Сандық өрнектер (Сканави (А) 1.1-1.25)

Шешуі: $${\dfrac{{(7 - 6,35):6,5 + 9,9}}{{\left( {1,2:36 + 1,2:0,25 - 1\dfrac{5}{{16}}} \right):\dfrac{{169}}{{24}}}} = }$$ $${ = \dfrac{{0,65:6,5 + 9,9}}{{\left( {\dfrac{1}{{30}} + \dfrac{{24}}{5} - \dfrac{{21}}{{16}}} \right) \cdot \dfrac{{24}}{{169}}}} = \dfrac{{0,1 + 9,9}}{{\dfrac{{169}}{{48}} \cdot \dfrac{{24}}{{169}}}} = \dfrac{{10}}{{\dfrac{1}{2}}} = 20.}$$

Шешуі: $${\left( {\left( {\dfrac{7}{9} - \dfrac{{47}}{{72}}} \right):1,25 + \left( {\dfrac{6}{7} - \dfrac{{17}}{{28}}} \right):(0,358 - 0,108)} \right) \cdot 1,6 - \dfrac{{19}}{{25}} = }$$ $${ = \left( {\dfrac{{56 - 47}}{{72}} \cdot \dfrac{4}{5} + \dfrac{{24 - 17}}{{28}}:0,25} \right) \cdot 1,6 - \dfrac{{19}}{{25}} = }$$ $${ = (0,1 + 1) \cdot 1,6 - \dfrac{{19}}{{25}} = 1,76 - 0,76 = 1.}$$

Шешуі: $${\dfrac{{\left( {0,5:1,25 + \dfrac{7}{5}:1\dfrac{4}{7} - \dfrac{3}{{11}}} \right) \cdot 3}}{{\left( {1,5 + \dfrac{1}{4}} \right):18\dfrac{1}{3}}} = \dfrac{{\left( {\dfrac{2}{5} + \dfrac{{49}}{{55}} - \dfrac{3}{{11}}} \right) \cdot 3}}{{\dfrac{7}{4} \cdot \dfrac{3}{{55}}}} = \dfrac{{168}}{{55}} \cdot \dfrac{4}{7} \cdot \dfrac{{55}}{3} = 32.}$$

Шешуі: $${\left( {\dfrac{{(2,7 - 0,8) \cdot 2\dfrac{1}{3}}}{{(5,2 - 1,4):\dfrac{3}{{70}}}} + 0,125} \right):2\dfrac{1}{2} + 0,43 = \left( {\dfrac{{\dfrac{{19}}{{10}} \cdot \dfrac{7}{3}}}{{\dfrac{{38}}{{10}} \cdot \dfrac{{70}}{3}}} + \dfrac{1}{8}} \right) \cdot \dfrac{2}{5} + 0,43 = }$$ $${ = \dfrac{1}{{20}} \cdot \dfrac{2}{5} + \dfrac{1}{{20}} + 0,43 = 0,02 + 0,05 + 0,43 = 0,5.}$$

Шешуі: $${\dfrac{{2\dfrac{3}{4}:1,1 + 3\dfrac{1}{3}}}{{2,5 - 0,4 \cdot 3\dfrac{1}{3}}}:\dfrac{5}{7} - \dfrac{{\left( {2\dfrac{1}{6} + 4,5} \right) \cdot 0,375}}{{2,75 - 1\dfrac{1}{2}}} = \dfrac{{\dfrac{5}{2} + \dfrac{{10}}{3}}}{{\dfrac{5}{2} - \dfrac{4}{3}}} \cdot \dfrac{7}{5} - \dfrac{{\dfrac{{20}}{3} \cdot \dfrac{3}{8}}}{{1,25}} = 7 - 2 = 5.}$$

Шешуі: $${\dfrac{{\left( {13,75 + 9\dfrac{1}{6}} \right) \cdot 1,2}}{{\left( {10,3 - 8\dfrac{1}{2}} \right) \cdot \dfrac{5}{9}}} + \dfrac{{\left( {6,8 - 3\dfrac{3}{5}} \right) \cdot 5\dfrac{5}{6}}}{{\left( {3\dfrac{2}{3} - 3\dfrac{1}{6}} \right) \cdot 56}} - 27\dfrac{1}{6} = \dfrac{{\left( {\dfrac{{55}}{4} + \dfrac{{55}}{6}} \right) \cdot \dfrac{6}{5}}}{{(2,3 - 0,5) \cdot \dfrac{5}{9}}} + \dfrac{{\left( {\dfrac{{34}}{5} - \dfrac{{18}}{5}} \right) \cdot \dfrac{{35}}{6}}}{{\left( {\dfrac{4}{6} - \dfrac{1}{6}} \right) \cdot 56}} - }$$ $${ - \dfrac{{163}}{6} = \dfrac{{11\left( {1 + \dfrac{3}{2}} \right)}}{{\dfrac{{18}}{{10}} \cdot \dfrac{5}{9}}} + \dfrac{{\dfrac{{16}}{5} \cdot \dfrac{{35}}{6}}}{{28}} - \dfrac{{163}}{6} = \dfrac{{55}}{2} + \dfrac{2}{3} - \dfrac{{163}}{6} = \dfrac{{169}}{6} - \dfrac{{163}}{6} = 1.}$$

