Final answer:
Sam collected a total of 4127 7/18 insects in 2008 by multiplying the number of jars (193/3) by the number of insects per jar (385/6).
Step-by-step explanation:
To calculate the total number of insects that Sam collected in 2008, we need to multiply the number of jars by the number of insects per jar. First, let's express the mixed numbers as improper fractions to make the multiplication easier:
64 1/3 jars becomes (64 × 3 + 1)/3 = 193/3 jars.
64 1/6 insects per jar becomes (64 × 6 + 1)/6 = 385/6 insects.
Now, let's multiply the two fractions:
(193/3) jars × (385/6) insects/jar = (193 × 385)/(3 × 6) insects = 74285/18 insects.
To convert the improper fraction back to a mixed number, we divide 74285 by 18:
74285 ÷ 18 = 4127 with a remainder of 7, so we have 4127 7/18 insects.
Therefore, Sam collected 4127 7/18 insects in total in 2008.