To determine how many full cakes can be made from the gluten-free flour order, we first need to convert the amount of flour into a decimal or an improper fraction.
The order is for \( 6 + \frac{1}{2} \) pounds of flour, which can be converted as follows:
\[ 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \text{ pounds of flour} \]
Next, each gluten-free cake uses \( \frac{3}{4} \) pound of flour. To find out how many cakes can be made, we need to divide the total amount of flour by the amount of flour needed for one cake:
\[ \text{Number of cakes} = \frac{\text{Total flour}}{\text{Flour per cake}} = \frac{\frac{13}{2}}{\frac{3}{4}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{13}{2} \times \frac{4}{3} = \frac{13 \times 4}{2 \times 3} = \frac{52}{6} \]
Now, simplify \( \frac{52}{6} \):
\[ \frac{52}{6} = \frac{26}{3} \approx 8.67 \]
Since we want to find the number of full cakes that can be made, we take the whole number part of \( 8.67 \):
\[ \text{Number of full cakes} = 8 \]
Thus, the bakery can make 8 full cakes from the ordered flour.