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

Let p and q be two rational numbers.

One rational number = p = -3

Other rational number = q = ?

Sum of two rational numbers = (p + q) = $\dfrac{-5}{4}$

q = $\dfrac{-5}{4}$ - p

Substituting the values in above, we get:

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

L.C.M. of 4 and 1 is 4.

Now, expressing each fraction with denominator 4:

$\dfrac{-5 \times 1}{4 \times 1} + \dfrac{3 \times 4}{1 \times 4} \\[1em] = \dfrac{-5}{4} + \dfrac{12}{4} \\[1em] = \dfrac{-5 + 12}{4} \\[1em] = \dfrac{7}{4}$

The other rational number q is $\dfrac{7}{4}$.