Chapter 1: Q9. (page 18)

9. Name the additive inverse and multiplicative inverse $\frac{6}{7}$

Short Answer

Expert verified

Additive inverse of $\frac{6}{7}$ is $- \frac{6}{7}$ and multiplicative inverse of $\frac{6}{7}$ is $\frac{7}{6}$

Step by step solution

- Define additive inverse

Let ‘a’ be a real number such that

$a + (- a) = 0 = (- a) + a$

Then ‘-a’ is the additive inverse of ‘a’

- Additive inverse of -10

Substitute $\frac{6}{7}$ for $a$

$a = \frac{6}{7}$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (\frac{6}{7}) \\ - a = - \frac{6}{7} \end{matrix}$

Thus additive inverse of $\frac{6}{7}$ is $- \frac{6}{7}$

- Define multiplicative inverse

Let ‘a’ be a real number with $a = 0$ such that

$a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$

Then ‘ $\frac{1}{a}$ ’ is the multiplicative inverse of ‘a’

- Multiplicative inverse of -10

Substitute $\frac{6}{7}$ for $a$

$a = \frac{6}{7}$

Reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{\frac{6}{7}} \\ \frac{1}{a} = \frac{7}{6} \end{matrix}$

Thus multiplicative inverse of $\frac{6}{7}$ is $\frac{7}{6}$

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9. Name the additive inverse and multiplicative inverse $\frac{6}{7}$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

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9. Name the additive inverse and multiplicative inverse 67

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Applied Mathematics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

9. Name the additive inverse and multiplicative inverse $\frac{6}{7}$