To find the additive and multiplicative inverses of \(-\frac{7}{5}\), we can define each type of inverse:
-
Additive Inverse: The additive inverse of a number is what you add to that number to get zero. For any number \(x\), the additive inverse is \(-x\).
For \(-\frac{7}{5}\), the additive inverse is: \[ -\left(-\frac{7}{5}\right) = \frac{7}{5} \]
-
Multiplicative Inverse: The multiplicative inverse of a number is what you multiply that number by to get one. For any number \(x\) (where \(x \neq 0\)), the multiplicative inverse is \(\frac{1}{x}\).
For \(-\frac{7}{5}\), the multiplicative inverse is: \[ \frac{1}{-\frac{7}{5}} = -\frac{5}{7} \]
Summary:
- The additive inverse of \(-\frac{7}{5}\) is \(\frac{7}{5}\).
- The multiplicative inverse of \(-\frac{7}{5}\) is \(-\frac{5}{7}\).