To arrange the given rational numbers in ascending order, we need to find their least common multiple (LCM) of the denominators. The LCM of 2, 5, 15, and 10 is 30.
Converting the given rational numbers to have a common denominator of 30, we get:
2/5 = 12/30 -1/2 = -15/30 8/-15 = -16/30 -3/-10 = 9/30
Therefore, the ascending order of the given rational numbers is:
-16/30 < -15/30 < 9/30 < 12/30
Hence, the ascending order of the given rational numbers is -16/30, -15/30, 9/30, 12/30.