Сандық өрнектерді ықшамдау (Cканави (А) 1.26-1.50)

Амалдарды орындаңыз.

№ 1.26 ${\dfrac{{(3,4 - 1,275) \cdot \dfrac{{16}}{{17}}}}{{\dfrac{5}{{18}} \cdot \left( {1\dfrac{7}{{85}} + 6\dfrac{2}{{17}}} \right)}} + 0,5\left( {2 + \dfrac{{12,5}}{{5,75 + \dfrac{1}{2}}}} \right)}$

Шешуі: $${\dfrac{{(3,4 - 1,275) \cdot \dfrac{{16}}{{17}}}}{{\dfrac{5}{{18}} \cdot \left( {1\dfrac{7}{{85}} + 6\dfrac{2}{{17}}} \right)}} + 0,5\left( {2 + \dfrac{{12,5}}{{5,75 + \dfrac{1}{2}}}} \right) = \dfrac{{2,125 \cdot \dfrac{{16}}{{17}}}}{{\dfrac{5}{{18}}\left( {\dfrac{{92}}{{85}} + \dfrac{{104}}{{17}}} \right)}} + \dfrac{1}{2}\left( {2 + \dfrac{{12,5}}{{6,25}}} \right) = }$$ $${ = \dfrac{{\dfrac{{17}}{8}}}{{\dfrac{5}{{18}} \cdot \dfrac{{612}}{{85}}}} + 1 + 1 = 1 + 2 = 3.}$$

№ 1.27 ${\left( {\dfrac{{3,75 + 2\dfrac{1}{2}}}{{2\dfrac{1}{2} - 1,875}} - \dfrac{{2\dfrac{3}{4} + 1,5}}{{2,75 - 1\dfrac{1}{2}}}} \right) \cdot \dfrac{{10}}{{11}}}$

Шешуі: $${\left( {\dfrac{{3,75 + 2\dfrac{1}{2}}}{{2\dfrac{1}{2} - 1,875}} - \dfrac{{2\dfrac{3}{4} + 1,5}}{{2,75 - 1\dfrac{1}{2}}}} \right) \cdot \dfrac{{10}}{{11}} = \left( {\dfrac{{3,75 + 2,5}}{{2,5 - 1,875}} - \dfrac{{2,75 + 1,5}}{{2,75 - 1,5}}} \right) \cdot \dfrac{{10}}{{11}} = }$$ $${ = \left( {\dfrac{{6,25}}{{0,625}} - \dfrac{{4,25}}{{1,25}}} \right) \cdot \dfrac{{10}}{{11}} = \left( {10 - \dfrac{{17}}{5}} \right) \cdot \dfrac{{10}}{{11}} = \dfrac{{33}}{5} \cdot \dfrac{{10}}{{11}} = 6.}$$

№ 1.28 $((21,85:43,7 + 8,5:3,4):4,5):1\dfrac{2}{5} + 1\dfrac{{11}}{{21}}$

Шешуі: $$((21,85:43,7 + 8,5:3,4):4,5):1\dfrac{2}{5} + 1\dfrac{{11}}{{21}} = \left( {(0,5 + 2,5):4\dfrac{1}{2}} \right):\dfrac{7}{5} + \dfrac{{32}}{{21}} = $$ $$ = \left( {3 \cdot \dfrac{2}{9}} \right) \cdot \dfrac{5}{7} + \dfrac{{32}}{{21}} = \dfrac{{10}}{{21}} + \dfrac{{32}}{{21}} = \dfrac{{42}}{{21}} = 2.$$

№ 1.29 $\left( {1\dfrac{2}{5} + 3,5:1\dfrac{1}{4}} \right):2\dfrac{2}{5} + 3,4:2\dfrac{1}{8} - 0,35$

Шешуі: $$\left( {1\dfrac{2}{5} + 3,5:1\dfrac{1}{4}} \right):2\dfrac{2}{5} + 3,4:2\dfrac{1}{8} - 0,35 = $$ $$ = (1,4 + 3,5:1,25):2,4 + 3,4:2,125 - 0,35 = $$ $$ = (1,4 + 2,8):2,4 + 1,6 - 0,35 = $$ $$ = 4,2:2,4 + 1,25 = 1,75 + 1,25 = 3$$

№ 1.30 $\dfrac{{\left( {0,3275 - \left( {2\dfrac{{15}}{{88}} + \dfrac{4}{{33}}} \right):12\dfrac{2}{9}} \right):0,07}}{{(13 - 0,416):6,05 + 1,92}}$

