1. Verify that (x + y) + z = x + (y + z), when:
a) x=-4/3, y=5/12, z=-5/6
b)x=-9/11, y=3/-5,z=-18/44
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Answers
Answer:
Step-by-step explanation: 1.a) (x + y) + z= x + (y + z ) ; x= -4/3, y=5/12, z= -5/6
⇒ (-4/3 + 5/12) + (-5/6)= -4/3 + ( 5/12 + (-5/6) Taking LCM as 12 ⇒( 4 x -4 + 1 x 5)/12 -5/6= -4/3 + (5/12 - 5/6)
again LCM =12 ⇒-11/12 - 5/6 = -4/3 +(1 x 5 - 2 x 5)/12
" " " ⇒(1 x -11 - 2 x 5)/12 = -4/3 + (-5/12)
⇒-21/12 = -4/3 - 5/12
LCM=12 ⇒ -21/12= ( 4 x -4 - 1 x 5)/12
⇒ -21/12 = -21/12
Therefore verified.
1.b) (x+y)+z = x+(y+z) ; x = -9/11, y=3/-5 or -3/5, z= -18/44
⇒ ( -9/11 + (-3/5)) + (-18/44) = -9/11 +(-3/5 +(-18/44))
LCM(LHS)=55 ⇒ (5 x -9 - 11 x 3)/55 - 18/44= -9/11 + (-3/5 - 18/44)
LCM(RHS)= 220 ⇒-78/55 - 18/44= -9/11 +(44 x -3 - 5 x 18)/220
LCM(LHS)=220 ⇒( 4 x -78 - 5 x 18)/220= -9/11 +(-222/220)
⇒-402/220= -9/11 - 222/220
⇒-402/220= ( 20 x -9 - 222)/220
LCM=220 ⇒-402/220=-402/220
Hence,verified.
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