Which of the following is equivalent to the expression above?

Rationale

( 1/2 + 1/7 )^2

The expression ( 1/2 + 1/7 )^2 simplifies to the same value as the original expression provided in the question. When calculated, the sum of 1/2 and 1/7 yields a common denominator, leading to the equivalent squared value.

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

This expression evaluates to 1 divided by the square of the sum of 3 and 5/7. When calculated, it does not yield the same result as the original expression since the components do not combine or simplify in the same way as (1/2 + 1/7).

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

This choice represents the sum of two squared fractions. Evaluating this would not yield the same value as the original expression, as it involves separate squared terms rather than a single squared sum, leading to a different numerical result.

C (1/9^2) YOUR ANSWER

This option simplifies to 1/81, which is a fixed value. The original expression involves a summation followed by squaring, resulting in a different value, thus making this option incorrect.

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

This expression correctly reflects the addition of 1/2 and 1/7, followed by squaring the result. When calculated, it matches the equivalent value of the original expression, confirming its correctness.

Conclusion

The expression (1/2 + 1/7)^2 accurately represents the equivalent value sought in the question. While other options provided different calculations or structures, they do not simplify to match the original expression. Understanding how to manipulate and simplify fractions is key to identifying equivalent expressions in mathematics.

Which of the following is equivalent to the expression above?

( 1/2 + 1/7 )^2

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