QuestionFind the additive inverse and multiplicative inverse of the expression $-\frac{2}{5}$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $-\frac{}{5}$

STEP 2

The additive inverse of a number is the number that, when added to the original number, yields zero. In mathematical terms, for a given number $x$ , its additive inverse is $-x$ .

STEP 3

Let's find the additive inverse of the given expression $-\frac{2}{5}$ .
$Additive\, inverse = -(-\frac{2}{5})$

STEP 4

Calculate the additive inverse.
$Additive\, inverse = -(-\frac{2}{}) = \frac{2}{}$

STEP 5

The multiplicative inverse of a number is the number that, when multiplied by the original number, yields1. In mathematical terms, for a given number $x$ , its multiplicative inverse is $\frac{1}{x}$ .

STEP 6

Let's find the multiplicative inverse of the given expression $-\frac{2}{5}$ .
$Multiplicative\, inverse = \frac{1}{-\frac{2}{5}}$

STEP 7

Calculate the multiplicative inverse.
$Multiplicative\, inverse = \frac{1}{-\frac{2}{5}} = -\frac{5}{2}$ The additive inverse of $-\frac{2}{5}$ is $\frac{2}{5}$ and the multiplicative inverse of $-\frac{2}{5}$ is $-\frac{5}{2}$ .

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