Question

Which are the correct answers

Answer 1

`1) -(3)/(4) +(3)/(4)    =0` TRUE

`2) -(3)/(4) + 0    =(3)/(4)` TRUE

`3) -(3)/(4)  + (3)/(4)    =(3)/(4) + (-(3)/(4))` TRUE

`4) -(3)/(4)  - (3)/(4)    =-((3)/(4) + (3)/(4))` TRUE

`5) -(3)/(4)  + (3)/(4)    =(3)/(4) - (-(3)/(4))` FALSE

`6) (3)/(4)  - (3)/(4)    =(3)/(4) + (-(3)/(4))` FALSE,

Explanation:

ADDITIVE INVERSE:

Given number B is the additive inverse of a given number A if:

A + B = 0 ⇒ A = - B

Now here, the given statements are:

`1) -(3)/(4) +(3)/(4)    =0`

TRUE, as the additive inverse of (3/4) is (-3/4).

`2) -(3)/(4) + 0    =(3)/(4)`

TRUE, as the zero is the zero element ⇒ A+0 = A.

`3) -(3)/(4)  + (3)/(4)    =(3)/(4) + (-(3)/(4))`

TRUE, as the addition of the fraction is ASSOCIATIVE ⇒ A+B = B+A.

`4) -(3)/(4)  - (3)/(4)    =-((3)/(4) + (3)/(4))`

TRUE, as - A - B = - (A+B)

`5) -(3)/(4)  + (3)/(4)    =(3)/(4) - (-(3)/(4))`

FALSE, as A - (-B) = A. + B

`6) (3)/(4)  - (3)/(4)    =(3)/(4) + (-(3)/(4))`

FALSE, as the (3/4) is the additive inverse of (-3/4) ⇒ A- B = 0.