Express 0.9 as:
[tex]0.9=\frac{9}{10}[/tex]Use distributive property:
[tex]\begin{gathered} a(b+c)=ab+ac \\ so\colon \\ \frac{9}{10}(\frac{5}{9}-\frac{2}{9})=\frac{9}{10}\cdot\frac{5}{9}-\frac{9}{10}\cdot\frac{2}{9} \\ \end{gathered}[/tex]In order to multuply fractions you can use the following formula:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]so:
[tex]\frac{9}{10}\cdot\frac{5}{9}-\frac{9}{10}\cdot\frac{2}{9}=\frac{9\cdot5}{10\cdot9}-\frac{9\cdot2}{10\cdot9}=\frac{45}{90}-\frac{18}{90}[/tex]Finally, use this property:
[tex]\frac{a}{c}\pm\frac{b}{c}=\frac{a\pm b}{c}[/tex]so:
[tex]\frac{45}{90}-\frac{18}{90}=\frac{45-18}{90}=\frac{27}{90}=\frac{3}{10}[/tex]Answer:
[tex]\frac{3}{10}=0.3[/tex]