To determine the net gain or loss of the stock over these three days, we need to combine the losses and gains together.
First, let's convert the mixed fractions to improper fractions and then to decimal form for easier calculations:
1. Loss on Monday:
The stock lost [tex]\(8 \frac{3}{8}\)[/tex] points.
[tex]\[
8 \frac{3}{8} = 8 + \frac{3}{8}
\][/tex]
Converting this to a decimal:
[tex]\[
8 + \frac{3}{8} = 8 + 0.375 = 8.375
\][/tex]
Since it is a loss, it will be [tex]\(-8.375\)[/tex].
2. Loss on Tuesday:
The stock lost [tex]\(1 \frac{5}{8}\)[/tex] points.
[tex]\[
1 \frac{5}{8} = 1 + \frac{5}{8}
\][/tex]
Converting this to a decimal:
[tex]\[
1 + \frac{5}{8} = 1 + 0.625 = 1.625
\][/tex]
Since it is a loss, it will be [tex]\(-1.625\)[/tex].
3. Gain on Wednesday:
The stock gained [tex]\(13\)[/tex] points.
[tex]\[
13
\][/tex]
Now, combine these together:
[tex]\[
\text{Net Change} = \text{Monday's Loss} + \text{Tuesday's Loss} + \text{Wednesday's Gain}
\][/tex]
[tex]\[
\text{Net Change} = -8.375 + (-1.625) + 13
\][/tex]
[tex]\[
\text{Net Change} = -8.375 - 1.625 + 13
\][/tex]
[tex]\[
\text{Net Change} = -10 + 13
\][/tex]
[tex]\[
\text{Net Change} = 3
\][/tex]
Thus, the net gain of the stock over these three days is 3 points.
Among the provided options:
- A gain of [tex]$6 \frac{1}{4}$[/tex] points
- A loss of 23 points
- A gain of [tex]$19 \frac{3}{4}$[/tex] points
- A gain of 3 points
The correct option is:
[tex]\[
\boxed{\text{a gain of 3 points}}
\][/tex]
