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
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
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
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
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.
