To solve this problem, we'll determine how many ounces are in a cup when it is filled to [tex]\(\frac{2}{3}\)[/tex] of its capacity.
1. Identify the total capacity of the cup: The cup holds 8 ounces of liquid when it is full.
2. Determine the fraction of the cup that is filled: The cup is [tex]\(\frac{2}{3}\)[/tex] full.
3. Calculate the amount of liquid in the cup: To find out how many ounces are in the cup when it is [tex]\(\frac{2}{3}\)[/tex] full, we multiply the total capacity of the cup by the fraction that it is filled.
[tex]\[
\text{Amount of liquid} = \text{Total capacity} \times \text{Fraction filled}
\][/tex]
4. Substituting the values into the equation:
[tex]\[
\text{Amount of liquid} = 8 \, \text{ounces} \times \frac{2}{3}
\][/tex]
5. Perform the multiplication:
[tex]\[
8 \times \frac{2}{3} = \frac{8 \times 2}{3} = \frac{16}{3}
\][/tex]
6. Simplify the fraction:
[tex]\[
\frac{16}{3} \approx 5.3333 \, \text{ounces}
\][/tex]
So, when the cup is [tex]\(\frac{2}{3}\)[/tex] full, it contains approximately 5.3333 ounces of liquid.
