First:
[tex]1\dfrac{2}{9}-0.4=1\dfrac{2}{9}-\dfrac{4}{10}=\dfrac{9+2}{9}-\dfrac{2}{5}=\dfrac{11}{9}-\dfrac{2}{5}=\dfrac{11\cdot5}{9\cdot5}-\dfrac{2\cdot9}{5\cdot9}\\\\=\dfrac{55}{45}-\dfrac{18}{45}=\dfrac{37}{45}\\\\3.7\div\left(1\dfrac{2}{9}-0.4\right)=\dfrac{37}{10}\div\dfrac{37}{45}=\dfrac{37}{10}\cdot\dfrac{45}{37}=\dfrac{45}{10}=\dfrac{45:9}{10:5}=\dfrac{9}{2}=4\dfrac{1}{2}=4.5[/tex]