Шешуі: $${\dfrac{{\left( {\dfrac{1}{6} + 0,1 + \dfrac{1}{{15}}} \right):\left( {\dfrac{1}{6} + 0,1 - \dfrac{1}{{15}}} \right) \cdot 2,52}}{{\left( {0,5 - \dfrac{1}{3} + 0,25 - \dfrac{1}{5}} \right):\left( {0,25 - \dfrac{1}{6}} \right) \cdot \dfrac{7}{{13}}}} = \dfrac{{\left( {\dfrac{1}{6} + \dfrac{1}{{10}} + \dfrac{1}{{15}}} \right):\left( {\dfrac{1}{6} + \dfrac{1}{{10}} - \dfrac{1}{{15}}} \right) \cdot \dfrac{{63}}{{25}}}}{{\left( {\dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{4} - \dfrac{1}{5}} \right):\left( {\dfrac{1}{4} - \dfrac{1}{6}} \right) \cdot \dfrac{7}{{13}}}} = }$$ $${ = \dfrac{{\dfrac{1}{3} \cdot 5 \cdot \dfrac{{63}}{{25}}}}{{\dfrac{{13}}{{60}} \cdot 12 \cdot \dfrac{7}{{13}}}} = \dfrac{{21}}{5} \cdot \dfrac{5}{7} = 3.}$$

Шешуі: $${ = \left( {\dfrac{{\dfrac{{10}}{3} + \dfrac{5}{2}}}{{\dfrac{5}{2} - \dfrac{4}{3}}} \cdot \dfrac{{\dfrac{{23}}{5} - \dfrac{7}{3}}}{{\dfrac{{23}}{5} + \dfrac{7}{3}}} \cdot \dfrac{{26}}{5}} \right):\left( {\dfrac{{\dfrac{1}{{20}}}}{{\dfrac{1}{7} - \dfrac{1}{8}}} + \dfrac{{57}}{{10}}} \right) = \left( {\dfrac{{35}}{7} \cdot \dfrac{{34}}{{104}} \cdot \dfrac{{26}}{5}} \right):\left( {\dfrac{{28}}{{10}} + \dfrac{{57}}{{10}}} \right) = \dfrac{{17}}{2} \cdot \dfrac{2}{{17}} = 1}$$

Шешуі: $${\dfrac{{\left( {0,4 + 40 - 4 - 5 \cdot \dfrac{2}{5}} \right) \cdot 90}}{{\left( {\dfrac{{15}}{8} \cdot 8 - \dfrac{{89}}{{10}} + \dfrac{{13}}{5} \cdot \dfrac{3}{2}} \right) \cdot \dfrac{{172}}{5}}} = \dfrac{{34,4 \cdot 90}}{{\left( {\dfrac{{150}}{{10}} - \dfrac{{89}}{{10}} + \dfrac{{39}}{{10}}} \right) \cdot \dfrac{{172}}{5}}} = \dfrac{{344 \cdot 9}}{{2 \cdot 172}} = 9}$$

Шешуі: $${ = \dfrac{{\left( {\dfrac{{229}}{{45}} - \dfrac{{25}}{6}} \right):\dfrac{{83}}{{15}}}}{{\left( {\dfrac{{14}}{3} + \dfrac{3}{4}} \right) \cdot \dfrac{{48}}{{13}}}} \cdot \dfrac{{240}}{7} + \dfrac{{30}}{{70}} + \dfrac{2}{7} = \dfrac{{\dfrac{{83}}{{90}} \cdot \dfrac{{15}}{{83}}}}{{\dfrac{{65}}{{12}} \cdot \dfrac{{48}}{{13}}}} \cdot \dfrac{{240}}{7} + \dfrac{5}{7} = \dfrac{1}{{6 \cdot 20}} \cdot \dfrac{{240}}{7} + \dfrac{5}{7} = \dfrac{2}{7} + \dfrac{5}{7} = 1.}$$

