To find out how much the stock is worth after an increase of \( \frac{1}{4} \) when it currently has a value of \( 11.50 \), we can set up and evaluate the following addition expression:
\[ 11.50 + \frac{1}{4} \]
To evaluate this expression, we first need to convert \( \frac{1}{4} \) into a decimal. Since \( \frac{1}{4} = 0.25 \), we can rewrite the expression as:
\[ 11.50 + 0.25 \]
Now, we can add these two values:
\[ 11.50 + 0.25 = 11.75 \]
Therefore, the stock is worth $11.75 after the increase. We know this is the correct expression because we are simply adding the increase of \( \frac{1}{4} \) (or \( 0.25 \)) to the original stock value of \( 11.50 \).
Next, for Malik's quiz average, we know that he earns an average of \( 4 \frac{1}{2} \) points and that his average decreases by \( \frac{3}{4} \) points. First, we can rewrite \( 4 \frac{1}{2} \) as a mixed number, which is:
\[ 4 \frac{1}{2} = 4.5 \]
Now we set up the subtraction expression:
\[ 4.5 - \frac{3}{4} \]
To evaluate this expression, we need to convert \( \frac{3}{4} \) into a decimal, which is \( 0.75 \). Thus, we can rewrite the expression as:
\[ 4.5 - 0.75 \]
Now we subtract:
\[ 4.5 - 0.75 = 3.75 \]
Therefore, Malik's current quiz grade average is 3.75 points. We know this is the correct expression because we are subtracting the amount by which his average decreased (\( \frac{3}{4} \)) from his original average of \( 4.5 \).