$$1\frac{1}{5}-[(\frac{2}{3}\times\frac{1}{3}+\frac{1}{5})\times\frac{4}{9}]$$
$\frac{82}{81}\approx 1.012345679$
$$\frac{5+1}{5}-\left(\frac{2}{3}\times \frac{1}{3}+\frac{1}{5}\right)\times \frac{4}{9}$$
$$\frac{6}{5}-\left(\frac{2}{3}\times \frac{1}{3}+\frac{1}{5}\right)\times \frac{4}{9}$$
$$\frac{6}{5}-\left(\frac{2\times 1}{3\times 3}+\frac{1}{5}\right)\times \frac{4}{9}$$
$$\frac{6}{5}-\left(\frac{2}{9}+\frac{1}{5}\right)\times \frac{4}{9}$$
$$\frac{6}{5}-\left(\frac{10}{45}+\frac{9}{45}\right)\times \frac{4}{9}$$
$$\frac{6}{5}-\frac{10+9}{45}\times \frac{4}{9}$$
$$\frac{6}{5}-\frac{19}{45}\times \frac{4}{9}$$
$$\frac{6}{5}-\frac{19\times 4}{45\times 9}$$
$$\frac{6}{5}-\frac{76}{405}$$
$$\frac{486}{405}-\frac{76}{405}$$
$$\frac{486-76}{405}$$
$$\frac{410}{405}$$
$$\frac{82}{81}$$
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$\frac{2 \cdot 41}{3 ^ {4}} = 1\frac{1}{81} = 1.0123456790123457$
