Arrange the following fractions in ascending order.
$$\frac{5}{9}, \frac{8}{3}, \frac{7}{5}, \frac{3}{5}, \frac{1}{9}​.$$​

The fractions to be arranged are

​$$\frac{5}{9}, \frac{8}{3}, \frac{7}{5}, \frac{3}{5}, \frac{1}{9}​.$$​​

To arrange fractions in ascending order, we need to compare their values by converting them to equivalent fractions with the same denominator or by converting them to decimals.

Making denominator same for all fraction;

LCM of 9, 3, 5, 9 = 45

Now, $$\frac{5}{9} = \frac{25}{45},\quad\frac{8}{3} = \frac{120}{45},\quad\frac{7}{5} = \frac{63}{45},\quad\frac{3}{5} = \frac{27}{45},\quad \frac{1}{9} = \frac{5}{45},$$​​

Thus, the fractions in ascending order are:

Convert the fractions to decimals:

​$$\frac{5}{9} = 0.555, \quad \frac{8}{3} = 2.666, \quad \frac{7}{5} = 1.4, \quad \frac{3}{5} = 0.6, \quad \frac{1}{9} = 0.111$$​​

Now, arrange the decimal values in ascending order:

0.111, 0.555, 0.6, 1.4, 2.6660.

Thus, the fractions in ascending order are:

​$$\frac{1}{9}, \frac{5}{9}, \frac{3}{5}, \frac{7}{5}, \frac{8}{3}$$​​