Шешуі: $${ = \dfrac{{(0,6 + 0,42) \cdot 10}}{{\dfrac{{61}}{2} + \dfrac{1}{6} + \dfrac{{10}}{3}}} + \dfrac{{12\dfrac{1}{4} \cdot 26}}{{26 \cdot 7}} - 0,05 = \dfrac{{10,2}}{{34}} + \dfrac{7}{4} - \dfrac{1}{{20}} = \dfrac{3}{{10}} + \dfrac{7}{4} - \dfrac{1}{{20}} = 2 = }$$

Шешуі: $${ = \dfrac{{\dfrac{{10}}{3} \cdot \dfrac{{19}}{{10}} + \dfrac{{39}}{2} \cdot \dfrac{2}{9}}}{{\dfrac{{62}}{{75}} - \dfrac{4}{{25}}}} \cdot \dfrac{{\dfrac{1}{2} \cdot \left( {\dfrac{{21}}{{20}} + \dfrac{{41}}{{10}}} \right)}}{{\dfrac{7}{2} + \dfrac{{14}}{3} + \dfrac{{32}}{{15}}}} = \dfrac{{\dfrac{{19}}{3} + \dfrac{{13}}{3}}}{{\dfrac{2}{3}}} \cdot \dfrac{{\dfrac{{103}}{{40}}}}{{\dfrac{{103}}{{10}}}} = \dfrac{{16}}{4} = 4.}$$

Шешуі: $${ = \dfrac{{\dfrac{6}{5}:\left( {\dfrac{{17}}{{40}} + \dfrac{3}{5} - \dfrac{1}{{200}}} \right) \cdot \dfrac{{17}}{{10}}}}{{\dfrac{5}{6} + \dfrac{4}{3} - \dfrac{{53}}{{30}}}} + \dfrac{{\dfrac{{19}}{4} + \dfrac{{15}}{2}}}{{33 \cdot \dfrac{7}{{33}}}} \cdot 4 = 5 + 7 = 12.}$$

Шешуі: $${ = \dfrac{{\left( {\dfrac{9}{2} \cdot \dfrac{5}{3} - \dfrac{{27}}{4}} \right) \cdot \dfrac{2}{3}}}{{\left( {\dfrac{{10}}{3} \cdot \dfrac{3}{{10}} + \dfrac{{16}}{3} \cdot \dfrac{1}{8}} \right) \cdot \dfrac{3}{8}}} + \dfrac{{\dfrac{{15}}{{11}} \cdot \dfrac{{11}}{{50}} \cdot \dfrac{{10}}{3} - \dfrac{{24}}{{25}}}}{{\left( {\dfrac{1}{5} - \dfrac{3}{{40}}} \right) \cdot \dfrac{8}{5}}} = \dfrac{{\left( {\dfrac{{30}}{4} - \dfrac{{27}}{4}} \right) \cdot \dfrac{2}{3}}}{{\left( {1 + \dfrac{2}{3}} \right) \cdot \dfrac{3}{8}}} + \dfrac{{1 - \dfrac{{24}}{{25}}}}{{\dfrac{1}{8} \cdot \dfrac{8}{5}}} = \dfrac{1}{2} \cdot \dfrac{8}{5} + \dfrac{1}{5} = 1}$$

Шешуі: $${\dfrac{{(1,88 + 2,12) \cdot \dfrac{3}{{16}}}}{{\dfrac{5}{8} - \dfrac{{13}}{{18}} \cdot \dfrac{9}{{26}}}} + \dfrac{{\left( {\dfrac{{216}}{{150}} + \dfrac{{56}}{{100}}} \right) \cdot 2}}{{\left( {\dfrac{{77}}{{10}} \cdot \dfrac{4}{{99}} + \dfrac{2}{{15}}} \right) \cdot \dfrac{9}{2}}} = \dfrac{{4 \cdot \dfrac{3}{{16}}}}{{\dfrac{5}{8} - \dfrac{1}{4}}} + \dfrac{{\left( {\dfrac{{72}}{{50}} + \dfrac{{28}}{{50}}} \right) \cdot 2}}{{\left( {\dfrac{{14}}{{45}} + \dfrac{6}{{45}}} \right) \cdot \dfrac{9}{2}}} = 4 \cdot \dfrac{3}{{16}} \cdot \dfrac{8}{3} + \dfrac{4}{2} = 4.}$$

Шешуі: $${ = \left( {\dfrac{{33}}{2} - \dfrac{{124}}{9}} \right) \cdot \dfrac{6}{{11}} + \dfrac{{22}}{{10}} \cdot \left( {\dfrac{8}{{33}} - \dfrac{3}{{33}}} \right) + \dfrac{2}{{11}} = \dfrac{{49}}{{18}} \cdot \dfrac{6}{{11}} + \dfrac{1}{3} + \dfrac{2}{{11}} = \dfrac{{49}}{{33}} + \dfrac{{17}}{{33}} = 2.}$$

