What should be added to $\dfrac{2}{5}$ to get -1 ?

Let the required number be x. Then,

$\dfrac{2}{5} + x = -1 \\[1em] \Rightarrow x = -1 - \dfrac{2}{5} \\[1em] = \dfrac{-1}{1} + \left(\text{additive inverse of } \dfrac{2}{5}\right) \\[1em] = \dfrac{-1}{1} + \dfrac{-2}{5}$

L.C.M. of denominators 1 and 5 is 5.

Now, expressing each fraction with denominator 5:

$\dfrac{-1 \times 5}{1 \times 5} + \dfrac{-2 \times 1}{5 \times 1} \\[1em] = \dfrac{-5}{5} + \dfrac{-2}{5} \\[1em] = \dfrac{-5 + (-2)}{5} \\[1em] = \dfrac{-7}{5}$

The required number is $\dfrac{-7}{5}$.