Question

8 michelle has 8 cups of flour. she covers the countertop and the rolling pin with \\(\frac{1}{2}\\) cup of flour. then she uses \\(2\frac{1}{4}\\) cups of flour for each batch of biscuits she bakes. how many full batches of biscuits can michelle bake? show your work.

Explanation:

Step1: Subtract the flour used for covering from the total flour.

Total flour is 8 cups, and she uses \(\frac{1}{2}\) cup for covering. So the remaining flour is \(8 - \frac{1}{2}\). We can write 8 as \(\frac{16}{2}\), so \(\frac{16}{2}-\frac{1}{2}=\frac{15}{2}\) cups.

Step2: Divide the remaining flour by the flour used per batch.

Each batch uses \(2\frac{1}{4}\) cups, which is \(\frac{9}{4}\) cups. Now we divide \(\frac{15}{2}\) by \(\frac{9}{4}\). Dividing by a fraction is multiplying by its reciprocal, so \(\frac{15}{2}\times\frac{4}{9}\). Simplify this: 15 and 9 have a common factor of 3, 2 and 4 have a common factor of 2. So it becomes \(\frac{5}{1}\times\frac{2}{3}=\frac{10}{3}\approx 3.33\). But we need the number of full batches, so we take the integer part.

Answer:

3