Rationale
The product of 2,2/3 and 3,3/8 is 9.
To arrive at this result, we first convert each mixed number to an improper \fraction: 2,2/3 becomes 8/3, and 3,3/8 becomes 27/8. We then multiply these \fractions together and simplify the resulting \fraction, which yields the number 9.
A) 5,5/11
This is incorrect. Multiplying 2,2/3 by 3,3/8 does not result in the mixed number 5,5/11. When each mixed number is converted to an improper \fraction and multiplied together, the result is 72/8, or 9, not 5,5/11.
B) 6,1/24
This is incorrect. Multiplying 2,2/3 by 3,3/8 does not result in the mixed number 6,1/24. When each mixed number is converted to an improper \fraction and multiplied together, the result is 72/8, or 9, not 6,1/24.
C) 7
This is incorrect. Multiplying 2,2/3 by 3,3/8 does not result in 7. When each mixed number is converted to an improper \fraction and multiplied together, the result is 72/8, or 9, not 7.
D) 9
This is the correct result. When 2,2/3 and 3,3/8 are converted to improper \fractions, they become 8/3 and 27/8 respectively. Multiplying these together yields 72/8, which simplifies to 9.
Conclusion
The product of the mixed numbers 2,2/3 and 3,3/8 is 9. The incorrect answers reflect either incorrect conversion of the mixed numbers to improper \fractions, incorrect multiplication of the \fractions, or incorrect simplification of the resulting \fraction. Understanding the process of converting mixed numbers to improper \fractions, correctly multiplying \fractions, and simplifying the result is crucial to correctly solving this type of problem.
