Есептеңіз.
№ 17 Есептеңіз: $80 - \left( {\left( {\dfrac{4}{5} \cdot 7 + 0,64} \right) \cdot \left( {1,25 \cdot 7 - \dfrac{4}{5} \cdot 1,25} \right) + 31,64} \right)$
Шешуі: $$ = 80 - \left( {\dfrac{4}{5} \cdot \left( {7 + \dfrac{4}{5}} \right) \cdot \dfrac{5}{4} \cdot \left( {7 - \dfrac{4}{5}} \right) + 31,64} \right) = $$ $$ = 80 - \left( {{7^2} - {{\left( {\dfrac{4}{5}} \right)}^2} + 31,64} \right) = 80 - 49 + \dfrac{{16}}{{25}} - 31\dfrac{{16}}{{25}} = 31 - 31 = 0$$
№ 18 Есептеңіз: ${\left( {22,385:3,7 - 2,9 \cdot 1\dfrac{2}{3}} \right):9\dfrac{{11}}{{15}}}$
Шешуі: $${\left( {\dfrac{{22385}}{{37000}} - \dfrac{{29}}{{10}} \cdot \dfrac{5}{3}} \right):\dfrac{{146}}{{15}} = \left( {\dfrac{{121}}{{20}} - \dfrac{{29}}{6}} \right) \cdot \dfrac{{15}}{{146}}}$$ $${ = \dfrac{{363 - 290}}{{60}} \cdot \dfrac{{15}}{{146}} = \dfrac{{73}}{4} \cdot \dfrac{1}{{146}} = \dfrac{1}{8}}$$
№ 19 Есептеңіз: $\dfrac{{45\dfrac{{10}}{{63}} - 44\dfrac{{25}}{{84}}}}{{\dfrac{3}{4} - \left( {2\dfrac{1}{3} - 1\dfrac{1}{9}} \right):4}}:31$
Шешуі: $$ = \dfrac{{45\dfrac{{10}}{{21 \cdot 3}} - 44\dfrac{{25}}{{21 \cdot 4}}}}{{\dfrac{3}{4} - \left( {2\dfrac{3}{9} - 1\dfrac{1}{9}} \right):4}}:31 = \dfrac{{1\dfrac{{40 - 75}}{{21 \cdot 12}}}}{{\dfrac{3}{4} - 1\dfrac{2}{9}:4}}:31 = $$ $$ = \dfrac{{\dfrac{{252 + 40 - 75}}{{252}}}}{{\dfrac{3}{4} - \dfrac{{11}}{9} \cdot \dfrac{1}{4}}}:31 = \dfrac{{\dfrac{{217}}{{252}}}}{{\dfrac{{27}}{{36}} - \dfrac{{11}}{{36}}}}:31 = $$ $$ = \dfrac{{217}}{{252}} \cdot \dfrac{{36}}{{16}}:31 = \dfrac{{217}}{{7 \cdot 16}}:31 = \dfrac{{31}}{{16}} \cdot \dfrac{1}{{31}} = \dfrac{1}{{16}}$$
№ 20 Есептеңіз: ${\dfrac{{12\dfrac{4}{5} \cdot 3\dfrac{3}{4} - 4\dfrac{4}{{11}} \cdot 4,125}}{{2\dfrac{4}{7}:\dfrac{3}{{35}}}}}$
Шешуі: $$={\dfrac{{\dfrac{{64}}{5} \cdot \dfrac{{15}}{4} - \dfrac{{48}}{{11}} \cdot 4\dfrac{1}{8}}}{{\dfrac{{18}}{7} \cdot \dfrac{{35}}{3}}} = \dfrac{{48 - \dfrac{{48}}{{11}} \cdot \dfrac{{33}}{8}}}{{30}} = \dfrac{{48 - 3\dfrac{4}{4} - 4\dfrac{4}{{11}} \cdot 4,125}}{{2\dfrac{4}{7}:\dfrac{3}{{35}}}} = 1}$$
№ 21 ${71 \cdot 72 \cdot 73 \cdot \ldots \cdot 79}$ саны қандай цифрмен аяқталады?
Шешуі: $${72 \cdot 75 = \ldots 0}$$ 0-мен аяқталады.
