Using suitable rearrangement and find the sum: $\left(\frac{4}{7}\right)+\left(\frac{-4}{9}\right)+\left(\frac{3}{7}\right)+\left(\frac{-13}{9}\right)$

On rearrangeing the rational numbers then adding the numbers with same denominator we obtain

$$\begin{gathered} =\left(\frac{4}{7}\right)+\left(\frac{3}{7}\right)-\left(\frac{4}{9}\right)-\left(\frac{13}{9}\right) \\ =\left(\frac{4+3}{7}\right)-\left(\frac{4+13}{9}\right) \\ =\frac{7}{7}-\frac{17}{9} \\ =1-\frac{17}{9} \end{gathered}$$

On taking LCM of $1$and $9$

LCM of $1$and $9$$=9$

$$\begin{gathered} =9-\frac{17}{9} \\ =\frac{-8}{9} \end{gathered}$$