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?

Understand the Problem

The question is asking for the number of pies left after a baker sold a certain quantity in the morning and afternoon. We will calculate the total sold and subtract it from the initial amount.

Answer

The baker has $3 \frac{1}{4}$ pies left.

Steps to Solve

Convert Mixed Numbers to Improper Fractions

First, we need to convert the mixed numbers of pies sold into improper fractions.

For the morning:
$7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4}$

For the afternoon:
$4 \frac{2}{4} = 4 + \frac{2}{4} = \frac{16}{4} + \frac{2}{4} = \frac{18}{4}$

Calculate Total Sold Pies

Now, we add the total pies sold in the morning and afternoon.

Total sold:
$$\frac{29}{4} + \frac{18}{4} = \frac{29 + 18}{4} = \frac{47}{4}$$

Convert Total Sold to a Mixed Number

Convert the total sold back to a mixed number for easier understanding:
$$\frac{47}{4} = 11 \frac{3}{4}$$

Subtract Total Sold from Initial Amount

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

Initial amount = 15 pies = $\frac{60}{4}$ (to have a common denominator)

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

Convert Result to Mixed Number

Finally, convert $\frac{13}{4}$ back to a mixed number:

$$\frac{13}{4} = 3 \frac{1}{4}$$

The baker has $3 \frac{1}{4}$ pies left.

More Information

This problem involves converting mixed numbers into improper fractions and performing basic addition and subtraction with fractions. It's a common scenario in practical math where you track quantities.

Tips

Failing to convert mixed numbers to improper fractions before performing arithmetic.
Forgetting to find a common denominator when adding or subtracting fractions.
Not converting the final result back to a mixed number if required.

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