Final answer:
To multiply 4 2/3 by 9/10, convert the mixed number to an improper fraction, then multiply the numerators and the denominators separately. The answer in simplest form is 21/5.
Step-by-step explanation:
To multiply 4 2/3 by 9/10, you can convert the mixed number to an improper fraction. 4 2/3 is equal to (4x3 + 2)/3 = 14/3. Now, you can multiply the numerators (14 and 9) to get 126, and multiply the denominators (3 and 10) to get 30. So, 4 2/3 x 9/10 = 126/30, which can be simplified to 21/5 in simplest form.
After simplification, the fraction is 21/5. Since the numerator is larger than the denominator, it can also be expressed as a mixed number. Thus, dividing 21 by 5, we get 4 with a remainder of 1, giving us the mixed number 4 1/5.