How do you find the additive and multiplicative inverse of 2.5?

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Answer 1 · 2017-03-26T19:46:50

Additive inverse, $- \frac{5}{2}$ $- 5/2$ or $- 2.5$ $-2.5$
Multiplicative inverse, $\frac{2}{5}$ $2/5$ or $0.4$ $0.4$

For a number $a$ $a$ , it's multiplicative inverse $b$ $b$ is such that $a \cdot b = 1$ $a*b = 1$ which is the multiplicative identity.

For a number $a$ $a$ , it's additive inverse $c$ $c$ would be such that $a + c = 0$ $a + c = 0$ where $0$ $0$ is additive identity.

Thus, for $a = 2.5 = \frac{5}{2}$ $a = 2.5 = 5/2$
It's additive inverse be $c$ $c$ .

Then $\frac{5}{2} + c = 0$ $5/2 + c = 0$

Now, adding $- \frac{5}{2}$ $-5/2$ to both sides,

$c = - \frac{5}{2}$ $c = -5/2$ .

Let the multiplicative inverse be $b$ $b$ .

Then $a \cdot b = 1$ $a*b = 1$
$\Rightarrow \frac{5}{2} \cdot b = 1$ $implies 5/2*b = 1$

Multiplying both sides with $\frac{2}{5}$ $2/5$

$b = \frac{2}{5}$ $b = 2/5$