// i / to kreski ułamkowe ! zad. 1. Oblicz a) 2/3 + 1/5 // 2/5 - 1/2 + (3 2/17 - 4 6/13) * (0,75

January 2019 1 19 Report

// i / to kreski ułamkowe !

zad. 1. Oblicz
a) 2/3 + 1/5 // 2/5 - 1/2 + (3 2/17 - 4 6/13) * (0,75 - 3/4)
b) 2/3 -[0,8 * 3/(-2)^2 - (-2)^2/5] : (-1 1/2)
c) (1/3 - 1/2) : (5/3 - 5/4) - (0,25 - 3/8 : 0,625)
d) ((-1/2)^2 - (-1/2)^3) : ((-2/3)^2 - (-1/3)^2)

Pomóżcie

krysta $a)\\\\\frac{ 2}{3} + \frac{\frac{1}{5}}{\frac{2}{5}} -\frac{ 1}{2} + (3\frac{ 2}{17} - 4 \frac{6}{13} ) * (0,75 - \frac{3}{4} )=\frac{ 2}{3} + \frac{1}{5}:\frac{2}{5} -\frac{ 1}{2} + (3\frac{ 2}{17} - 4 \frac{6}{13} ) * (\frac{ 75}{100} - \frac{3}{4} )=\\\\=\frac{ 2}{3} + \frac{1}{5}*\frac{5}{2} -\frac{ 1}{2} + (3\frac{ 2}{17} - 4 \frac{6}{13} ) * (\frac{ 3}{4} - \frac{3}{4} )= \\\\=\frac{ 2}{3} + \frac{1}{2} -\frac{ 1}{2} + (3\frac{ 2}{17} - 4 \frac{6}{13} ) * 0= \frac{ 2}{3} + \frac{1}{2} -\frac{ 1}{2} + 0= \frac{2}{3}$

$b)\\\\ \frac{2}{3}-[0,8 * \frac{3}{(-2)^2} - \frac{(-2)^2}{5} ] : (-1 \frac{1}{2}) = \frac{2}{3}-[ \frac{8 }{10}* \frac{3}{4} - \frac{4}{5 } ] : (- \frac{3}{2}) =\\\\=\frac{2}{3}-[ \frac{3}{5} - \frac{4}{5 } ] * (- \frac{2}{3}) = \frac{2}{3}- ( - \frac{1}{5 }) * (- \frac{2}{3}) = \frac{2}{3}- \frac{2}{15 }=\frac{30}{45}- \frac{6}{45}= \frac{24}{45}=\frac{8}{15}$

$c) \\\\( \frac{1}{3} - \frac{1}{2}) : ( \frac{5}{3} - \frac{5}{4}) - (0,25 - \frac{3}{8} : 0,625)\\\\=( \frac{2}{6} - \frac{3}{6}) : ( \frac{20}{12} - \frac{15}{12}) - ( \frac{25}{100} - \frac{3}{8} : \frac{625}{1000})= ( - \frac{1}{6}) : ( \frac{5}{12} ) - ( \frac{25}{100} - \frac{3}{8} * \frac{1000}{625})=$

$= ( - \frac{1}{6}) * ( \frac{12}{5} ) - ( \frac{1}{4} - \frac{3}{5} )= ( - \frac{2}{5}) - ( \frac{5}{20} - \frac{12}{20} )=( - \frac{2}{5}) - ( - \frac{7}{20} )= \\\\=( - \frac{8}{20}) + \frac{7}{20} = - \frac{1}{20}$

$d)\\\\ ((- \frac{1}{2})^2 - (- \frac{1}{2})^3) : ((-\frac{2}{3} )^2 - (- \frac{1}{3})^2)= ( \frac{1}{ 4} + \frac{1}{8} ) : ( \frac{4}{9} - \frac{1}{9} )=\\\\= ( \frac{2}{8} + \frac{1}{8} ) : \frac{3}{9} = \frac{3}{8} : \frac{3}{9} = \frac{3}{8} * \frac{9}{3} = \frac{9}{8}$

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