The sum of two rational numbers is -4. If one of them is $\dfrac{-3}{5}$, find the other.

Let p and q be two rational numbers.

One rational number = p = $\dfrac{-3}{5}$

Other rational number = q = ?

Sum of two rational numbers = (p + q) = -4

q = -4 - p

Substituting the values in above, we get:

$q = -4 - \Big(\dfrac{-3}{5}\Big) \\[1em] = -4 + \Big(\text{additive inverse of } \dfrac{-3}{5}\Big) \\[1em] q = \dfrac{-4}{1} + \dfrac{3}{5}$

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

Now, expressing each fraction with denominator 5:

$\dfrac{-4 \times 5}{1 \times 5} + \dfrac{3 \times 1}{5 \times 1} \\[1em] = \dfrac{-20}{5} + \dfrac{3}{5} \\[1em] = \dfrac{-20 + 3}{5} \\[1em] = \dfrac{-17}{5}$

The other rational number q is $\dfrac{-17}{5}$.