Question

verify x + (Y + Z) is equal to (X + Y) + z for following values of x,y and z x=3/5, y=-6/9 z=2/10​

Answer 1

Answer:

=12/90

Step-by-step explanation:

Given:

LEFT hand side=LHS=x+(y+z)

putting values

x=3/5, y=-6/9  z=2/10

we get

LHS=3/5+(-6/9+2/10)

fraction -6/9 multiplying and dividing by 10

fraction 2/10 multiplying and dividing by 9

LHS=3/5 + (-6*10/9*10 + 2*9/10*9)

=3/5 + (-60/90+18/90)

using distributive law of multiplication over addition

LHS=3/5 + (-60+18)/90

=3/5 + (-42)/90  

=3/5-42)/90

fraction -3/5 multiplying and dividing by 18

LHS=(3*18/5*18) - (42/90)

=(54/90) - ( 42/90)

=(54 - 42)/90

=12/90

This shows LHS=12/90    ....(1)

NOW:

Right hand side =RHS=(x+y)+z

putting values

x=3/5, y=-6/9  z=2/10

we get

RHS=(3/5 - 6/9) + 2/10

fraction 3/5 multiplying and dividing by 9

fraction -6/9 multiplying and dividing by 5

RHS=(3*9/5*9 - 6*5/9*5) + 2/10

=(27/45 - 30/45) + 2/10

using distributive law of multiplication over addition

RHS=(27 - 30)/45 + 2/10

=-3/45 + 2/10

fraction 3/45 multiplying and dividing by 2

fraction 2/10 multiplying and dividing by  9

RHS=-3*2/45*2 + 2*9/10*9

=-6/90 + 18/90

= (-6 + 18)/90

=12/90