№ 22 Пропорциядан $x$-ті табыңыз: $\dfrac{{3,2}}{{\dfrac{4}{9}}} = \dfrac{x}{{\dfrac{{216 - 21}}{{90}}}}$
Шешуі: $$x = \dfrac{{\dfrac{{195}}{{90}} \cdot 3,2}}{{\dfrac{4}{9}}} = \dfrac{{\dfrac{{195 \cdot 3,2}}{{10}}}}{4} = \dfrac{{195 \cdot 3,2}}{{40}} = \dfrac{{195 \cdot 0,8}}{{10}} = 19,5 \cdot 0,8 = 15,6$$
№ 23 Пропорциядан $x$-ті табыңыз: $\dfrac{{\dfrac{7}{8}}}{{\dfrac{7}{9}}} = \dfrac{x}{{\dfrac{{316 - 31}}{{90}}}}$
Шешуі: $$x = \dfrac{{\dfrac{7}{8} \cdot \dfrac{{285}}{{90}}}}{{\dfrac{7}{9}}} = \dfrac{1}{8} \cdot \dfrac{{285}}{{10}} = \dfrac{{57}}{{16}} = 3\dfrac{9}{{16}}$$
№ 24 Пропорциядан $x$-ті табыңыз: $\dfrac{{\dfrac{7}{9}}}{{\dfrac{{31 - 3}}{9}}} = \dfrac{{1\dfrac{7}{8}}}{x}$
Шешуі: $$x = \dfrac{{\dfrac{{28}}{9} \cdot \dfrac{{15}}{8}}}{{\dfrac{7}{9}}} = \dfrac{{15}}{2} = 7,5$$
№ 25 Есептеңіз: $\dfrac{{\left( {\dfrac{2}{3} + 0,(3)} \right):0,25}}{{0,12(3):0,0925}}$
Шешуі: $$\dfrac{{\left( {\dfrac{2}{3} + \dfrac{1}{3}} \right):\dfrac{1}{4}}}{{\dfrac{{123 - 12}}{{900}}:\dfrac{{37}}{{400}}}} = \dfrac{4}{{\dfrac{{111}}{{900}} \cdot \dfrac{{400}}{{37}}}} = \dfrac{4}{{\dfrac{4}{3}}} = 3$$
№ 26 $m$ санының $72\% $-ын табыңыз: $m = \dfrac{{\left( {13\dfrac{1}{4} - 2\dfrac{5}{{27}} - 10\dfrac{5}{6}} \right) \cdot 230,04 + 46,75}}{{0,01}}$
Шешуі: $$m = \left( {\left( {13\dfrac{1}{4} - 2\dfrac{5}{{27}} - 10\dfrac{5}{6}} \right) \cdot 230,04 + 46,75} \right) \cdot 100 = $$ $$ = \left( {13\dfrac{1}{4} - 2\dfrac{5}{{27}} - 10\dfrac{5}{6}} \right) \cdot 23004 + 4675 = $$ $$ = 1\dfrac{{27 - 20 - 90}}{{108}} \cdot 23004 + 4675 = \dfrac{{25}}{{108}} \cdot 23004 + 4675 = 25 \cdot 213 + 4675$$ $${ = 5325 + 4675 = 10000}$$ $${m = 10000;\,\,\,m \cdot 72\% = 10000 \cdot \dfrac{{72}}{{100}} = 7200}$$
№ 27 Пропорциядан $x$-ті табыңыз: $\dfrac{{3,6}}{{14 - 15\dfrac{1}{8}:2,2}} = \dfrac{x}{{1,5 + 2\dfrac{2}{3} + 3,75}}$
Шешуі: $$\dfrac{{3,6}}{{14 - \dfrac{{121}}{8} \cdot \dfrac{{10}}{{22}}}} = \dfrac{x}{{\dfrac{3}{2} + \dfrac{8}{3} + 3\dfrac{3}{4}}}$$ $$\dfrac{{\dfrac{{18}}{5}}}{{14 - \dfrac{{55}}{8}}} = \dfrac{x}{{1\dfrac{1}{2} + 2\dfrac{2}{3} + 3\dfrac{3}{4}}} = $$ $$x = \dfrac{{\dfrac{{18}}{5} + \dfrac{{11}}{{12}}}}{{13\dfrac{8}{8} - 6\dfrac{7}{8}}} = \dfrac{{\dfrac{{18}}{5} \cdot \dfrac{{95}}{{12}}}}{{7 - \dfrac{1}{8}}} = \dfrac{{\dfrac{{19 \cdot 3}}{{\dfrac{2}{{57}}}}}}{{\dfrac{5}{8}}} = \dfrac{{157}}{2} \cdot \dfrac{8}{{57}} = 4$$
№ 28 $3,6\% $-ы $\dfrac{{3 + 4,2:0,1}}{{\left( {1:0,3 - 2\dfrac{1}{3}} \right) \cdot 0,3125}}$ өрнегінің мәніне тең санды табыңыз.
Шешуі: $$\dfrac{{3 + 42}}{{\left( {\dfrac{{10}}{3} - \dfrac{7}{3}} \right) \cdot \dfrac{5}{{16}}}} = \dfrac{{45}}{{\dfrac{5}{{16}}}} = 45 \cdot \dfrac{{16}}{5} = 144$$ $$144:3,6\% = 144 \cdot \dfrac{{1000}}{{36}} = 4000$$
№ 29\( \text{ЕҮ ОБ} \left( {38;b} \right) = 4,\quad \text{ЕК ОЕ} \left( {38;b} \right) = 1216\). $b$-ны табыңыз.
Шешуі: $$38 = 2 \cdot 19;\,\,\,\,b = 2 \cdot \dfrac{b}{2}$$ $$19 \cdot 2 \cdot \dfrac{b}{2} = 1216,$$ $$b = 1216:19 = 64$$
№ 30 ${\text{ЕҮ ОБ}}\left( {68;b} \right) = 4,\,\,\,{\text{ЕК ОЕ}}\left( {68;b} \right) = 1292$. $b$-ны табыңыз.
Шешуі: $$68 = 4 \cdot 17;\,\,\,\,b = 4 \cdot \dfrac{b}{4}$$ $$17 \cdot 4 \cdot \dfrac{b}{4} = 1292,$$ $$b = 1292:17 = 76$$