Find the multiplicative inverse (or reciprocal) of:

$\dfrac{2}{-5}$

To find the multiplicative inverse (or reciprocal) of a non-zero rational number, interchange its numerator and denominator.

First express the rational number with a positive denominator.

$\dfrac{2}{-5} = \dfrac{2 \times (-1)}{-5 \times (-1)} = \dfrac{-2}{5}$

Interchanging the numerator and the denominator of $\dfrac{-2}{5}$, we get $\dfrac{5}{-2} = \dfrac{-5}{2}$

$[\text{Check : } \dfrac{-2}{5} \times \dfrac{-5}{2} = 1]$

Hence, the multiplicative inverse of $\mathbf{\dfrac{2}{-5} \text{ is } \dfrac{-5}{2}}$.