What is the additive inverse and multiplicative inverse of \( \frac{1}{5} \)

To find the additive and multiplicative inverses of \( \frac{1}{5} \), we can follow these definitions: 1. **Additive Inverse**: The additive inverse of a number \( a \) is the number \( b \) such that \( a + b = 0 \). For \( \frac{1}{5} \), the additive inverse is: \[ b = -\frac{1}{5} \] This is because: \[ \frac{1}{5} + \left(-\frac{1}{5}\right) = 0 \] 2. **Multiplicative Inverse**: The multiplicative inverse of a number \( a \) is the number \( c \) such that \( a \cdot c = 1 \). For \( \frac{1}{5} \), the multiplicative inverse is: \[ c = 5 \] This is because: \[ \frac{1}{5} \cdot 5 = 1 \] In summary: - The additive inverse of \( \frac{1}{5} \) is \( -\frac{1}{5} \). - The multiplicative inverse of \( \frac{1}{5} \) is \( 5 \).