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.
