Question 3

3/5 < 2/3 < 5/7

The inequality 3/5 < 2/3 < 5/7 accurately represents the correct relationship among these fractions when evaluated. Each fraction is compared to the others to determine their relative sizes, confirming that 3/5 is indeed less than 2/3, which in turn is less than 5/7.

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

This option is incorrect because it suggests that 2/3 is less than 3/5. When evaluated, 2/3 is actually greater than 3/5, making this inequality false.

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

This option is incorrect as well. It incorrectly places 5/7 between 2/3 and 3/5. In reality, 5/7 is greater than both 2/3 and 3/5, which contradicts the sequence presented in this option.

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

This option is correct. When comparing the fractions, 3/5 is indeed less than 2/3, and 2/3 is less than 5/7, making this inequality valid.

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

This option is incorrect because it suggests that 5/7 is less than 2/3. In fact, 5/7 is greater than 2/3, which invalidates the entire inequality.

Conclusion

Option C is definitively the correct choice as it accurately reflects the order of the fractions based on their values. All other options fail due to misrepresentations of the relationships between the fractions, leading to incorrect inequalities. Thus, understanding the comparative sizes of fractions is crucial for solving such problems accurately.