To find out how many full gluten-free cakes the bakery can make, you need to divide the total amount of gluten-free flour by the amount needed for one cake.
The bakery ordered \( 6 \frac{1}{2} \) pounds of gluten-free flour, which can be converted to an improper fraction:
\[ 6 \frac{1}{2} = \frac{13}{2} \text{ pounds} \]
Each gluten-free cake uses \( \frac{3}{4} \) pound of flour. To find the number of cakes, divide the total flour by the flour needed for one cake:
\[ \text{Number of cakes} = \frac{\frac{13}{2}}{\frac{3}{4}} \]
To divide fractions, multiply by the reciprocal of the second fraction:
\[ \text{Number of cakes} = \frac{13}{2} \times \frac{4}{3} = \frac{13 \times 4}{2 \times 3} = \frac{52}{6} \]
Now simplify \( \frac{52}{6} \):
\[ \frac{52}{6} = \frac{26}{3} \approx 8.67 \]
Since the bakery can only make whole cakes, we take the whole number part:
\[ \text{Full cakes} = 8 \]
Therefore, the bakery can make 8 full cakes from the order of gluten-free flour.
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