Шешуі: $$\dfrac{{\left( {0,3275 - \left( {2\dfrac{{15}}{{88}} + \dfrac{4}{{33}}} \right):12\dfrac{2}{9}} \right):0,07}}{{(13 - 0,416):6,05 + 1,92}} = \dfrac{{\left( {0,3275 - \left( {\dfrac{{191}}{{88}} + \dfrac{4}{{33}}} \right) \cdot \dfrac{9}{{110}}} \right):0,07}}{{12,584:6,05 + 1,92}} = $$ $$ = \dfrac{{\left( {\dfrac{{131}}{{400}} - \dfrac{{605}}{{264}} \cdot \dfrac{9}{{110}}} \right) \cdot \dfrac{{100}}{7}}}{{2,08 + 1,92}} = \dfrac{{\left( {\dfrac{{131}}{{400}} - \dfrac{3}{{16}}} \right) \cdot \dfrac{{100}}{7}}}{4} = \dfrac{7}{{50}} \cdot \dfrac{{100}}{7} \cdot \dfrac{1}{4} = \dfrac{1}{2} = 0,5.$$

№ 1.31 $\dfrac{{\dfrac{5}{6} - \dfrac{{21}}{{45}}}}{{1\dfrac{5}{6}}} \cdot \dfrac{{1,125 + 1\dfrac{3}{4} - \dfrac{5}{{12}}}}{{0,59}}$

Шешуі: $$\dfrac{{\dfrac{5}{6} - \dfrac{{21}}{{45}}}}{{1\dfrac{5}{6}}} \cdot \dfrac{{1,125 + 1\dfrac{3}{4} - \dfrac{5}{{12}}}}{{0,59}} = \dfrac{{\dfrac{5}{6} - \dfrac{7}{{15}}}}{{\dfrac{{11}}{6}}} \cdot \dfrac{{\dfrac{9}{8} + \dfrac{7}{4} - \dfrac{5}{{12}}}}{{\dfrac{{59}}{{100}}}} = \dfrac{{11}}{{30}} \cdot \dfrac{6}{{11}} \cdot \dfrac{{59}}{{24}} \cdot \dfrac{{100}}{{59}} = \dfrac{1}{5} \cdot \dfrac{{25}}{6} = \dfrac{5}{6}$$

№ 1.32 $\dfrac{{{{\left( {{3^{ - 1}} - \sqrt {1\dfrac{7}{9}} } \right)}^{ - 2}}:0,25}}{{\dfrac{{37}}{{300}}:0,0925}} + 12,5 \cdot 0,64$

Шешуі: $$\dfrac{{{{\left( {{3^{ - 1}} - \sqrt {1\dfrac{7}{9}} } \right)}^{ - 2}}:0,25}}{{\dfrac{{37}}{{300}}:0,0925}} + 12,5 \cdot 0,64 = \dfrac{{{{\left( {\dfrac{1}{3} - \sqrt {\dfrac{{16}}{9}} } \right)}^{ - 2}} \cdot 4}}{{\dfrac{{37}}{{300}} \cdot \dfrac{{400}}{{37}}}} + 8 = \dfrac{{{{\left( {\dfrac{1}{3} - \dfrac{4}{3}} \right)}^{ - 2}} \cdot 4}}{{\dfrac{4}{3}}} + 8 = $$ $$ = 3{( - 1)^{ - 2}} + 8 = 3 + 8 = 11.$$

№ 1.33 $\dfrac{{\left( {\dfrac{5}{8} + 2\dfrac{{17}}{{24}}} \right):2,5}}{{\left( {1,3 + \dfrac{{23}}{{30}} + \dfrac{4}{{11}}} \right) \cdot \dfrac{{110}}{{401}}}} \cdot 0,5$

Шешуі: $$\dfrac{{\left( {\dfrac{5}{8} + 2\dfrac{{17}}{{24}}} \right):2,5}}{{\left( {1,3 + \dfrac{{23}}{{30}} + \dfrac{4}{{11}}} \right) \cdot \dfrac{{110}}{{401}}}} \cdot 0,5 = \dfrac{{\left( {\dfrac{5}{8} + \dfrac{{65}}{{24}}} \right) \cdot \dfrac{2}{5} \cdot \dfrac{1}{2}}}{{\left( {\dfrac{{13}}{{10}} + \dfrac{{23}}{{30}} + \dfrac{4}{{11}}} \right) \cdot \dfrac{{110}}{{401}}}} = \dfrac{{\dfrac{{10}}{3} \cdot \dfrac{1}{5}}}{{\dfrac{{401}}{{165}} \cdot \dfrac{{110}}{{401}}}} = \dfrac{2}{3}:\dfrac{2}{3} = 1$$

