Which of the following inequalities is correct?

Rationale

3/5 < 2/3 < 5/7 is the correct inequality.

This correct inequality sequence is achieved by converting each fraction into a decimal format to simplify comparison. The decimal equivalents are approximately 0.60 for 3/5, 0.67 for 2/3, and 0.71 for 5/7.

A (2/3 < 3/5 < 5/7) YOUR ANSWER

This inequality is incorrect. While 2/3 (approximately 0.67) is less than 5/7 (approximately 0.71), it is not less than 3/5 (approximately 0.60). Therefore, this sequence does not represent an increasing order.

B (2/3 < 5/7 < 3/5) YOUR ANSWER

This inequality sequence is also incorrect. Although 2/3 (approximately 0.67) is less than 5/7 (approximately 0.71), 5/7 is not less than 3/5 (approximately 0.60). This sequence is not in ascending order.

C (3/5 < 2/3 < 5/7) CORRECT

This is the correct inequality sequence. When converted to decimal form, 3/5 (approximately 0.60) is less than 2/3 (approximately 0.67), and 2/3 is less than 5/7 (approximately 0.71). This sequence correctly represents an increasing order.

D (3/5 < 5/7 < 2/3) YOUR ANSWER

This inequality is incorrect. Although 3/5 (approximately 0.60) is less than 5/7 (approximately 0.71), 5/7 is not less than 2/3 (approximately 0.67). Therefore, this sequence does not present an increasing order.

Conclusion

The correct inequality sequence is 3/5 < 2/3 < 5/7. When these fractions are converted into decimal form for easy comparison, it is clear that 3/5 (approximately 0.60) is less than 2/3 (approximately 0.67), and 2/3 is less than 5/7 (approximately 0.71). All the other options do not accurately represent an increasing sequence of these three fractions.

Which of the following inequalities is correct?

3/5 < 2/3 < 5/7 is the correct inequality.

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