To determine how many full gluten-free cakes the bakery can make, we need to divide the total amount of flour ordered by the amount of flour needed for each cake.
First, convert the mixed number \(6 \frac{1}{2}\) to an improper fraction:
\[ 6 \frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2} \]
Next, calculate how many \( \frac{3}{4} \) pound portions fit into \( \frac{13}{2} \) pounds of flour. This is done by dividing \( \frac{13}{2} \) by \( \frac{3}{4} \):
\[ \frac{13}{2} \div \frac{3}{4} = \frac{13}{2} \times \frac{4}{3} = \frac{13 \times 4}{2 \times 3} = \frac{52}{6} = \frac{26}{3} \]
Now, we need to convert \( \frac{26}{3} \) to a mixed number to find out how many full cakes can be made:
\[ \frac{26}{3} = 8 \frac{2}{3} \]
Since we can only make full cakes, the bakery can make 8 full gluten-free cakes from the ordered flour.
Therefore, the answer is:
\[ \boxed{8} \]
1 answer