№ 1.34 $\dfrac{{((7 - 6,35):6,5 + 9,9) \cdot \dfrac{1}{{12,8}}}}{{\left( {1,2:36 + 1\dfrac{1}{5}:0,25 - 1\dfrac{5}{6}} \right) \cdot 1\dfrac{1}{4}}}:0,125$

Шешуі: $$\dfrac{{((7 - 6,35):6,5 + 9,9) \cdot \dfrac{1}{{12,8}}}}{{\left( {1,2:36 + 1\dfrac{1}{5}:0,25 - 1\dfrac{5}{6}} \right) \cdot 1\dfrac{1}{4}}}:0,125 = \dfrac{{(0,65:6,5 + 9,9) \cdot \dfrac{5}{{64}} \cdot 8}}{{\left( {\dfrac{6}{5} \cdot \dfrac{1}{{36}} + \dfrac{6}{5} \cdot 4 - \dfrac{{11}}{6}} \right) \cdot \dfrac{5}{4}}} = $$ $$ = \dfrac{{(0,1 + 9,9) \cdot \dfrac{5}{8}}}{{\left( {\dfrac{1}{{30}} + \dfrac{{24}}{5} - \dfrac{{11}}{6}} \right) \cdot \dfrac{5}{4}}} = \dfrac{{10 \cdot \dfrac{1}{2}}}{{\dfrac{{90}}{{30}}}} = \dfrac{5}{3}$$

№ 1.35 $\dfrac{{\left( {2\dfrac{{38}}{{45}} - \dfrac{1}{{15}}} \right):13\dfrac{8}{9} + 3\dfrac{3}{{65}} \cdot \dfrac{{26}}{{99}}}}{{\left( {18\dfrac{1}{2} - 13\dfrac{7}{9}} \right) \cdot \dfrac{1}{{85}}}} \cdot 0,5$

Шешуі: $$\dfrac{{\left( {2\dfrac{{38}}{{45}} - \dfrac{1}{{15}}} \right):13\dfrac{8}{9} + 3\dfrac{3}{{65}} \cdot \dfrac{{26}}{{99}}}}{{\left( {18\dfrac{1}{2} - 13\dfrac{7}{9}} \right) \cdot \dfrac{1}{{85}}}} \cdot 0,5 = \dfrac{{\dfrac{{25}}{9} \cdot \dfrac{9}{{125}} + \dfrac{{198}}{{65}} \cdot \dfrac{{26}}{{99}}}}{{\left( {\dfrac{{37}}{2} - \dfrac{{124}}{9}} \right) \cdot \dfrac{2}{{85}}}} = \dfrac{{\dfrac{1}{5} + \dfrac{{52}}{{65}}}}{{\dfrac{{85}}{{18}} \cdot \dfrac{2}{{85}}}} = \dfrac{1}{{\dfrac{1}{9}}} = 9.$$

№ 1.36 $\dfrac{{3,75:1\dfrac{1}{2} + \left( {1,5:3\dfrac{3}{4}} \right) \cdot 2\dfrac{1}{2} + \left( {1\dfrac{1}{7} - \dfrac{{23}}{{49}}} \right):\dfrac{{22}}{{147}}}}{{2:3\dfrac{1}{5} + \left( {3\dfrac{1}{4}:13} \right):\dfrac{2}{3} - \left( {2\dfrac{5}{{18}} - \dfrac{{17}}{{36}}} \right) \cdot \dfrac{{18}}{{65}}}}$

