Question

Identify the additive inverse and multiplicative inverse for each number

44. $2.5$

Short answer

Additive inverse of $2.5$ is $-2.5$ and multiplicative inverse of $2.5$ is $0.4$

Step-by-step solution

- 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’

- Additive inverse of 2.5

Substitute $2.5$ for a

$a=2.5$

Multiply both sides by $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(2.5\right)\\ -a=-2.5\end{array}$

Thus additive inverse of $2.5$is $-2.5$

- 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’

- Multiplicative inverse of 2.5

Substitute $2.5$ for a

$a=2.5$

Convert decimal form of rational number to fraction form

$a=\frac{5}{2}$

Take reciprocal on both sides

$\begin{array}{c}\frac{1}{a}=\frac{1}{\frac{5}{2}}\\ \frac{1}{a}=\frac{2}{5}\end{array}$

Convert fraction form again into decimal form

$\frac{1}{a}=0.4$

Thus multiplicative inverse of $2.5$ is $0.4$