If $\mathrm{x}=\frac{-4}{9}$, $\mathrm{y}=\frac{5}{12}$, and $\mathrm{z}=\frac{7}{18}$, then find the rational number which when added to z gives x.

Given: $\mathrm{x}=\frac{-4}{9}$, $\mathrm{y}=\frac{5}{12}$, and $\mathrm{z}=\frac{7}{18}$
So, let us assume the rational number as ‘a’. 
Now, according to the question,
$\mathbf{a}\mathbf{+}\mathbf{z}\mathbf{=}\mathbf{x}$
Substituting the value of x and y in the above equation, we get:
$\begin{array}{l}\mathrm{a}+\frac{7}{18}=\frac{-4}{9}\\ \mathrm{Subtracting} \frac{7}{18} \mathrm{on} \mathrm{both} \mathrm{sides}, \mathrm{we} \mathrm{get};\\ \mathrm{a}+\frac{7}{18}-\frac{7}{18}=\frac{-4}{9}-\frac{7}{18}\\ \mathrm{a}=\frac{-8-7}{18}\\ \mathrm{a}=\frac{-15}{18}\\ \mathrm{a}=\frac{-5}{6}\end{array}$
So, the rational number which when added to z gives x, is obtained as $\frac{\mathbf{-}\mathbf{5}}{\mathbf{6}}$.