Шешуі: $$\dfrac{{3,75:1\dfrac{1}{2} + \left( {1,5:3\dfrac{3}{4}} \right) \cdot 2\dfrac{1}{2} + \left( {1\dfrac{1}{7} - \dfrac{{23}}{{49}}} \right):\dfrac{{22}}{{147}}}}{{2:3\dfrac{1}{5} + \left( {3\dfrac{1}{4}:13} \right):\dfrac{2}{3} - \left( {2\dfrac{5}{{18}} - \dfrac{{17}}{{36}}} \right) \cdot \dfrac{{18}}{{65}}}} = \dfrac{{3\dfrac{3}{4} \cdot \dfrac{2}{3} + \left( {\dfrac{3}{2}:\dfrac{{15}}{4}} \right) \cdot \dfrac{5}{2} + \left( {\dfrac{8}{7} - \dfrac{{23}}{{49}}} \right) \cdot \dfrac{{147}}{{22}}}}{{2 \cdot \dfrac{5}{{16}} + \left( {\dfrac{{13}}{4}:13} \right) \cdot \dfrac{3}{2} - \left( {\dfrac{{41}}{{18}} - \dfrac{{17}}{{36}}} \right) \cdot \dfrac{{18}}{{65}}}} = $$ $$ = \dfrac{{\dfrac{5}{2} + 1 + \dfrac{{33}}{{49}} \cdot \dfrac{{147}}{{22}}}}{{\dfrac{5}{8} + \dfrac{3}{8} - \dfrac{{65}}{{36}} \cdot \dfrac{{18}}{{65}}}} = \dfrac{{\dfrac{7}{2} + \dfrac{9}{2}}}{{1 - \dfrac{1}{2}}} = \dfrac{8}{{\dfrac{1}{2}}} = 16.$$

№ 1.37 $\dfrac{{\left( {\left( {4,625 - \dfrac{{13}}{{18}} \cdot \dfrac{9}{{26}}} \right):\dfrac{9}{4} + 2,5:1,25:6,75} \right):1\dfrac{{53}}{{68}}}}{{\left( {\dfrac{1}{2} - 0,375} \right):0,125 + \left( {\dfrac{5}{6} - \dfrac{7}{{12}}} \right):(0,358 - 1,4796:13,7)}}$

Шешуі: $$\dfrac{{\left( {\left( {4,625 - \dfrac{{13}}{{18}} \cdot \dfrac{9}{{26}}} \right):\dfrac{9}{4} + 2,5:1,25:6,75} \right):1\dfrac{{53}}{{68}}}}{{\left( {\dfrac{1}{2} - 0,375} \right):0,125 + \left( {\dfrac{5}{6} - \dfrac{7}{{12}}} \right):(0,358 - 1,4796:13,7)}} = $$ $$ = \dfrac{{\left( {\left( {\dfrac{{37}}{8} - \dfrac{1}{4}} \right) \cdot \dfrac{4}{9} + 2:6,75} \right) \cdot \dfrac{{68}}{{121}}}}{{0,125:0,125 + 0,25:(0,358 - 0,108)}} = \dfrac{{\left( {\dfrac{{35}}{{18}} + 2:\dfrac{{27}}{4}} \right)\dfrac{{68}}{{121}}}}{{1 + 0,25:0,25}} = $$ $$ = \dfrac{{121}}{{54}} \cdot \dfrac{{68}}{{121}} \cdot \dfrac{1}{2} = \dfrac{{17}}{{27}}.$$

№ 1.38 $\dfrac{{\left( {\left( {3\dfrac{7}{{12}} - 2\dfrac{{11}}{{18}} + 2\dfrac{1}{{24}}} \right) \cdot 1\dfrac{5}{{31}} - \dfrac{3}{{52}}\left( {3\dfrac{1}{2} + \dfrac{5}{6}} \right)} \right) \cdot 1\dfrac{7}{{13}}}}{{\dfrac{{19}}{{84}}:\left( {5\dfrac{{13}}{{42}} - 2\dfrac{{13}}{{28}} + \dfrac{5}{{24}}} \right) + 1\dfrac{2}{{27}} - \dfrac{1}{3} \cdot \dfrac{4}{9}}}$

Шешуі: $$\dfrac{{\left( {\left( {3\dfrac{7}{{12}} - 2\dfrac{{11}}{{18}} + 2\dfrac{1}{{24}}} \right) \cdot 1\dfrac{5}{{31}} - \dfrac{3}{{52}}\left( {3\dfrac{1}{2} + \dfrac{5}{6}} \right)} \right) \cdot 1\dfrac{7}{{13}}}}{{\dfrac{{19}}{{84}}:\left( {5\dfrac{{13}}{{42}} - 2\dfrac{{13}}{{28}} + \dfrac{5}{{24}}} \right) + 1\dfrac{2}{{27}} - \dfrac{1}{3} \cdot \dfrac{4}{9}}} = $$ $$ = \dfrac{{\left( {\left( {\dfrac{{43}}{{12}} - \dfrac{{47}}{{18}} + \dfrac{{49}}{{24}}} \right) \cdot \dfrac{{36}}{{31}} - \dfrac{3}{{52}}\left( {\dfrac{7}{2} + \dfrac{5}{6}} \right)} \right) \cdot \dfrac{{20}}{{13}}}}{{\dfrac{{19}}{{84}}:\left( {\dfrac{{223}}{{42}} - \dfrac{{69}}{{28}} + \dfrac{5}{{24}}} \right) + \dfrac{{29}}{{27}} - \dfrac{4}{{27}}}} = \dfrac{{\left( {\dfrac{{217}}{{72}} \cdot \dfrac{{36}}{{31}} - \dfrac{3}{{52}} \cdot \dfrac{{13}}{3}} \right) \cdot \dfrac{{20}}{{13}}}}{{\dfrac{{19}}{{84}}:\dfrac{{171}}{{56}} + \dfrac{{25}}{{27}}}} = $$ $$ = \dfrac{{\left( {\dfrac{7}{2} - \dfrac{1}{4}} \right) \cdot \dfrac{{20}}{{13}}}}{{\dfrac{2}{{27}} + \dfrac{{25}}{{27}}}} = \dfrac{{13}}{4} \cdot \dfrac{{20}}{{13}} = 5.$$

