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
Answers
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