kinds of pies. Each pie pan was the same size. He served $$ \frac{1}{2} $$ of the blueberry pie. He served $$ \frac{1}{4} $$ of the apple pie. If each pie had 8 pieces to start, what fraction in eighths of the apple pie did he serve? How many more pieces of the blueberry pie than the apple pie did he serve?

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UpStudy AI · Accepted Answer

To solve the problem, we need to break it down step by step.

1. **Determine the number of pieces served from each pie:**
   - Each pie has 8 pieces.
   - For the blueberry pie, he served $$ \frac{1}{2} $$ of it:
     $$
     \text{Pieces of blueberry pie served} = \frac{1}{2} \times 8 = 4 \text{ pieces}
     $$
   - For the apple pie, he served $$ \frac{1}{4} $$ of it:
     $$
     \text{Pieces of apple pie served} = \frac{1}{4} \times 8 = 2 \text{ pieces}
     $$

2. **Convert the pieces of apple pie served into eighths:**
   - Since each pie has 8 pieces, we can express the pieces of apple pie served in eighths:
     $$
     \text{Fraction of apple pie served in eighths} = \frac{2 \text{ pieces}}{8 \text{ pieces}} = \frac{2}{8} = \frac{1}{4}
     $$

3. **Calculate how many more pieces of blueberry pie were served than apple pie:**
   - We already found that 4 pieces of blueberry pie were served and 2 pieces of apple pie were served:
     $$
     \text{Difference} = 4 \text{ pieces (blueberry)} - 2 \text{ pieces (apple)} = 2 \text{ pieces}
     $$

### Summary of Results:
- The fraction of the apple pie served in eighths is $$ \frac{1}{4} $$.
- He served 2 more pieces of blueberry pie than apple pie.

Thus, the final answers are:
- Fraction of apple pie served in eighths: $$ \frac{1}{4} $$
- More pieces of blueberry pie served than apple pie: 2 pieces.
He served $$ \frac{1}{4} $$ of the apple pie in eighths and 2 more pieces of blueberry pie than apple pie.

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