Question 10

11 11/15

To solve the multiplication of mixed numbers, first convert them to improper fractions. Thus, 4 2/5 becomes 22/5 and 2 2/3 becomes 8/3. Multiplying these fractions gives us (22/5) x (8/3) = 176/15, which simplifies to 11 11/15.

A) 11 11/15

This option is correct as it accurately represents the result of multiplying 4 2/5 by 2 2/3. The calculation of (22/5) x (8/3) results in 176/15, which simplifies to the mixed number 11 11/15.

B) 10 13/30

This option is incorrect. The multiplication of 4 2/5 and 2 2/3 does not yield this result. A detailed calculation shows that 10 13/30 represents a different numerical value that does not align with the correct product of the given mixed numbers.

C) 8 1/2

This option is also incorrect. The value 8 1/2 does not correspond to the outcome of the multiplication of the two mixed numbers. The process of multiplication and simplification does not lead to this value, making it an invalid choice.

D) 6 4/15

This option is incorrect as well. The multiplication of the two mixed numbers does not produce this result. The calculations clearly show that 6 4/15 represents a significantly lower value than the computed product of 11 11/15.

E) None of the Above

This option is incorrect since the correct answer, 11 11/15, is among the choices provided. Therefore, this selection fails to hold true as the correct answer is explicitly listed.

Conclusion

The correct answer, 11 11/15, is the only valid solution derived from the multiplication of the mixed numbers. All other options fail to reflect the correct mathematical outcome, either by representing different values or by being outright invalid in relation to the calculation performed. Thus, 11 11/15 stands as the definitive answer.