Question

Verify that (a+b)+c = a+ (b+c) by taking a = -8 , b = (-8/11) , c = (-8/12)

Answer 1

Explanation:

`(-8+-(8)/(11) ) + (-(8)/(12)) = -(96)/(11) + (-(2)/(3)) = -(288 + 22)/(33)) = -(310)/(33)\\ (-8) + (-(8)/(11) + (-(2)/(3))) = (-8) + (-(46)/(33))= -(310)/(33)`

Answer 2

The expression is true

Explanation:

The expression (a+b)+c = a+ (b+c) is an associative law. Given a = -8 , b = (-8/11) , c = (-8/12), we need to verify that the expression is true. To do that we need to substitute the values given into the right hand side and the also left hand side of the expression and the values gotten for both sides must be equal.

Given the left hand side to be (a+b)+c, substituting the values of a,b and c into the expression, we have:

{-8+(-8/11)}+(-8/12)

= (-8-(8/11))-8/12

= (-88-8)/11-8/12

= -96/11-8/12

= (-1152-88)/132

= -1240/132

= -620/-66

= -310/33

Similarly for the right hand side of the expression a+(b+c)

= -8+(-8/11+(-8/12))

= -8+(-8/11-8/12)

= -8+{(-96-88)/132}

= -8+(-184/132)

= (-1056-184)/132

= -1240/132

= -310/33

Since both expression are equal to -310/33, then the associative law given above is true.