(i) Given (3/5), (-17/-30), (8/-15), (-7/10)

The LCM of 5, 30, 15 and 10 is 30

Multiplying the numerators and denominators to get the denominator equal to the LCM i.e. 30

Consider (3/5)

Multiply both numerator and denominator by 6, then we get

(3/5) × (6/6) = (18/30) ….. (1)

Consider (8/-15)

Multiply both numerator and denominator by 2, then we get

(8/-15) × (2/2) = (16/-30) ….. (2)

Consider (-7/10)

Multiply both numerator and denominator by 3, then we get

(-7/10) × (3/3) = (-21/30) ….. (3)

In the above equation, denominators are same

Now on comparing the ascending order is:

(-7/10) < (8/-15) < (-17/30) < (3/5)

(ii) Given (-4/9), (5/-12), (7/-18), (2/-3)

The LCM of 9, 12, 18 and 3 is 36

Multiplying the numerators and denominators to get the denominator equal to the LCM i.e. 36

Consider (-4/9)

Multiply both numerator and denominator by 4, then we get

(-4/9) × (4/4) = (-16/36) ….. (1)

Consider (5/-12)

Multiply both numerator and denominator by 3, then we get

(5/-12) × (3/3) = (15/-36) ….. (2)

Consider (7/-18)

Multiply both numerator and denominator by 2, then we get

(7/-18) × (2/2) = (14/-36) ….. (3)

Consider (2/-3)

Multiply both numerator and denominator by 12, then we get

(2/-3) × (12/12) = (24/-36) ….. (4)

In the above equation, denominators are same

Now on comparing the ascending order is:

(2/-3) < ((-4/9) < (5/-12) < (7/-18)