QUESTION 6
Easy
Can you think of other way(s) to find a rational number between any two rational numbers?
SOLUTION
We can always find another rational number between two rational numbers by taking their average.
Example: \(\frac{3}{2}\) and \(\frac{5}{4}\)
To find a number between \(\frac{3}{2}\) and \(\frac{5}{4}\), we find their average.
\(\begin{aligned} \frac{\frac{3}{2} + \frac{5}{4}}{2} &= \frac{\frac{3(2) + 5}{4}}{2} \\ &= \frac{6 + 5}{4} × \frac{1}{2} \\ &= \frac{11}{4} × \frac{1}{2} \\ &= \frac{11}{8}\end{aligned}\)
So, \(\frac{11}{8}\) lies between \(\frac{3}{2}\) and \(\frac{5}{4}\).
Example: \(\frac{3}{2}\) and \(\frac{5}{4}\)
To find a number between \(\frac{3}{2}\) and \(\frac{5}{4}\), we find their average.
\(\begin{aligned} \frac{\frac{3}{2} + \frac{5}{4}}{2} &= \frac{\frac{3(2) + 5}{4}}{2} \\ &= \frac{6 + 5}{4} × \frac{1}{2} \\ &= \frac{11}{4} × \frac{1}{2} \\ &= \frac{11}{8}\end{aligned}\)
So, \(\frac{11}{8}\) lies between \(\frac{3}{2}\) and \(\frac{5}{4}\).