Arrange the following rational numbers in ascending order.

(i) -1/3,  (-4)/3,  (-2)/9

(ii) -2/3, 4/5, 6/7, -1/6

(i) We have -1/3, -4/3, -2/9

LCM of 3, 3, and 9 = 9

∴ (-1 × 3)/(3 × 3), (-4 × 3)/(3 × 3), (-2 × 1)/(9 × 1)

[Converting denominators as same number]

⇒ -3/9, -12/9, -2/9

Since -12/9 < -3/9 < -2/9

∴ -4/3 < -1/3 < -2/9

(ii) We have -2/3, 4/5, 6/7, -1/6

LCM of 3, 5, 6, and 7 = 210

∴ (-2 × 70)/(3 × 70), (4 × 42)/(5 × 42), (6 × 30)/(7 × 30), (-1 × 35)/(6 × 35)

[Converting denominators as same numbers]

⇒ -140/210, 168/210, 180/210, -35/210

Since -140/210 < -35/210 < 168/210 < 180/210

∴ -2/3 < -1/6 < 4/5 < 6/7