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

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UpStudy AI · Accepted Answer

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 $$ 5 $$.
The additive inverse of $$ \frac{1}{5} $$ is $$ -\frac{1}{5} $$, and the multiplicative inverse is $$ 5 $$.

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

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