To solve this problem, we need to find the values of [tex]\( n \)[/tex] such that the fraction [tex]\( \frac{n}{16} \)[/tex] lies strictly between [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex].
First, let's express these bounds in terms of their decimal equivalents to understand the range better:
[tex]\[
\frac{1}{2} = 0.5 \quad \text{and} \quad \frac{3}{4} = 0.75
\][/tex]
We are tasked with finding [tex]\( n \)[/tex] such that:
[tex]\[
0.5 < \frac{n}{16} < 0.75
\][/tex]
Next, we multiply the entire inequality by 16 to solve for [tex]\( n \)[/tex]. This gives us:
[tex]\[
0.5 \times 16 < n < 0.75 \times 16
\][/tex]
[tex]\[
8 < n < 12
\][/tex]
Now, [tex]\( n \)[/tex] must be an integer, so the possible values of [tex]\( n \)[/tex] within this range are:
[tex]\[
n = 9, 10, 11
\][/tex]
These values satisfy the inequality and are the only integers between 8 and 12. Therefore, the possible values of [tex]\( n \)[/tex] are:
[tex]\[
n = 9, 10, 11
\][/tex]