Шешуі: $${\dfrac{{0,04 + 0,86}}{{1 + 0,8}} \cdot \dfrac{{\left( {\dfrac{{95}}{{63}} - \dfrac{{39}}{{63}}} \right) \cdot \dfrac{{18}}{5}}}{{0,202 - 0,002}} = \dfrac{9}{{18}} \cdot \dfrac{8}{9} \cdot \dfrac{{18}}{{0,2 \cdot 5}} = 8.}$$

Шешуі: $${\dfrac{{\dfrac{1}{3} + \dfrac{1}{2}}}{{\dfrac{7}{4} - \dfrac{{28}}{{17}} \cdot \dfrac{{51}}{{56}}}} - \dfrac{{\dfrac{{49}}{{90}} \cdot \dfrac{5}{7}}}{{\dfrac{7}{{18}} \cdot 3}} = \dfrac{5}{{6 \cdot \left( {\dfrac{7}{4} - \dfrac{3}{2}} \right)}} - \dfrac{{7 \cdot 18}}{{18 \cdot 7 \cdot 3}} = \dfrac{{10}}{3} - \dfrac{1}{3} = 3}$$

Шешуі: $${\dfrac{{\dfrac{1}{2} + \dfrac{5}{8}}}{{\left( {10 - \dfrac{{220}}{{23}}} \right) \cdot \dfrac{{23}}{{50}} + \dfrac{8}{5}}} + \dfrac{{17}}{{40}} + \dfrac{{19}}{{20}} = \dfrac{{\dfrac{9}{8}}}{{\dfrac{1}{5} + \dfrac{8}{5}}} + \dfrac{{17}}{{40}} + \dfrac{{38}}{{40}} = \dfrac{5}{8} + \dfrac{{11}}{8} = 2.}$$

Шешуі: $${\left( {\left( {\dfrac{8}{7} - \dfrac{{23}}{{49}}} \right) \cdot \dfrac{{147}}{{22}} - 0,16 \cdot 2,5 + 2,5} \right):2,2 = \left( {\dfrac{{33}}{{49}} \cdot \dfrac{{147}}{{22}} - 0,4 + 2,5} \right):2,2 = }$$ $${ = (4,5 - 0,4 + 2,5) \cdot \dfrac{{10}}{{22}} = 3.}$$

Шешуі: $${ = \left( {2 \cdot \dfrac{5}{{16}} + \dfrac{1}{4} \cdot \dfrac{3}{2} + \dfrac{{65}}{{36}} \cdot \dfrac{{18}}{{65}}} \right) \cdot \dfrac{1}{3} = \left( {\dfrac{5}{8} + \dfrac{3}{8} + \dfrac{4}{8}} \right) \cdot \dfrac{1}{3} = \dfrac{1}{2} = 0,5.}$$

Шешуі: $${\dfrac{{\dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{6} + \dfrac{1}{8}}}{{\dfrac{1}{3} + \dfrac{2}{5} + \dfrac{{14}}{{15}}}} + \dfrac{{3,125 \cdot 48}}{{3,2 \cdot 125}} = \dfrac{{25}}{{24}} \cdot \dfrac{3}{5} + \dfrac{{1,2}}{{3,2}} = 0,625 + 0,375 = 1.}$$

Шешуі: $${\left( {\dfrac{{80}}{3} \cdot \dfrac{5}{{32}}} \right) \cdot \left( {\dfrac{{96}}{5} \cdot \dfrac{9}{{32}}} \right) - \dfrac{1}{{18}} = \dfrac{{25}}{6} \cdot \dfrac{{27}}{5} - \dfrac{{11 \cdot 112}}{{3 \cdot 33}} - \dfrac{1}{{18}} = }$$ $${ = \dfrac{{45}}{2} - \dfrac{{112}}{9} - \dfrac{1}{{18}} = \dfrac{1}{{18}}(45 \cdot 9 - 112 \cdot 2 - 1) - 10.}$$

Шешуі: $${\dfrac{{1,325 + \dfrac{{29}}{{40}}}}{{0,128 \cdot 6,25 - 0,0345:0,12}} \cdot 0,25 = \dfrac{{1,325 + 0,725}}{{0,8 - 0,2875}} \cdot 0,25 = \dfrac{{2,05}}{{0,5125}} \cdot 0,25 = 1.}$$

Шешуі: $${\left( {223,6:0,26 - 217 \cdot \dfrac{{17}}{7}} \right) - \left( {\dfrac{{63}}{2} \cdot \dfrac{5}{{63}} + 114 \cdot \dfrac{7}{3} + \dfrac{{123}}{2}} \right) = }$$ $${ = (860 - 527) - \left( {\dfrac{5}{2} + 266 + \dfrac{{123}}{2}} \right) = 333 - 330 = 3.}$$