list a fraction that lies between the fractions 9/8 and 5/4

Explanation:

Step1: Convert to common denominator

First, find a common denominator for $\frac{9}{8}$ and $\frac{5}{4}$. The denominator of $\frac{5}{4}$ can be made 8 by multiplying numerator and denominator by 2: $\frac{5}{4}=\frac{5\times2}{4\times2}=\frac{10}{8}$.

Step2: Find a fraction in between

Now we have $\frac{9}{8}$ and $\frac{10}{8}$. To find a fraction between them, we can increase the denominator (or use other methods). Let's use a denominator of 16. Convert both fractions: $\frac{9}{8}=\frac{9\times2}{8\times2}=\frac{18}{16}$, $\frac{10}{8}=\frac{10\times2}{8\times2}=\frac{20}{16}$. A fraction between $\frac{18}{16}$ and $\frac{20}{16}$ is $\frac{19}{16}$. (Alternatively, we could see that $\frac{9}{8}=1.125$ and $\frac{10}{8}=1.25$, so a number like $1.1875=\frac{19}{16}$ works, or even simpler, take the average: $\frac{\frac{9}{8}+\frac{10}{8}}{2}=\frac{\frac{19}{8}}{2}=\frac{19}{16}$)

Answer:

$\frac{19}{16}$ (or other valid fractions like $\frac{39}{32}$ etc., but $\frac{19}{16}$ is a simple one)