-step explanation:1/2, 2/3 and -1/6Show that:1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)∵ 1/2 + (2/3 + (-1/6)∴ LCM of 3 and 6 = 6= 1/2 + (2 × 2/3 × 2) + (-1 × 1/6 ×1)= 1/2 + (4/6 – 1/6)= 1/2 + [(4-1)/6]=1/2 + (3/6)= (1 × 3/2 × 3) + (3 × 1/6 × 1) (∵ LCM of 2 and 6 = 3)= (3 + 3)/6 = 6/6 = 1And, (1/2 + 2/3) + (-1/6)∴ LCM of 2 and 3 = 6= (1 × 3/2 × 3) + (2 × 2/3 × 2) + (-1/6)= (3 + 4)/6 + -1/6= (7 – 1)/6 = 6/6 = 1∴ 1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)This verifies associative property of the addition of rational NUMBERS.(ii) -2/5, 4/15 and -7/10Show that:-2/5 + (4/15 + (-7/10) = (-2/5 + 4/15) + (-7/10)∵ -2/5 + (4/15 + (-7/10)∴ LCM of 15, 10 = 2 × 3 × 5 = 30= -2/5 + (4 × 2/15 × 2) + (-7 × 3/10 × 3)(∵ LCM of 15 and 10 = 30)= -2/5 + [(8 – 21)/30]= -2/5 – 13/30 = (-2 × 6/5 × 6) – (13 × 1/30 × 1)= (-12 -13)/30 = -25/30 = -5/6And, (-2/5 + 4/15) + -7/10∴ LCM of 5 and 15 = 3 × 5 = 15= (-2 × 3/5 × 3) + (4 × 1/15 ×1) + -7/10∴ LCM of 5 and 15 = 15= (-6 + 4)/15 + (-7/10)= -2/15 + (-7/10)= (-2 × 2/15 × 2) – (7 × 3/10 × 3)= -4/30 – 21/30 = -25/30 = -5/6∴ -2/5 + (4/15 + (-7/10) = (-2 /5 + 4/15) + (-7/10)This verifies associative property of the addition of rational numbers.