№ 1.39 $\left( {\dfrac{{(3,2 - 1,7):0,003}}{{\left( {\dfrac{{29}}{{35}} - \dfrac{3}{7}} \right) \cdot 4:0,2}} - \dfrac{{\left( {1\dfrac{{13}}{{20}} - 1,5} \right) \cdot 1,5}}{{\left( {2,44 + 1\dfrac{{14}}{{25}}} \right) \cdot \dfrac{1}{8}}}} \right):62\dfrac{1}{{20}} + 1,364:0,124$

Шешуі: $$\left( {\dfrac{{(3,2 - 1,7):0,003}}{{\left( {\dfrac{{29}}{{35}} - \dfrac{3}{7}} \right) \cdot 4:0,2}} - \dfrac{{\left( {1\dfrac{{13}}{{20}} - 1,5} \right) \cdot 1,5}}{{\left( {2,44 + 1\dfrac{{14}}{{25}}} \right) \cdot \dfrac{1}{8}}}} \right):62\dfrac{1}{{20}} + 1,364:0,124 = $$ $$ = \left( {\dfrac{{1,5:0,003}}{{\dfrac{{14}}{{35}} \cdot 4 \cdot 5}} - \dfrac{{\dfrac{3}{{20}} \cdot \dfrac{3}{2}}}{{4 \cdot \dfrac{1}{8}}}} \right):\dfrac{{1241}}{{20}} + 11 = \left( {\dfrac{{500}}{8} - \dfrac{9}{{40}} \cdot 2} \right) \cdot \dfrac{{20}}{{1241}} + 11 = $$ $$ = \left( {\dfrac{{125}}{2} - \dfrac{9}{{20}}} \right) \cdot \dfrac{{20}}{{1241}} + 11 = \dfrac{{1241}}{{20}} \cdot \dfrac{{20}}{{1241}} + 11 = 12.$$

№ 1.40 $5\dfrac{4}{7}:\left( {8,4 \cdot \dfrac{6}{7} \cdot \left( {6 - \dfrac{{(2,3 + 5:6,25) \cdot 7}}{{8 \cdot 0,0125 + 6,9}}} \right) - 20,384:1,3} \right)$

Шешуі: $$5\dfrac{4}{7}:\left( {8,4 \cdot \dfrac{6}{7} \cdot \left( {6 - \dfrac{{(2,3 + 5:6,25) \cdot 7}}{{8 \cdot 0,0125 + 6,9}}} \right) - 20,384:1,3} \right) = $$ $$\dfrac{{39}}{7}:\left( {\dfrac{{42}}{5} \cdot \dfrac{6}{7}\left( {6 - \dfrac{{(2,3 + 0,8) \cdot 7}}{{0,1 + 6,9}}} \right) - 15,68} \right) = \dfrac{{39}}{7}:\left( {\dfrac{{36}}{5}\left( {6 - \dfrac{{3,1 \cdot 7}}{7}} \right) - 15,68} \right) = $$ $$ = \dfrac{{39}}{7}:\left( {\dfrac{{36}}{5} \cdot 2,9 - 15,68} \right) = \dfrac{{39}}{7}:(7,2 \cdot 2,9 - 15,68) = \dfrac{{39}}{7}:(20,88 - 15,68) = $$ $$ = \dfrac{{39}}{7}:5,2 = \dfrac{{39}}{7}:\dfrac{{26}}{5} = \dfrac{{15}}{{14}}.$$

