A baker made 15 pies. She sold 7 1/4 pies in the morning and 4 2/4 pies in the afternoon. How many pies did she have left?

Steps to Solve

1. Identify the total amount of pies sold

   First, we need to find out how many pies were sold in total. The baker sold $7 \frac{1}{4}$ pies in the morning and $4 \frac{2}{4}$ pies in the afternoon.

2. Convert mixed numbers to improper fractions

   Convert the mixed numbers to improper fractions:

   • For $7 \frac{1}{4}$: $$ 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4} $$
   • For $4 \frac{2}{4}$: $$ 4 \frac{2}{4} = \frac{4 \times 4 + 2}{4} = \frac{16 + 2}{4} = \frac{18}{4} $$

3. Add the fractions of pies sold

   Next, we need to add the two improper fractions:

   To do that, we can add: $$ \frac{29}{4} + \frac{18}{4} = \frac{29 + 18}{4} = \frac{47}{4} $$

4. Subtract the total pies sold from the initial amount

   Now, we subtract the total pies sold from the initial amount of pies:

   • Initial pies: 15 (can be expressed as $\frac{60}{4}$ for consistency): $$ 15 = \frac{15 \times 4}{4} = \frac{60}{4} $$

   So: $$ \frac{60}{4} - \frac{47}{4} = \frac{60 - 47}{4} = \frac{13}{4} $$

5. Convert the result back to a mixed number

   Finally, convert the improper fraction back to a mixed number: $$ \frac{13}{4} = 3 \frac{1}{4} $$