Final answer:
To turn the product of 4/3 and 3/5 into a mixed number, first multiply the numerators and denominators respectively to get 12/15, then reduce this fraction to 4/5. As 4/5 is a proper fraction and less than 1, it cannot be expressed as a mixed number.
Step-by-step explanation:
To convert the product of two fractions into a mixed number, first, multiply the numerators (top numbers) of the fractions and then multiply the denominators (bottom numbers). For the fractions 4/3 × 3/5, you multiply 4 by 3 to get the new numerator (12) and 3 by 5 to get the new denominator (15). Now, you have a new fraction of 12/15.
Reduce the fraction by dividing both the numerator and the denominator by their greatest common factor, which in this case is 3. This simplification gives us 4/5, which is already in its simplest form and is a proper fraction, meaning the numerator is smaller than the denominator. Therefore, it cannot be further expressed as a mixed number because it is less than 1.