To find the weight of each science textbook, we need to divide the total weight of the textbooks by the number of textbooks.
The total weight of the 5 science textbooks is \(6 \frac{2}{3}\) pounds. First, we convert this mixed number into an improper fraction.
\[ 6 \frac{2}{3} = 6 \times 3 + 2 = 18 + 2 = 20 \] So, \(6 \frac{2}{3} = \frac{20}{3}\) pounds.
Now, we divide this total weight by the number of books (5):
\[ \text{Weight of each book} = \frac{\frac{20}{3}}{5} \]
Dividing by 5 is the same as multiplying by \(\frac{1}{5}\):
\[ \frac{\frac{20}{3}}{5} = \frac{20}{3} \times \frac{1}{5} = \frac{20}{15} \]
Now, simplify \(\frac{20}{15}\):
\[ \frac{20}{15} = \frac{4}{3} \]
Now we convert \(\frac{4}{3}\) back into a mixed number:
\(\frac{4}{3}\) can be expressed as:
\[ 1 \frac{1}{3} \]
Therefore, the weight of each science textbook is \(1 \frac{1}{3}\) pounds.