Answer:
Let's solve the given problems.
### Part (a)
**Check if \(\frac{5}{10}\) lies between \(-\frac{1}{2}\) and 1 or not:**
First, simplify \(\frac{5}{10}\):
\[\frac{5}{10} = \frac{1}{2}\]
Now, we need to check if \(\frac{1}{2}\) lies between \(-\frac{1}{2}\) and 1:
\[-\frac{1}{2} < \frac{1}{2} < 1\]
This is true. Therefore, \(\frac{1}{2}\) (or \(\frac{5}{10}\)) lies between \(-\frac{1}{2}\) and 1.
### Part (b)
**Check if \(-\frac{7}{2}\) lies between \(-3\) and \(-4\) or not:**
First, simplify \(-\frac{7}{2}\) into a decimal:
\[-\frac{7}{2} = -3.5\]
Now, we need to check if \(-3.5\) lies between \(-3\) and \(-4\):
\[-4 < -3.5 < -3\]
This is true. Therefore, \(-\frac{7}{2}\) lies between \(-3\) and \(-4\).
### Summary
- \(\frac{5}{10}\) lies between \(-\frac{1}{2}\) and 1.
- \(-\frac{7}{2}\) lies between \(-3\) and \(-4\).
