To solve the problem of determining how many more quarts of water the pot can hold, let's break it down step-by-step.
1. Determine the total capacity of the pot: The pot's capacity is given as [tex]\( 5 + \frac{1}{\frac{1}{2}} \)[/tex] quarts.
- The expression [tex]\( \frac{1}{\frac{1}{2}} \)[/tex] can be simplified as follows:
[tex]\[ \frac{1}{\frac{1}{2}} = 1 \div \frac{1}{2} = 1 \times 2 = 2 \][/tex]
- So, the total capacity of the pot is:
[tex]\[ 5 + 2 = 7 \text{ quarts} \][/tex]
2. Calculate the filled fraction of the pot: The pot is filled [tex]\( \frac{2}{3} \)[/tex] of the way with water.
- This means the amount of water currently in the pot is:
[tex]\[ \text{filled amount} = \frac{2}{3} \times 7 = \frac{14}{3} \][/tex]
- Simplifying [tex]\( \frac{14}{3} \)[/tex]:
[tex]\[ \frac{14}{3} \approx 4.67 \text{ quarts (or expressed as a fraction: } 4 \frac{2}{3} \text{ quarts)} \][/tex]
3. Determine the remaining capacity: To find the remaining amount of water the pot can hold, subtract the filled amount from the total capacity.
- The remaining capacity is:
[tex]\[ \text{remaining capacity} = 7 - \frac{14}{3} \][/tex]
- Convert 7 to an improper fraction with a denominator of 3:
[tex]\[ 7 = \frac{21}{3} \][/tex]
- Subtract the fractions:
[tex]\[ \frac{21}{3} - \frac{14}{3} = \frac{21 - 14}{3} = \frac{7}{3} \][/tex]
4. Simplify the remaining capacity: Finally, simplify [tex]\( \frac{7}{3} \)[/tex]:
- [tex]\( \frac{7}{3} \)[/tex] is equivalent to:
[tex]\[ 2 \frac{1}{3} \text{ quarts} \][/tex]
So, the pot can hold an additional [tex]\( 2 \frac{1}{3} \)[/tex] quarts of water.
