To find the additive inverse of a fraction, you simply change its sign. The additive inverse of a fraction \( \frac{a}{b} \) is \( -\frac{a}{b} \). This means if the fraction is positive, its additive inverse will be negative, and if the fraction is negative, its additive inverse will be positive.
Let's go through each fraction step by step:
(a) For \( \frac{7}{9} \):
The additive inverse is \( -\frac{7}{9} \).
Numerically, it is approximately \(-0.7777777777777778\).
(b) For \( \frac{-15}{9} \):
The additive inverse is \( -\left(\frac{-15}{9}\right) = \frac{15}{9} \).
Numerically, it is approximately \(1.6666666666666667\).
(c) For \( \frac{25}{8} \):
The additive inverse is \( -\frac{25}{8} \).
Numerically, it is approximately \(-3.125\).
(d) For \( \frac{-6}{13} \):
The additive inverse is \( -\left(\frac{-6}{13}\right) = \frac{6}{13} \).
Numerically, it is approximately \(0.46153846153846156\).
(e) For \( \frac{-14}{9} \):
The additive inverse is \( -\left(\frac{-14}{9}\right) = \frac{14}{9} \).
Numerically, it is approximately \(1.5555555555555556\).
(f) For \( \frac{31}{-9} \):
The fraction \( \frac{31}{-9} \) is equivalent to \( \frac{-31}{9} \). Therefore, the additive inverse is \( -\left(\frac{-31}{9}\right) = \frac{31}{9} \).
Numerically, it is approximately \(3.4444444444444446\).
Thus, the additive inverses of the given fractions are:
(a) \(-0.7777777777777778\)
(b) \(1.6666666666666667\)
(c) \(-3.125\)
(d) \(0.46153846153846156\)
(e) \(1.5555555555555556\)
(f) [tex]\(3.4444444444444446\)[/tex]
