Answer:
[tex]1) -\frac{3}{4} +\frac{3}{4} =0[/tex] TRUE
[tex]2) -\frac{3}{4} + 0 =\frac{3}{4} [/tex] TRUE
[tex]3) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4}) [/tex] TRUE
[tex]4) -\frac{3}{4} - \frac{3}{4} =-(\frac{3}{4} + \frac{3}{4}) [/tex] TRUE
[tex]5) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} - (-\frac{3}{4}) [/tex] FALSE
[tex]6) \frac{3}{4} - \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4}) [/tex] 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:
[tex]1) -\frac{3}{4} +\frac{3}{4} =0[/tex]
TRUE, as the additive inverse of (3/4) is (-3/4).
[tex]2) -\frac{3}{4} + 0 =\frac{3}{4} [/tex]
TRUE, as the zero is the zero element ⇒ A+0 = A.
[tex]3) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4}) [/tex]
TRUE, as the addition of the fraction is ASSOCIATIVE ⇒ A+B = B+A.
[tex]4) -\frac{3}{4} - \frac{3}{4} =-(\frac{3}{4} + \frac{3}{4}) [/tex]
TRUE, as - A - B = - (A+B)
[tex]5) -\frac{3}{4} + \frac{3}{4} =\frac{3}{4} - (-\frac{3}{4}) [/tex]
FALSE, as A - (-B) = A. + B
[tex]6) \frac{3}{4} - \frac{3}{4} =\frac{3}{4} + (-\frac{3}{4}) [/tex]
FALSE, as the (3/4) is the additive inverse of (-3/4) ⇒ A- B = 0.
