Упр.1 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)
Найдите значение выражения:
- $$9\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot 4\frac{1}{2}-10\frac{4}{5}\cdot 4\frac{7}{12}$$;
- $$1\frac{1}{22}\cdot 3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot\frac{7}{23}\right)\cdot\frac{3}{5}$$;
- $$\left(3\frac{1}{4}+2\frac{1}{6}\right):2\frac{3}{5}-\frac{2}{3}:\frac{4}{9}$$;
- $$\left(5{,}07:\frac{1}{20}-23{,}4:\frac{13}{50}\right)\cdot\frac{1}{4}+0{,}074\cdot\frac{1}{2}$$;
- $$\left(-31{,}7:63{,}4-23{,}4:(-11{,}7)\right)\cdot(-2{,}4)$$;
- $$\left(-1{,}2+4{,}32:(-1{,}8)\right):(-0{,}001)\cdot(-0{,}3)$$;
- $$\left(\frac{7}{16}-\left(-\frac{5}{24}\right)\right):\left(-1\frac{15}{16}\right)$$;
- $$\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$$;
- $$-2\frac{2}{3}+2\frac{1}{3}\cdot\left(-15\frac{3}{7}-(-4{,}8):\frac{4}{15}\right)$$.
$$9\frac{1}{4}\cdot 8-3\frac{2}{3}\cdot 4\frac{1}{2}-10\frac{4}{5}\cdot 4\frac{7}{12}$$
$$=\frac{37}{4}\cdot 8-\frac{11}{3}\cdot \frac{9}{2}-\frac{54}{5}\cdot \frac{55}{12}$$
$$=74-\frac{33}{2}-\frac{99}{2}=74-16\frac{1}{2}-49\frac{1}{2}=8.$$
$$1\frac{1}{22}\cdot 3\frac{2}{3}-\left(2\frac{5}{6}+3\frac{5}{6}\cdot \frac{7}{23}\right)\cdot \frac{3}{5}$$
$$=\frac{23}{22}\cdot \frac{11}{3}-\left(\frac{17}{6}+\frac{23}{6}\cdot \frac{7}{23}\right)\cdot \frac{3}{5}$$
$$=\frac{23}{2\cdot 3}-\left(\frac{17}{6}+\frac{7}{6}\right)\cdot \frac{3}{5}$$
$$=\frac{23}{6}-4\cdot \frac{3}{5}=\frac{23}{6}-\frac{12}{5}=\frac{115-72}{30}=\frac{43}{30}=1\frac{13}{30}.$$
$$\left(3\frac{1}{4}+2\frac{1}{6}\right):2\frac{3}{5}-\frac{2}{3}:\frac{4}{9}$$
$$=\left(\frac{13}{4}+\frac{13}{6}\right):\frac{13}{5}-\frac{2}{3}\cdot \frac{9}{4}$$
$$=\frac{65}{12}\cdot \frac{5}{13}-\frac{18}{12}=\frac{25}{12}-\frac{18}{12}=\frac{7}{12}.$$
$$\left(5{,}07:\frac{1}{20}-23{,}4:\frac{13}{50}\right)\cdot \frac{1}{4}+0{,}074\cdot \frac{1}{2}$$
$$=\left(\frac{507}{100}\cdot 20-\frac{234}{10}\cdot \frac{50}{13}\right)\cdot \frac{1}{4}+\frac{74}{1000}\cdot \frac{1}{2}$$
$$=\left(101\frac{2}{5}-90\right)\cdot \frac{1}{4}+0{,}037$$
$$=11\frac{2}{5}\cdot \frac{1}{4}+0{,}037=\frac{57}{20}\cdot \frac{1}{4}+0{,}037=2{,}85+0{,}037=2{,}887.$$
$$\left(-31{,}7:63{,}4-23{,}4:(-11{,}7)\right)\cdot (-2{,}4)$$
$$=\left(-0{,}5+2\right)\cdot (-2{,}4)=1{,}5\cdot (-2{,}4)=-3{,}6.$$
$$\left(-1{,}2+4{,}32:(-1{,}8)\right):(-0{,}001)\cdot (-0{,}3)$$
$$=\left(-1{,}2-2{,}4\right):(-0{,}001)\cdot (-0{,}3)$$
$$=-3{,}6:(-0{,}001)\cdot (-0{,}3)=3600\cdot (-0{,}3)=-1080.$$
$$\left(\frac{7}{16}-\left(-\frac{5}{24}\right)\right):\left(-1\frac{15}{16}\right)$$
$$=\left(\frac{21}{48}+\frac{10}{48}\right):\left(-\frac{31}{16}\right)=\frac{31}{48}\cdot \left(-\frac{16}{31}\right)=-\frac{1}{3}.$$
$$\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$$
$$=\left(\frac{40}{84}-\frac{75}{84}\right):\left(-\frac{55}{70}+\frac{48}{70}\right)$$
$$=-\frac{35}{84}:\left(-\frac{7}{70}\right)=-\frac{5}{12}:\left(-\frac{1}{10}\right)=\frac{5}{12}\cdot 10=\frac{25}{6}=4\frac{1}{6}.$$
$$-2\frac{2}{3}+2\frac{1}{3}\cdot \left(-15\frac{3}{7}-(-4{,}8):\frac{4}{15}\right)$$
$$=-2\frac{2}{3}+\frac{7}{3}\cdot \left(-15\frac{3}{7}+4{,}8\cdot \frac{15}{4}\right)$$
$$=-2\frac{2}{3}+\frac{7}{3}\cdot \left(-15\frac{3}{7}+18\right)$$
$$=-2\frac{2}{3}+\frac{7}{3}\cdot 2\frac{4}{7}=-2\frac{2}{3}+\frac{7}{3}\cdot \frac{18}{7}=-2\frac{2}{3}+6=3\frac{1}{3}.$$