№ 1.41 $\dfrac{{\left( {4 - 3,5 \cdot \left( {2\dfrac{1}{7} - 1\dfrac{1}{5}} \right)} \right):0,16}}{X} = \dfrac{{3\dfrac{2}{7} - \dfrac{3}{{14}}:\dfrac{1}{6}}}{{41\dfrac{{23}}{{84}} - 40\dfrac{{49}}{{60}}}},\,\,X - ?$

Шешуі: $${X = \dfrac{{\left( {4 - 3,5 \cdot \left( {2\dfrac{1}{7} - 1\dfrac{1}{5}} \right)} \right):0,16 \cdot \left( {41\dfrac{{23}}{{84}} - 40\dfrac{{49}}{{60}}} \right)}}{{3\dfrac{2}{7} - \dfrac{3}{{14}}:\dfrac{1}{6}}} = }$$ $${ = \dfrac{{\left( {4 - 3,5 \cdot \left( {\dfrac{{15}}{7} - \dfrac{6}{5}} \right)} \right):0,16 \cdot \dfrac{{16}}{{35}}}}{{\dfrac{{23}}{7} \cdot \dfrac{9}{7}}} = \dfrac{{\left( {4 - \dfrac{7}{2} \cdot \dfrac{{33}}{{35}}} \right):\dfrac{4}{{25}} \cdot \dfrac{{16}}{{35}}}}{2} = }$$ $${ = \dfrac{{\left( {4 - \dfrac{{33}}{{10}}} \right):\dfrac{4}{{25}} \cdot \dfrac{{16}}{{35}}}}{2} = \dfrac{{\dfrac{7}{{10}} \cdot \dfrac{{25}}{4} \cdot \dfrac{{16}}{{35}}}}{2} = 1.}$$

№ 1.42 $\dfrac{{1,2:0,375 - 0,2}}{{6\dfrac{4}{{25}}:15\dfrac{2}{5} + 0,8}} = \dfrac{{0,016:0,12 + 0,7}}{X},\,X - ?$

Шешуі: $${X = \dfrac{{(0,016:0,12 + 0,7)\left( {6\dfrac{4}{{25}}:15\dfrac{2}{5} + 0,8} \right)}}{{1,2:0,375 - 0,2}} = \dfrac{{\left( {\dfrac{2}{{125}} \cdot \dfrac{3}{{25}} + \dfrac{7}{{10}}} \right)\left( {\dfrac{{154}}{{25}} \cdot \dfrac{{77}}{5} + \dfrac{4}{5}} \right)}}{{3,2 - 0,2}} = }$$ $${ = \dfrac{{\left( {\dfrac{2}{{15}} + \dfrac{7}{{10}}\left( {\dfrac{2}{5} + \dfrac{4}{5}} \right)} \right.}}{3} = \dfrac{{\dfrac{5}{6} \cdot \dfrac{6}{5}}}{3} = \dfrac{1}{3}}$$

№ 1.43 $\dfrac{{0,125X}}{{\left( {\dfrac{{19}}{{24}} - \dfrac{{21}}{{40}}} \right) \cdot 8\dfrac{7}{{16}}}} = \dfrac{{\left( {1\dfrac{{28}}{{63}} - \dfrac{{17}}{{21}}} \right) \cdot 0,7}}{{0,675 \cdot 2,4 - 0,02}},\,X - ?$

Шешуі: $${X = \dfrac{{\left( {1\dfrac{{28}}{{63}} - \dfrac{{17}}{{21}}} \right) \cdot 0,7 \cdot \left( {\dfrac{{19}}{{24}} - \dfrac{{21}}{{40}}} \right) \cdot 8\dfrac{7}{{16}}}}{{(0,675 \cdot 2,4 - 0,02) \cdot 0,125}} = \dfrac{{\left( {\dfrac{{91}}{{63}} - \dfrac{{17}}{{21}}} \right) \cdot \dfrac{7}{{10}} \cdot \dfrac{4}{{15}} \cdot \dfrac{{135}}{{16}}}}{{(1,62 - 0,02) \cdot 0,125}} = }$$ $${ = \dfrac{{\dfrac{{40}}{{63}} \cdot \dfrac{{63}}{{40}}}}{{1,6 \cdot 0,125}} = \dfrac{1}{{0,2}} = 5.}$$

№ 1.44 $\dfrac{X}{{10,5 \cdot 0,24 - 15,15:7,5}} = \dfrac{{9\left( {1\dfrac{{11}}{{20}} - 0,945:0,9} \right)}}{{1\dfrac{3}{{40}} - 4\dfrac{3}{8}:7}},\,X - ?$

