Which of the following expressions is one way to represent 3/4 as a sum using only unit fractions?

Rationale

1/2 + 1/4 represents 3/4 as a sum using only unit fractions.

This expression correctly sums to 3/4, as 1/2 is equivalent to 2/4, and when added to 1/4, it totals 3/4, demonstrating a valid representation using unit fractions.

A (1/8 + 1/8 + 1/8 + 1/4 + 1/4) YOUR ANSWER

This expression sums to 1/2, since 1/8 + 1/8 + 1/8 equals 3/8, and adding 1/4 (which is 2/8) results in 5/8. The final addition of another 1/4 (2/8) brings the total to 1, not 3/4, making it an incorrect representation.

B (2/8 + 1/4 + 4/16) YOUR ANSWER

This expression also does not equal 3/4. Converting to a common denominator, 2/8 is equivalent to 1/4, and 4/16 is also equivalent to 1/4. Therefore, the sum becomes 1/4 + 1/4 + 1/4, totaling 3/4, but the presence of non-unit fractions makes this option invalid.

C (5/8 + 2/16) YOUR ANSWER

This expression sums to 3/4; however, 2/16 simplifies to 1/8, so the total is 5/8 + 1/8, which equals 6/8 or 3/4. Despite reaching the correct total, this option includes non-unit fractions, making it an improper representation.

D (1/2 + 1/4) CORRECT

This combination correctly adds up to 3/4, as explained earlier. Each fraction is a unit fraction, preserving the requirement of the question.

Conclusion

To represent 3/4 as a sum of unit fractions, 1/2 + 1/4 is the only valid choice. While other options may arrive at the correct total, they do not adhere strictly to the requirement of using only unit fractions. Thus, option D is the only answer that satisfies both the sum and the unit fraction condition.

Which of the following expressions is one way to represent 3/4 as a sum using only unit fractions?

1/2 + 1/4 represents 3/4 as a sum using only unit fractions.

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