To determine how many pounds of grapes were left after Alice ate some, we can follow these steps:
1. Understand the initial amount of grapes Alice bought:
Alice initially bought [tex]\(\frac{8}{9}\)[/tex] of a pound of grapes.
2. Determine the amount of grapes Alice ate:
Alice ate [tex]\(\frac{1}{3}\)[/tex] of a pound of grapes.
3. Convert the fraction of grapes Alice ate to have a common denominator with the initial amount:
Since the initial amount ([tex]\(\frac{8}{9}\)[/tex]) is expressed with a denominator of 9, and Alice ate [tex]\(\frac{1}{3}\)[/tex], we need to convert [tex]\(\frac{1}{3}\)[/tex] to an equivalent fraction with a denominator of 9:
[tex]\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\][/tex]
4. Subtract the amount of grapes Alice ate from the initial amount she bought:
Now we subtract [tex]\(\frac{3}{9}\)[/tex] (grapes she ate) from [tex]\(\frac{8}{9}\)[/tex] (initial amount):
[tex]\[
\frac{8}{9} - \frac{3}{9} = \frac{8 - 3}{9} = \frac{5}{9}
\][/tex]
Therefore, the remaining pounds of grapes are [tex]\(\frac{5}{9}\)[/tex].
The correct answer is:
D. [tex]\(\frac{5}{9}\)[/tex]
