Question 14

( 1/2 + 1/7 )^2

The expression (6/22 + 5/77)^2 simplifies to (1/2 + 1/7)^2 through common denominators and addition of fractions.

A) 1/( 3 + 5/7)^2

This option calculates a different expression entirely. It represents the reciprocal of the square of a sum, which does not align with the original expression being simplified.

B) ( 6/22)^2 +( 5/77)^2

This choice incorrectly separates the terms of the original expression. The original expression involves adding the fractions before squaring, while this option suggests squaring each fraction independently.

C) 1/9^2

This option suggests the expression evaluates to a specific numerical value, which is not correct. The original expression is a sum of fractions squared, not a numerical fraction squared.

D) ( 1/2 + 1/7)^2

This option is the correct simplification of the original expression. It correctly combines the fractions 6/22 and 5/77 into a single expression that represents their sum squared.

Conclusion

Option D is definitively correct as it accurately represents the simplified form of the original expression, capturing the necessary steps of combining and squaring the fractions. The other options fail to maintain the integrity of the original operation, leading to incorrect interpretations.