Q9. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1 - Define additive inverse

Let ‘a’ be a real number such that 

$a+\left(-a\right)=0=\left(-a\right)+a$

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

Step 2 - Additive inverse of - 10

Substitute $\frac{6}{7}$ for $a$

 $a=\frac{6}{7}$

Multiply both sides by $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(\frac{6}{7}\right)\\ -a=-\frac{6}{7}\end{array}$

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

Step 3 - Define multiplicative inverse

Let ‘a’ be a real number with $a\cancel{=}0$ such that

$a·\frac{1}{a}=1=\frac{1}{a}·a$

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

Step 4 - Multiplicative inverse of - 10

Substitute $\frac{6}{7}$ for $a$ 

 $a=\frac{6}{7}$

Reciprocal on both sides

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

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