Шешуі: $${X = \dfrac{{9\left( {1\dfrac{{11}}{{20}} - 0,945:0,9} \right) \cdot (10,5 \cdot 0,24 - 15,15:7,5)}}{{1\dfrac{3}{{40}} - 4\dfrac{3}{8}:7}} = }$$ $${ = \dfrac{{9 \cdot \left( {\dfrac{{31}}{{20}} - \dfrac{{21}}{{20}}} \right) \cdot (2,52 - 2,02)}}{{\dfrac{{43}}{{40}} - \dfrac{{35}}{8}:7}} = \dfrac{{9 \cdot \dfrac{1}{2} \cdot \dfrac{1}{2}}}{{\dfrac{{43}}{{40}} - \dfrac{5}{8}}} = \dfrac{{\dfrac{9}{4}}}{{\dfrac{9}{{20}}}} = 5}$$

№ 1.45 $\dfrac{{15,2 \cdot 0,25 - 48,51:14,7}}{X} = \dfrac{{\left( {\dfrac{{13}}{{44}} - \dfrac{2}{{11}} - \dfrac{5}{{66}}:2\dfrac{1}{2}} \right) \cdot 1\dfrac{1}{5}}}{{3,2 + 0,8\left( {5\dfrac{1}{2} - 3,25} \right)}},\,X - ?$

Шешуі: $${X = \dfrac{{(15,2 \cdot 0,25 - 48,51:14,7) \cdot \left( {3,2 + 0,8\left( {5\dfrac{1}{2} - 3,25} \right)} \right)}}{{\left( {\dfrac{{13}}{{44}} - \dfrac{2}{{11}} - \dfrac{5}{{66}}:2\dfrac{1}{2}} \right) \cdot 1\dfrac{1}{5}}} = }$$ $${ = \dfrac{{(3,8 - 3,3) \cdot (3,2 + 0,8 \cdot 2,25)}}{{\left( {\dfrac{5}{{44}} - \dfrac{5}{{66}}:\dfrac{5}{2}} \right) \cdot \dfrac{6}{5}}} = \dfrac{{0,5 \cdot (3,2 + 1,8)}}{{\left( {\dfrac{5}{{44}} - \dfrac{1}{{33}}} \right) \cdot \dfrac{6}{5}}} = \dfrac{{0,5 \cdot 5}}{{\dfrac{1}{{12}} \cdot \dfrac{6}{5}}} = 25}$$

№ 1.46 $\dfrac{{\sqrt {6,3 \cdot 1,7} \cdot \left( {\sqrt {\dfrac{{6,3}}{{1,7}}} - \sqrt {\dfrac{{1,7}}{{6,3}}} } \right)}}{{\sqrt {{{(6,3 + 1,7)}^2} - 4 \cdot 6,3 \cdot 1,7} }}$

Шешуі: $${\dfrac{{\sqrt {6,3 \cdot 1,7} \cdot \left( {\sqrt {\dfrac{{6,3}}{{1,7}}} - \sqrt {\dfrac{{1,7}}{{6,3}}} } \right)}}{{\sqrt {{{(6,3 + 1,7)}^2} - 4 \cdot 6,3 \cdot 1,7} }} = \dfrac{{\sqrt {6,3 \cdot 1,7} \cdot \left( {\sqrt {\dfrac{{6,3}}{{1,7}}} - \sqrt {\dfrac{{1,7}}{{6,3}}} } \right)}}{{\sqrt {{{6,3}^2} + 2 \cdot 6,3 \cdot 1,7 + {{1,7}^2} - 4 \cdot 6,3 \cdot 1,7} }} = }$$ $${ = \dfrac{{\sqrt {6,3 \cdot 1,7} \cdot \dfrac{{\sqrt {{{6,3}^2}} - \sqrt {{{1,7}^2}} }}{{\sqrt {6,3 \cdot 1,7} }}}}{{\sqrt {{{6,3}^2} - 2 \cdot 6,3 \cdot 1,7 + {{1,7}^2}} }} = \dfrac{{6,3 - 1,7}}{{\sqrt {{{(6,3 - 1,7)}^2}} }} = \dfrac{{6,3 - 1,7}}{{6,3 - 1,7}} = 1.}$$

№ 1.47 $\left( {\dfrac{{\sqrt {{{561}^2} - {{459}^2}} }}{{4\dfrac{2}{7} \cdot 0,15 + 4\dfrac{2}{7}:\dfrac{{20}}{3}}} + 4\sqrt {10} } \right):\dfrac{1}{3}\sqrt {40} $

