Write down the additive and multiplicative inverses of the fo $$ \begin{array}{ll} ext { (1) } 7 & ext { (2) } \frac{1}{7} \ ext { 3) }-5 & ext { (4) }-\frac{1}{5} \ ext { 5) } \frac{8}{5} & ext { (6) }-\frac{8}{5}\end{array} $$

Question

Write down the additive and multiplicative inverses of the fo $$ \begin{array}{ll}	ext { (1) } 7 & 	ext { (2) } \frac{1}{7} \ 	ext { 3) }-5 & 	ext { (4) }-\frac{1}{5} \ 	ext { 5) } \frac{8}{5} & 	ext { (6) }-\frac{8}{5}\end{array} $$

UpStudy AI · Accepted Answer

Certainly! Below are the **additive inverses** and **multiplicative inverses** for each of the given numbers:

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### 1. $$ 7 $$
- **Additive Inverse:** $$ -7 $$
- **Multiplicative Inverse:** $$ \frac{1}{7} $$

### 2. $$ \frac{1}{7} $$
- **Additive Inverse:** $$ -\frac{1}{7} $$
- **Multiplicative Inverse:** $$ 7 $$

### 3. $$ -5 $$
- **Additive Inverse:** $$ 5 $$
- **Multiplicative Inverse:** $$ -\frac{1}{5} $$

### 4. $$ -\frac{1}{5} $$
- **Additive Inverse:** $$ \frac{1}{5} $$
- **Multiplicative Inverse:** $$ -5 $$

### 5. $$ \frac{8}{5} $$
- **Additive Inverse:** $$ -\frac{8}{5} $$
- **Multiplicative Inverse:** $$ \frac{5}{8} $$

### 6. $$ -\frac{8}{5} $$
- **Additive Inverse:** $$ \frac{8}{5} $$
- **Multiplicative Inverse:** $$ -\frac{5}{8} $$

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**Definitions:**
- The **additive inverse** of a number $$ a $$ is the number that, when added to $$ a $$, yields zero. It is given by $$ -a $$.
- The **multiplicative inverse** (or reciprocal) of a non-zero number $$ a $$ is the number that, when multiplied by $$ a $$, yields one. It is given by $$ \frac{1}{a} $$.

**Note:** The multiplicative inverse does not exist for zero.
Here are the additive and multiplicative inverses for each number: 1. **7** - Additive Inverse: -7 - Multiplicative Inverse: 1/7 2. **1/7** - Additive Inverse: -1/7 - Multiplicative Inverse: 7 3. **-5** - Additive Inverse: 5 - Multiplicative Inverse: -1/5 4. **-1/5** - Additive Inverse: 1/5 - Multiplicative Inverse: -5 5. **8/5** - Additive Inverse: -8/5 - Multiplicative Inverse: 5/8 6. **-8/5** - Additive Inverse: 8/5 - Multiplicative Inverse: -5/8

Write down the additive and multiplicative inverses of the fo

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