To determine which rational number from the given options lies between the bounds of [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex], we need to check each number against these bounds.
The numbers to be evaluated are:
a) [tex]\(-\frac{1}{16}\)[/tex]
b) [tex]\(\frac{11}{16}\)[/tex]
c) [tex]\(\frac{3}{7}\)[/tex]
d) [tex]\(-\frac{3}{5}\)[/tex]
Let's recall the bounds:
- Lower bound: [tex]\(-\frac{1}{2}\)[/tex]
- Upper bound: [tex]\(\frac{3}{8}\)[/tex]
We'll check each option one by one:
1. Option (a): [tex]\(-\frac{1}{16}\)[/tex]
- Convert [tex]\(-\frac{1}{16}\)[/tex] to a decimal: [tex]\(-\frac{1}{16} = -0.0625\)[/tex].
- Compare with bounds:
[tex]\[
-\frac{1}{2} = -0.5 \quad \text{and} \quad \frac{3}{8} \approx 0.375
\][/tex]
[tex]\[
-0.5 < -0.0625 < 0.375
\][/tex]
- This number lies between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
2. Option (b): [tex]\(\frac{11}{16}\)[/tex]
- Convert [tex]\(\frac{11}{16}\)[/tex] to a decimal: [tex]\(\frac{11}{16} \approx 0.6875\)[/tex].
- Compare with bounds:
[tex]\[
-0.5 < 0.6875
\][/tex]
- This number does not lie between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
3. Option (c): [tex]\(\frac{3}{7}\)[/tex]
- Convert [tex]\(\frac{3}{7}\)[/tex] to a decimal: [tex]\(\frac{3}{7} \approx 0.4286\)[/tex].
- Compare with bounds:
[tex]\[
-0.5 < 0.4286
\][/tex]
- This number does not lie between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
4. Option (d): [tex]\(-\frac{3}{5}\)[/tex]
- Convert [tex]\(-\frac{3}{5}\)[/tex] to a decimal: [tex]\(-\frac{3}{5} = -0.6\)[/tex].
- Compare with bounds:
[tex]\[
-0.6 < -0.5
\][/tex]
- This number does not lie between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
Based on the comparisons, only option (a), [tex]\(-\frac{1}{16}\)[/tex], lies between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex].
Therefore, the rational number that lies between [tex]\(-\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex] is [tex]\(\boxed{-\frac{1}{16}}\)[/tex].
