Final answer:
To multiply mixed numbers, convert them into improper fractions, multiply the numerators and denominators separately, and simplify the resulting fraction.
Step-by-step explanation:
To multiply mixed numbers, we first convert them into improper fractions. Then, we multiply the numerators and denominators separately and simplify the resulting fraction if possible.
In this case, (2 4/5) can be written as 14/5 and (-5 2/3) can be written as -17/3. Therefore, (2 4/5) (-5 2/3) can be simplified to (-14/5) * (-17/3).
To multiply fractions, we multiply the numerators and denominators together. So, (-14/5) * (-17/3) = (14 * 17) / (5 * 3) = 238/15 = 15 13/15.