\(\frac{5}{9}:\frac{4}{7}+\frac{13}{9}\cdot\frac{7}{4}\)
\(=\frac{5}{9}\cdot\frac{7}{4}+\frac{13}{9}\cdot\frac{7}{4}\)
\(=\left(\frac{5}{9}+\frac{13}{9}\right)\cdot\frac{7}{4}\)
\(=2\cdot\frac{7}{4}\)
\(=\frac{14}{4}\)
=\(\frac{5}{9}\)*\(\frac{7}{4}\)+\(\frac{13}{9}\)*\(\frac{7}{4}\)
=\(\frac{7}{4}\)*(\(\frac{5}{9}+\frac{13}{9}\))
=\(\frac{7}{4}\)*2
=\(\frac{7}{2}\)