Упр.760 ГДЗ Ткачёва 6 класс (Математика)

Задача

1) 7/12 · (0,16 · 4,25 — 2,575 : 2,5) · 6 11/14;
2) 2/9 · (-3,6) + 5/12 : (1/3 · 2,5 — 7/8);
3) 1 1/4 — 3,075 : 1,5 + 5/6 · (0,04 — 3 4/25);
4) -8 + (2,87 : 1,4 — 2,505) · (-5/9) : (-0,46).

Подробный ответ

1) $$\frac{7}{12}\cdot(0{,}16\cdot 4{,}25-2{,}575:2{,}5)\cdot 6\frac{11}{14}$$

$$0{,}16\cdot 4{,}25=0{,}68$$

$$2{,}575:2{,}5=1{,}03$$

$$0{,}68-1{,}03=-0{,}35$$

$$\frac{7}{12}\cdot(-0{,}35)=\frac{7}{12}\cdot\left(-\frac{35}{100}\right)=-\frac{49}{240}$$

$$6\frac{11}{14}=\frac{95}{14}$$

$$-\frac{49}{240}\cdot\frac{95}{14}=-\frac{7\cdot 19}{48\cdot 2}=-\frac{133}{96}=-1\frac{37}{96}$$

2) $$\frac{2}{9}\cdot(-3{,}6)+\frac{5}{12}:\left(\frac{1}{3}\cdot 2{,}5-\frac{7}{8}\right)$$

$$\frac{1}{3}\cdot 2{,}5=\frac{1}{3}\cdot\frac{25}{10}=\frac{5}{6}$$

$$\frac{5}{6}-\frac{7}{8}=\frac{20}{24}-\frac{21}{24}=-\frac{1}{24}$$

$$\frac{2}{9}\cdot(-3{,}6)=\frac{2}{9}\cdot\left(-\frac{36}{10}\right)=-\frac{4}{5}$$

$$\frac{5}{12}:\left(-\frac{1}{24}\right)=\frac{5}{12}\cdot(-24)=-10$$

$$-\frac{4}{5}+(-10)=-10\frac{4}{5}=-10{,}8$$

3) $$1\frac{1}{4}-3{,}075:1{,}5+\frac{5}{6}\cdot\left(0{,}04-3\frac{4}{25}\right)$$

$$0{,}04-3\frac{4}{25}=0{,}04-3{,}16=-3{,}12$$

$$3{,}075:1{,}5=2{,}05$$

$$\frac{5}{6}\cdot(-3{,}12)=\frac{5}{6}\cdot\left(-\frac{312}{100}\right)=-2{,}6$$

$$1\frac{1}{4}-2{,}05=1{,}25-2{,}05=-0{,}8$$

$$-0{,}8+(-2{,}6)=-3{,}4$$

4) $$-8+\left(2{,}87:1{,}4-2{,}505\right)\cdot\left(-\frac{5}{9}\right):(-0{,}46)$$

$$2{,}87:1{,}4=2{,}05$$

$$2{,}05-2{,}505=-0{,}455$$

$$-0{,}455\cdot\left(-\frac{5}{9}\right)=\frac{455}{1000}\cdot\frac{5}{9}=\frac{91}{360}$$

$$\frac{91}{360}:(-0{,}46)=\frac{91}{360}:\left(-\frac{46}{100}\right)=-\frac{455}{828}$$

$$-8+\left(-\frac{455}{828}\right)=-8\frac{455}{828}$$