Шешуі: $${\left( {\dfrac{{\sqrt {{{561}^2} - {{459}^2}} }}{{4\dfrac{2}{7} \cdot 0,15 + 4\dfrac{2}{7}:\dfrac{{20}}{3}}} + 4\sqrt {10} } \right):\dfrac{1}{3}\sqrt {40} = \left( {\dfrac{{\sqrt {(561 + 459)(561 - 459)} }}{{\dfrac{{30}}{7} \cdot \dfrac{3}{{20}} + \dfrac{{30}}{7} \cdot \dfrac{3}{{20}}}} + 4\sqrt {10} } \right) \times }$$ $${ \times \dfrac{3}{{2\sqrt {10} }} = \left( {\dfrac{{\sqrt {1020 \cdot 102} }}{{\dfrac{9}{7}}} + 4\sqrt {10} } \right) \cdot \dfrac{3}{{2\sqrt {10} }} = \dfrac{{7\sqrt {{{102}^2} \cdot 10} + 36\sqrt {10} }}{9} \cdot \dfrac{3}{{2\sqrt {10} }} = }$$ $${ = \dfrac{{714\sqrt {10} + 36\sqrt {10} }}{9} \cdot \dfrac{3}{{2\sqrt {10} }} = \dfrac{{750\sqrt {10} }}{9} \cdot \dfrac{3}{{2\sqrt {10} }} = \dfrac{{375}}{3} = 125.}$$

№ 1.48 ${\left( {\sqrt {{{\left( {\sqrt 2 - \dfrac{3}{2}} \right)}^2}} - \sqrt[3]{{{{(1 - \sqrt 2 )}^3}}}} \right)^2}$

Шешуі: $${\left( {\sqrt {{{\left( {\sqrt 2 - \dfrac{3}{2}} \right)}^2}} - \sqrt[3]{{{{(1 - \sqrt 2 )}^3}}}} \right)^2} = {\left( {\dfrac{3}{2} - \sqrt 2 - 1 + \sqrt 2 } \right)^2} = {\left( {\dfrac{1}{2}} \right)^2} = \dfrac{1}{4}$$

№ 1.49 $\dfrac{{{2^{ - 2}} + {5^0}}}{{{{(0,5)}^{ - 2}} - 5{{( - 2)}^{ - 2}} + {{\left( {\dfrac{2}{3}} \right)}^{ - 2}}}} + 4,75$

Шешуі: $${\dfrac{{{2^{ - 2}} + {5^0}}}{{{{(0,5)}^{ - 2}} - 5{{( - 2)}^{ - 2}} + {{\left( {\dfrac{2}{3}} \right)}^{ - 2}}}} + 4,75 = \dfrac{{\dfrac{1}{{{2^2}}} + 1}}{{\dfrac{1}{{{{(0,5)}^2}}} - \dfrac{5}{{{{( - 2)}^2}}} + {{\left( {\dfrac{3}{2}} \right)}^2}}} + 4,75 = }$$ $${ = \dfrac{{\dfrac{1}{4} + 1}}{{\dfrac{1}{{0,25}} - \dfrac{5}{4} + \dfrac{9}{4}}} + 4,75 = - \dfrac{{\dfrac{5}{4}}}{{4 + 1}} + 4,75 = \dfrac{1}{4} + 4\dfrac{3}{4} = 5.}$$

№ 1.50 $\dfrac{{{{(0,6)}^0} - {{(0,1)}^{ - 1}}}}{{{{\left( {3:{2^3}} \right)}^{ - 1}} \cdot {{(1,5)}^3} + {{\left( { - \dfrac{1}{3}} \right)}^{ - 1}}}}$

Шешуі: $$\dfrac{{{{(0,6)}^0} - {{(0,1)}^{ - 1}}}}{{{{\left( {3:{2^3}} \right)}^{ - 1}} \cdot {{(1,5)}^3} + {{\left( { - \dfrac{1}{3}} \right)}^{ - 1}}}} = \dfrac{{1 - 10}}{{\dfrac{8}{3} \cdot {{\left( {\dfrac{3}{2}} \right)}^3} - 3}} = \dfrac{{ - 9}}{{\dfrac{8}{3} \cdot \dfrac{{27}}{8} - 3}} = \dfrac{{ - 9}}{{9 - 3}} = - \dfrac{9}{6} = - \dfrac{3}{2}$$

 

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