Hi Sophia,

I think you are looking for the rational number (fraction) that comes next after 3 1/2. If that is your question then the answer is that there is no next rational number. Suppose for example you might think it is 3 3/4. Then the two numbers you have are

\[3 \frac{1}{2} = \frac{7}{2} \mbox{ and } 3 \frac{3}{4} = \frac{15}{4}.\]

The average of these two numbers is

\[\frac{\frac{7}{2} + \frac{15}{4}}{2} = \frac{\frac{14}{4} + \frac{15}{4}}{2} = \frac{\frac{29}{4}}{2} = \frac{29}{8} = 3 \frac{5}{8}.\]

The point here is that if you have any two different rational numbers then their average is between them.

I hope this helps,
Penny