Rationale
6/15 < 4/8 < 6/10
To determine the correct relationship among the fractions 6/15, 4/8, and 6/10, we first simplify and compare each fraction. Upon simplification, we find that 6/15 equals 2/5, 4/8 equals 1/2, and 6/10 equals 3/5. This shows that 6/15 is less than 4/8, which is less than 6/10.
A) This choice suggests that 6/10 is less than 4/8, which is incorrect. In fact, 6/10 (or 3/5) is greater than 4/8 (or 1/2). Therefore, this inequality does not accurately represent the relationship between the fractions.
B) This is the correct choice. It accurately states that 6/15 (or 2/5) is less than 4/8 (or 1/2), and 4/8 is less than 6/10 (or 3/5). This correctly reflects the relationships after comparing the simplified values of the fractions.
C) This option incorrectly places 4/8 in the middle of 6/15 and 6/10. Although 4/8 is greater than 6/15, it is not less than 6/10, as 6/10 is greater than 4/8. Thus, the stated relationship does not hold true.
D) This choice suggests that 6/15 is less than 6/10 and less than 4/8, which is incorrect. While 6/15 is indeed less than 6/10, it is not less than 4/8 since 4/8 is greater than 6/10.
Conclusion
The correct order of the fractions is 6/15 < 4/8 < 6/10, confirmed by simplifying each fraction. By analyzing their values, we see that 6/15 is the smallest, followed by 4/8, and finally 6/10 as the largest. This understanding of fractional relationships is fundamental in comparing rational numbers effectively.