11 18 3 9 2 3

(i) –(11/18) + (-3)/9 + 2/(-3) (ii) (-9)/4 + 13/3 + 25/6 (iii) -5 + 5/(-8) + (-5)/(-12) (iv) –(2/3) + 5/2 + 2 (v) 5 + (-3)/4 +…

Answers:

(i) -(11/18)  + (-3)/9 + 2/(-3)

= (-11)/8 + (-3)/9 + (-2)/3

= (-11 × 1)/(18 × 1) + (-3 × 2)/(9 × 2) + (-2 × 6)/(3 × 6)   (∵ L.C.M. of  3, 9 and 18 = 18)

= (-11)/18 + (-6)/18 + (-12)/18

= (-11 – 6 – 12)/18

= (-29)/18

(ii) (-9)/4 + 13/3  + 25/6

 = (-9 × 6)/(4 × 6) + (13 × 8)/(3 × 8) + (25 × 4)/(6 × 4)     (∵ L.C.M  of  4, 3 and 6 = 24)

= (-54)/24 + 104/24 + 100/24

= (-54)/24 + 104/24 + 100/24

= (- 54 + 104 + 100)/24

= 150/24

= 25/6

(iii) (-5) + 5/(-8) + (-5/-12)

= (-5)/1 + (-5)/8 + 5/12

= (-5 × 24)/(1 × 24) + (-5 × 3)/(8 × 3) + (5 × 2)/(12 × 2)     (∵ L.C.M  of  1, 8 and 12 = 24)

= (-120)/24 + (-15)/24 + 10/24

= (- 120 – 15 + 10)/24

 = (-125)/24

(iv) –(2/3) + 5/2 + 2

= -(2/3) + 5/2 + 2/1

= (-2 × 2)/(3 × 2) + (5 × 3)/(2 × 3) + (2 × 6)/(1 × 6)    (∵   L.C.M.  of  3, 2 and 1 = 6)

= (-4)/6 + 15/6 + 12/6

= (-4 + 15 + 12)/6 = 23/6

(v) 5 + (-3)/4 + (-5)/8

= 5/1 + (-3)/4 + (-5)/8

= (5 × 8)/(1 × 8) + (-3 × 2)/(4 × 2) + (-5 × 1)/(8 × 1)    (∵  L.C.M  of 1, 4 and 8 = 8)

= 40/8 + (-6)/8 + (-5)/8

= (40 – 6 – 5)/8

= (40 – 11)/8

= 29/8