Question

Which are the correct answers

Answer 1

Answer:

$1) -\frac{3}{4} +\frac{3}{4} =0$ TRUE

$2) -\frac{3}{4} + 0 =\frac{3}{4}$ TRUE

$3) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4})$ TRUE

$4) -\frac{3}{4} - \frac{3}{4} =-(\frac{3}{4} + \frac{3}{4})$ TRUE

$5) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} - (-\frac{3}{4})$ FALSE

$6) \frac{3}{4} - \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4})$ FALSE,

Step-by-step 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:

$1) -\frac{3}{4} +\frac{3}{4} =0$

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

$2) -\frac{3}{4} + 0 =\frac{3}{4}$

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

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

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

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

TRUE, as - A - B  = - (A+B)

$5) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} - (-\frac{3}{4})$

FALSE, as A - (-B)  = A. + B

$6) \frac{3}{4} - \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4})$

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