To find the additive inverse of a given number, we need to find the number that, when added to the original number, results in zero. This means we simply change the sign of the original number.
Given the number [tex]\[ -\frac{2}{3} \][/tex],
1. The additive inverse is obtained by changing the sign of the fraction. For [tex]\[ -\frac{2}{3} \][/tex], its additive inverse is [tex]\[ \frac{2}{3} \][/tex].
Thus, we have:
[tex]\[ -\frac{2}{3} + \frac{2}{3} = 0 \][/tex]
Therefore, the additive inverse of [tex]\[ -\frac{2}{3} \][/tex] is [tex]\[ \frac{2}{3} \][/tex].
Among the given choices:
a) [tex]\[ -\frac{2}{3} \][/tex]
b) [tex]\[ \frac{2}{3} \][/tex]
c) [tex]\[ -\frac{3}{2} \][/tex]
d) [tex]\[ \frac{3}{2} \][/tex]
The correct answer is:
b) [tex]\[ \frac{2}{3} \][/tex]
