Question 3

3/5 < 2/3 < 5/7

The correct inequality order is 3/5 < 2/3 < 5/7, meaning that 3/5 is the smallest, followed by 2/3, and then 5/7 as the largest.

A) 2/3 < 3/5 < 5/7

This option is incorrect because 2/3 is actually greater than 3/5. When comparing the fractions, 2/3 equals approximately 0.6667 and 3/5 equals 0.6, indicating that 3/5 is less than 2/3.

B) 2/3 < 5/7 < 3/5

This option is also incorrect. While 2/3 is greater than both 5/7 and 3/5, 5/7 (approximately 0.7143) is actually greater than 2/3. Therefore, this order does not hold true.

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

This option is correct. When comparing the values, 3/5 (0.6) is less than 2/3 (approximately 0.6667), and 2/3 is less than 5/7 (approximately 0.7143), making this the correct inequality order.

D) 3/5 < 5/7 < 2/3

This option is incorrect because, although 3/5 is less than 5/7, it incorrectly places 2/3 as greater than 5/7, which is not true. The correct order should place 2/3 before 5/7.

Conclusion

The correct answer is C) 3/5 < 2/3 < 5/7, as it accurately reflects the numerical relationships between the fractions involved. All other options fail because they misrepresent the comparative values of the fractions, either by incorrectly ordering them or by making incorrect comparisons.