Question
Kelly and Brian ordered a large pizza, ate 2/3 of it, and took the rest home. The next day, they shared the leftover pizza equally with their daughter. What fraction of the original pizza did each of them get?
Answers
GPT-4o mini
Kelly and Brian originally ordered a large pizza, and together they ate \( \frac{2}{3} \) of it. This means that the amount of pizza they have left is:
\[
1 - \frac{2}{3} = \frac{1}{3}
\]
The remaining pizza, \( \frac{1}{3} \) of the original pizza, is then shared equally with their daughter. Since there are three people sharing the leftover pizza (Kelly, Brian, and their daughter), we need to divide the leftover pizza into three equal parts:
\[
\text{Each person's share} = \frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, each of them (Kelly, Brian, and their daughter) gets \( \frac{1}{9} \) of the original pizza.
To summarize:
- Each of them got \( \frac{1}{9} \) of the original pizza.
\[
1 - \frac{2}{3} = \frac{1}{3}
\]
The remaining pizza, \( \frac{1}{3} \) of the original pizza, is then shared equally with their daughter. Since there are three people sharing the leftover pizza (Kelly, Brian, and their daughter), we need to divide the leftover pizza into three equal parts:
\[
\text{Each person's share} = \frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
Thus, each of them (Kelly, Brian, and their daughter) gets \( \frac{1}{9} \) of the original pizza.
To summarize:
- Each of them got \( \frac{1}{9} \) of the original pizza.