Question 15

2 2/9

The result of the multiplication \( \frac{1}{2} \times 1 \frac{3}{5} \times 2 \frac{7}{9} \) simplifies to \( 2 \frac{2}{9} \), confirming that this is the correct answer.

A) 3 11/16

This option is incorrect as it does not represent the product of the fractions involved in the multiplication. The calculations show that the product results in a smaller value than 3, thus eliminating this choice.

B) 2 2/9

This is the correct answer. When multiplying the fractions \( \frac{1}{2} \times \frac{8}{5} \times \frac{25}{9} \) (the converted improper fractions of \( 1 \frac{3}{5} \) and \( 2 \frac{7}{9} \)), the result simplifies to \( \frac{20}{9} \), which converts to the mixed number \( 2 \frac{2}{9} \).

C) 2 21/90

This option is incorrect as the fraction \( \frac{21}{90} \) does not accurately represent the product obtained from the multiplication. The calculation does not yield a result with a denominator of 90, thus making this choice invalid.

D) 20/9

While this option represents the improper fraction form of the correct answer, it does not match the mixed number format that the question seems to imply. Hence, although related, it does not fulfill the requirement for the correct answer as specified.

Conclusion

The correct answer, \( 2 \frac{2}{9} \), is derived directly from the multiplication of the given fractions and confirms the requirement to express the result as a mixed number. Other options either miscalculate the product or do not fit the expected format, reinforcing that \( 2 \frac{2}{9} \) is the definitive and correct solution to the problem.