Упр.1347 ГДЗ Мерзляк Полонский 6 класс (Математика)
1) (3*1/4 + 0,25 — 1*5/24): (2*3/4- 4*1/2 — 0,75) : (-4*7/12);
2) -24,6 : (-2,35 + 0,7 : 2*1/3) — 15,36;
3) (5*5/28 — 5*1/3 * 1,25 — 1*16/21): (-1,5);
4) (-3*1/3 * 1,9 + 19,5 : 4*1/3) : (0,16 — 62/75);
5) (-2*2/11 * 4,125 + 1,6 * 3*3/4)/(9-5*5/6 * 2*4/7);
6) (-2*7/24 : 1*5/6 -1,6 * (-0,3))/(-9,5 : (5*7/10 — 4*12/35));
7) (-0,4 * (-6,3 : 3,15 + 5/6*0,9)/ (-18 — 2/7 *(-9));
8) (-13,6 + 5,1) * 1*3/17 + (2*7/23 — 1*45/46) : 1*7/23.
1) $$\left(3\frac{1}{4}+0{,}25-1\frac{5}{24}\right):\left(2\frac{3}{4}-4\frac{1}{2}-0{,}75\right):\left(-4\frac{7}{12}\right)$$
$$3\frac{1}{4}+0{,}25-1\frac{5}{24}=3\frac{1}{4}+\frac{1}{4}-1\frac{5}{24}=3\frac{1}{2}-1\frac{5}{24}=2\frac{7}{24}$$
$$2\frac{3}{4}-4\frac{1}{2}-0{,}75=2\frac{3}{4}-4\frac{2}{4}-\frac{3}{4}=-2\frac{1}{2}$$
$$2\frac{7}{24}:\left(-2\frac{1}{2}\right):\left(-4\frac{7}{12}\right)=\frac{55}{24}:\frac{5}{2}:\frac{55}{12}=\frac{55}{24}\cdot\frac{2}{5}\cdot\frac{12}{55}=\frac{1}{5}=0{,}2$$
2) $$-24{,}6:\left(-2{,}35+0{,}7:2\frac{1}{3}\right)-15{,}36$$
$$0{,}7:2\frac{1}{3}=0{,}7:\frac{7}{3}=\frac{7}{10}\cdot\frac{3}{7}=0{,}3$$
$$-2{,}35+0{,}3=-2{,}05$$
$$-24{,}6:(-2{,}05)=12$$
$$12-15{,}36=-3{,}36$$
3) $$\left(5\frac{5}{28}-5\frac{1}{3}\cdot1{,}25-1\frac{16}{21}\right):(-1{,}5)$$
$$5\frac{1}{3}\cdot1{,}25=\frac{16}{3}\cdot\frac{5}{4}=\frac{20}{3}=6\frac{2}{3}$$
$$5\frac{5}{28}-6\frac{2}{3}-1\frac{16}{21}=5\frac{15}{84}-6\frac{56}{84}-1\frac{64}{84}=-3\frac{1}{4}$$
$$-3\frac{1}{4}:(-1{,}5)=\frac{13}{4}:\frac{3}{2}=\frac{13}{4}\cdot\frac{2}{3}=\frac{13}{6}=2\frac{1}{6}$$
4) $$\left(-3\frac{1}{3}\cdot1{,}9+19{,}5:4\frac{1}{3}\right):\left(0{,}16-\frac{62}{75}\right)$$
$$-3\frac{1}{3}\cdot1{,}9=-\frac{10}{3}\cdot\frac{19}{10}=-\frac{19}{3}=-6\frac{1}{3}$$
$$19{,}5:4\frac{1}{3}=\frac{39}{2}:\frac{13}{3}=\frac{39}{2}\cdot\frac{3}{13}=\frac{9}{2}=4\frac{1}{2}$$
$$-6\frac{1}{3}+4\frac{1}{2}=-1\frac{5}{6}$$
$$0{,}16-\frac{62}{75}=\frac{4}{25}-\frac{62}{75}=\frac{12}{75}-\frac{62}{75}=-\frac{50}{75}=-\frac{2}{3}$$
