Question

calculeaza: 21) 0,(6)×(2/3)^2-1,(3)=
22)
[0,2(6)÷2^2+0,85]÷0,5=
23) [0,4(6)÷14/3+0,4]÷2,5=

Answer 1

$21) \\ 0.(6) \times ( \frac{2}{3}) {}^{2} - 1.(3) = \\ = \frac{6}{9} \times \frac{4}{9} - \frac{13 - 1}{9} = \\ \frac{2}{9} \times \frac{4}{3} - \frac{12}{9} = \\ \frac{8}{27} - \frac{12}{9} = \\ \frac{8 - 36}{27} = \\ = - \frac{28}{27}$

$22) \\ (0.2(6) \div 2 {}^{2} + 0.85) \div 0.5 = \\ = ( \frac{26 - 2}{90} \div 4 + \frac{85}{100} ) \div \frac{5}{10} = \\ = ( \frac{24}{90} \times \frac{1}{4} + \frac{85}{100} ) \times \frac{10}{5} = \\ = (\frac{6}{90} + \frac{85}{100} ) \times \frac{10}{5} = \\ = ( \frac{1}{15} + \frac{85}{100} ) \times \frac{10}{5} = \\ = ( \frac{1}{15} + \frac{17}{20} ) \times \frac{10}{5} = \\ = ( \frac{4 + 51}{60}) \times \frac{10}{5} = \\ = \frac{55}{60} \times \frac{10}{5} \\ = \frac{11}{6}$