Step-by-step EXPLANATION:

Given numbers are -10/11 , 5/6 and 4/3

To Verify the associative property for addition and multiplication of the rational numbers.

Associative Property for addition of the rational numbers is as FOLLOWS

( a + b ) + C = a + ( b + c )

Associative Property for multiplication of the rational numbers is as follows

( a × b ) × c = a × ( b × c )

let a = -10/11 , b = 5/6 and c = 4/3

So, First Associative property of addition:

LHS = ( a + b ) + c = ( -10/11 + 5/6 ) + 4/3

=(\frac{-60+55}{66})+\frac{4}{3}=(

66

−60+55

)+

3

4

=\frac{-5}{66}+\frac{4}{3}=

66

−5

+

3

4

=\frac{-5+88}{66}=\frac{83}{66}=

66

−5+88

=

66

83

RHS = a + ( b + c ) = -10/11 + ( 5/6 + 4/3 )

=\frac{-10}{11}+(\frac{5+8}{6})=

11

−10

+(

6

5+8

)

=\frac{-10}{11}+\frac{13}{6}=

11

−10

+

6

13

=\frac{-60+143}{66}=\frac{83}{66}=

66

−60+143

=

66

83

LHS = RHS

Hence Verified

Second, Associative property of multiplication:

LHS = ( a × b ) × c = ( -10/11 × 5/6 ) × 4/3

=(\frac{-50}{66})\times\frac{4}{3}=(

66

−50

)×

3

4

=\frac{-200}{198}=\frac{-11}{99}=

198

−200

=

99

−11

RHS = a × ( b × c ) = -10/11 × ( 5/6 × 4/3 )

=\frac{-10}{11}\times(\frac{20}{18})=

11

−10

×(

18

20

)

=\frac{-200}{198}=\frac{-100}{99}=

198

−200

=

99

−100

LHS = RHS

Hence Verified