$$-1\frac{5}{6}:\left(-\frac{2}{3}\right)=\frac{11}{6}\cdot\frac{3}{2}=\frac{11}{4}=2\frac{3}{4}$$
5) $$\frac{-2\frac{2}{11}\cdot4{,}125+1{,}6\cdot3\frac{3}{4}}{9-5\frac{5}{6}\cdot2\frac{4}{7}}$$
$$-2\frac{2}{11}\cdot4{,}125=-\frac{24}{11}\cdot\frac{4125}{1000}=-\frac{24}{11}\cdot\frac{33}{8}=-9$$
$$1{,}6\cdot3\frac{3}{4}=\frac{16}{10}\cdot\frac{15}{4}=6$$
$$-9+6=-3$$
$$5\frac{5}{6}\cdot2\frac{4}{7}=\frac{35}{6}\cdot\frac{18}{7}=15$$
$$9-15=-6$$
$$\frac{-3}{-6}=\frac{1}{2}=0{,}5$$
6) $$\frac{-2\frac{7}{24}:1\frac{5}{6}-1{,}6\cdot(-0{,}3)}{-9{,}5:\left(5\frac{7}{10}-4\frac{12}{35}\right)}$$
$$-2\frac{7}{24}:1\frac{5}{6}=-\frac{55}{24}:\frac{11}{6}=-\frac{55}{24}\cdot\frac{6}{11}=-\frac{5}{4}=-1{,}25$$
$$1{,}6\cdot(-0{,}3)=-0{,}48$$
$$-1{,}25-(-0{,}48)=-1{,}25+0{,}48=-0{,}77$$
$$5\frac{7}{10}-4\frac{12}{35}=\frac{49}{10}-\frac{172}{35}=\frac{343}{70}-\frac{344}{70}=-\frac{1}{70}$$
$$-9{,}5:\left(-\frac{1}{70}\right)=-\frac{19}{2}:\left(-\frac{1}{70}\right)=665$$
$$-0{,}77:665=-0{,}00116\ldots$$
7) $$\frac{-0{,}4\cdot\left(-6{,}3:3{,}15+\frac{5}{6}\cdot0{,}9\right)}{-48-\frac{2}{7}\cdot(-91)}$$
$$-6{,}3:3{,}15=-2$$
$$\frac{5}{6}\cdot0{,}9=\frac{5}{6}\cdot\frac{9}{10}=\frac{3}{4}$$
$$-2+\frac{3}{4}=-1\frac{1}{4}$$
$$-0{,}4\cdot\left(-1\frac{1}{4}\right)=\frac{2}{5}\cdot\frac{5}{4}=\frac{1}{2}$$
$$\frac{2}{7}\cdot(-91)=-26$$
$$-48-(-26)=-22$$
$$\frac{1}{2}:(-22)=-\frac{1}{44}$$
8) $$(-13{,}6+5{,}1)\cdot1\frac{3}{17}+\left(2\frac{7}{23}-1\frac{45}{46}\right):1\frac{7}{23}$$
$$-13{,}6+5{,}1=-8{,}5$$
$$-8{,}5\cdot1\frac{3}{17}=-\frac{17}{2}\cdot\frac{20}{17}=-10$$
$$2\frac{7}{23}-1\frac{45}{46}=2\frac{14}{46}-1\frac{45}{46}=1\frac{15}{46}=\frac{61}{46}$$
$$1\frac{7}{23}=\frac{30}{23}$$
$$\frac{61}{46}:\frac{30}{23}=\frac{61}{46}\cdot\frac{23}{30}=\frac{61}{60}$$
$$-10+\frac{61}{60}=-\frac{539}{60}=-8\frac{59}{60}$$
Ответ
1) $$0{,}2$$; 2) $$-3{,}36$$; 3) $$2\frac{1}{6}$$; 4) $$2\frac{3}{4}$$; 5) $$0{,}5$$; 6) $$-0{,}00116\ldots$$; 7) $$-\frac{1}{44}$$; 8) $$-8\frac{59}{60}$$.
