Question

How do you solve this 3.7÷(1 2/9 −0.4)?

Answer 1

3.7÷(1 2/9 −0.4) =  166.5/45 ÷ 37/45 = 4.5

0.4 = 40/100 = 2/5

2/5 = 18/45

1 2/9 = 11/9 = 55/45

55/45 - 18/45 = 37/45

3.7 = 370/100 = 18.5/5 = 166.5/45

ANSWER: 4.5

Answer 2

First:

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