Question

Verify x+(y+z)=(x+y)+z for the following values of x,y,z (i)x=3/4,y=5/6,z=-7/8(ii)x=2/3,y=-5/6,z=-7/9(iii)x=3/5,y=-6/9,z=2/10(iv)x=-3/5,y=-7/10,z=-8/15

Answer 1

Answer:

verified

Step-by-step explanation:

Verify x+(y+z)=(x+y)+z for the following values of x,y,z (i)x=3/4,y=5/6,z=-7/8(ii)x=2/3,y=-5/6,z=-7/9(iii)x=3/5,y=-6/9,z=2/10(iv)x=-3/5,y=-7/10,z=-8/15

To Verify x+(y+z)=(x+y)+z

(i)x=3/4,y=5/6,z=-7/8

LHS  = 3/4 + (5/6 + (-7/8)) = (3/4) + (5/6 -7/8)  = (3/4)  + ((20 - 21)/24) = 3/4  - 1/24

= (18 - 1)/24 = 17/24

RHS  = (3/4 + 5/6) + (-7/8) = (9 + 10)/12 - 7/8  = 19/12 - 7/8  = (38 - 21)/24 = 17/24

LHS = RHS = 17/24

(ii)x=2/3,y=-5/6,z=-7/9

LHS = 2/3 + (-5/6 + (-7/9) =  2/3 + ( -5/6  - 7/9) =  2/3 + (-29/18) = 2/3 - 29/18

= 12/18 - 29/18 = -17/18

RHS = (2/3 + (-5/6) ) + (-7/9) =  (2/3 - 5/6) - 7/9 = (-1/6) - 7/9 = -1/6 - 7/9 = -3/18 - 14/18 = -17/18

LHS = RHS

Hence verified