22. Which of the following inequalities shows the correct relationship between the fractions 6/15, 4/8, and 6/10?

Answer: B

Explanation:

6/15 < 4/8 < 6/10

The relationship between the fractions shows that 6/15 is less than 4/8, which in turn is less than 6/10. This order reflects the correct comparison of their decimal values.

A) 6/10 < 4/8 < 6/15

This option is incorrect because it suggests that 6/10 is the smallest fraction, which contradicts the actual values of the fractions. When calculated, 6/10 is greater than both 6/15 and 4/8.

B) 6/15 < 4/8 < 6/10

This option is correct as it accurately represents the comparative sizes of the fractions. When expressed in decimal form, 6/15 equals 0.4, 4/8 equals 0.5, and 6/10 equals 0.6, confirming the order.

C) 4/8 < 6/15 < 6/10

This option is incorrect because it incorrectly places 6/15 between 4/8 and 6/10. The value of 6/15 is less than 4/8, thus invalidating this inequality.

D) 6/15 < 6/10 < 4/8

This option is also incorrect as it suggests that 6/10 is less than 4/8, which is not true. The actual value of 6/10 is greater than 4/8, making this inequality false.

Conclusion

Option B is definitively correct as it correctly reflects the comparative sizes of the fractions based on their decimal values. All other options fail due to inaccuracies in the relationships they propose, demonstrating a misunderstanding of the fractions involved.