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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

01

- Define additive inverse

Let 鈥榓鈥� be a real number such that

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

Then 鈥�-a鈥� is the additive inverse of 鈥榓鈥�

02

- Additive inverse of -10

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

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

Multiply both sides by $- 1$

$\begin{matrix} (鈭� 1) 脳 a = (鈭� 1) 脳 (\frac{6}{7}) \\ 鈭� a = 鈭� \frac{6}{7} \end{matrix}$

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

03

- Define multiplicative inverse

Let 鈥榓鈥� be a real number with $a = 0$ such that

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

Then 鈥� $\frac{1}{a}$ 鈥� is the multiplicative inverse of 鈥榓鈥�

04

- 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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Most popular questions from this chapter

Name the sets of numbers to which all of the following numbers belong. Then arrange the numbers in order from least to greatest.

$2 . \overset{炉}{49}, 2.4 \overset{炉}{9}, 2.4, 2.49, 2 . \overset{炉}{9}$

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