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

Rationale

6/15 < 4/8 < 6/10

To determine the correct relationship between the fractions 6/15, 4/8, and 6/10, we can convert them to their decimal forms: 6/15 = 0.4, 4/8 = 0.5, and 6/10 = 0.6. This shows that 6/15 is the smallest, followed by 4/8, and finally 6/10 as the largest.

A (6/10 < 4/8 < 6/15) YOUR ANSWER

This inequality incorrectly suggests that 6/10 is less than both 4/8 and 6/15. However, as established, 6/10 equals 0.6, which is greater than both 4/8 (0.5) and 6/15 (0.4).

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

This choice accurately represents the order of the fractions when converted to decimal form, confirming that 6/15 is indeed the smallest, followed by 4/8, and then 6/10 as the largest.

C (4/8 < 6/15 < 6/10) YOUR ANSWER

This option misplaces the order by claiming 4/8 is less than 6/15. Since 4/8 (0.5) is greater than 6/15 (0.4), this inequality does not hold true.

D (6/15 < 6/10 < 4/8) YOUR ANSWER

This choice mistakenly suggests that 6/10 is less than 4/8. However, 6/10 (0.6) is greater than 4/8 (0.5), making this inequality inaccurate.

Conclusion

The correct ordering of the fractions 6/15, 4/8, and 6/10 is clearly represented by the inequality 6/15 < 4/8 < 6/10. This conclusion is supported by converting the fractions to decimal form, establishing their relative sizes accurately. Understanding these relationships among fractions is essential in mathematics, especially when comparing values.

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

6/15 < 4/8 < 6/10

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