To determine the fraction of the entire assignment that Celeste's mom checked, we can multiply the fraction of the problems that Celeste completed by the fraction of those that her mom checked.
First, we know:
- Celeste completed \( \frac{5}{6} \) of the problems.
- Her mom checked \( \frac{2}{3} \) of the assignment.
To find the fraction of the entire assignment that her mom checked, we multiply these two fractions:
\[ \text{Fraction checked} = \left(\frac{5}{6}\right) \times \left(\frac{2}{3}\right) \]
Now, multiply the numerators and the denominators:
\[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18} \]
Now, simplify \( \frac{10}{18} \):
\[ \frac{10}{18} = \frac{5}{9} \]
So, the fraction of the assignment that Celeste's mom checked is \( \frac{5}{9} \).
The correct answer is: 5/9.