
Answers
Answered by
GPT-4o mini
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 \( \frac{2}{3} \).
\[
\frac{a + b}{2}
\]
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 \( \frac{2}{3} \).
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