Question

verify the associative property for addition and multiplication of the rational numbers -10/11,5/6,4/3.​

Answer 1

Answer:

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

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

       $=\frac{-5}{66}+\frac{4}{3}$

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

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

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

       $=\frac{-10}{11}+\frac{13}{6}$

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

LHS = RHS

Hence Verified

Second, Associative property of multiplication:

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

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

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

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

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

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

LHS = RHS

Hence Verified

Answer 2

Answer:

1/8.

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Step-by-step explanation:

lhs =rhs