Final answer:
The multiplication of the mixed numbers 4 2/7 and 2 1/5 results in the mixed number 9 3/7 after converting them to improper fractions, multiplying, and simplifying. Therefore, the correct option is D.
Step-by-step explanation:
To multiply mixed numbers, first convert them into improper fractions. For the given problem, the mixed numbers are 4 2/7 and 2 1/5.
First, convert 4 2/7 to an improper fraction: (7 × 4) + 2 = 30/7. Next, convert 2 1/5 to an improper fraction: (5 × 2) + 1 = 11/5.
Now, multiply the improper fractions: (30/7) × (11/5). Multiply the numerators together and the denominators together: (30 × 11) / (7 × 5) = 330 / 35.
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 330 / 35 = 66/7.
Finally, convert the improper fraction back to a mixed number: 66/7 = 9 with a remainder of 3, so 66/7 = 9 3/7.
Therefore, the result of 4 2/7 multiplied by 2 1/5 is 9 3/7. Therefore, the correct option is D.