Final answer:
To multiply -3 1/3 and -2 7/10, convert the mixed numbers to improper fractions, multiply the numerators and denominators, then simplify the fraction by canceling out common factors. The product is 9.
Step-by-step explanation:
To calculate the product of -3 1/3 and -2 7/10, we need to convert both mixed numbers to improper fractions. -3 1/3 can be written as -10/3 and -2 7/10 can be written as -27/10. To multiply these fractions, we multiply the numerators together and the denominators together. So, (-10/3) x (-27/10) = 270/30.
To simplify the fraction, we can cancel out common factors between the numerator and denominator. The greatest common factor of 270 and 30 is 30. Dividing both the numerator and denominator by 30, we get 9/1, which is equivalent to 9. Therefore, the product of -3 1/3 and -2 7/10 is 9.