Упр.641 Часть 1 ГДЗ Виленкин Жохов 6 класс (Математика)

Задача

а) 3/4 : 5/6 + 2 1/2 * 2/5 — 1 : 1 1/6;
б) 2 3/4 : (1 1/2 — 2/5) + (3/4 + 5/6) : 3 1/6;
в) (2/15 + 7/12) * 30/43 — 2 : 2 1/2 * 5/32;
г) (3 1/2 : 4 2/3 + 4 2/3 : 3 1/2) * 4 4/5;
д) (11 5/11 — 8 21/22) : 1 2/3;
е) ((1 1/2)3 — 3/4) : 7/8.

Подробный ответ

а) $$\frac34 : \frac56 + 2\frac12 \cdot \frac25 — 1 : 1\frac16$$

$$\frac34 : \frac56 = \frac34 \cdot \frac65 = \frac9{10}$$
$$2\frac12 \cdot \frac25 = \frac52 \cdot \frac25 = 1$$
$$1 : 1\frac16 = 1 : \frac76 = \frac67$$
$$\frac9{10} + 1 — \frac67 = 1\frac9{10} — \frac67 = 1\frac{63}{70} — \frac{60}{70} = 1\frac3{70}$$

б) $$2\frac34 : \left(1\frac12 — \frac25\right) + \left(\frac34 + \frac56\right) : 3\frac16$$

$$1\frac12 — \frac25 = \frac32 — \frac25 = \frac{15}{10} — \frac4{10} = \frac{11}{10}$$
$$2\frac34 : \frac{11}{10} = \frac{11}{4} \cdot \frac{10}{11} = \frac52$$
$$\frac34 + \frac56 = \frac9{12} + \frac{10}{12} = \frac{19}{12}$$
$$3\frac16 = \frac{19}{6}$$
$$\frac{19}{12} : \frac{19}{6} = \frac{19}{12} \cdot \frac6{19} = \frac12$$
$$\frac52 + \frac12 = 3$$

в) $$\left(\frac2{15} + \frac7{12}\right)\cdot \frac{30}{43} — 2 : 2\frac12 \cdot \frac5{32}$$

$$\frac2{15} + \frac7{12} = \frac8{60} + \frac{35}{60} = \frac{43}{60}$$
$$\frac{43}{60}\cdot \frac{30}{43} = \frac12$$
$$2 : 2\frac12 \cdot \frac5{32} = 2 : \frac52 \cdot \frac5{32} = 2 \cdot \frac25 \cdot \frac5{32} = \frac14$$
$$\frac12 — \frac14 = \frac14$$

г) $$\left(3\frac12 : 4\frac23 + 4\frac23 : 3\frac12\right)\cdot 4\frac45$$

$$3\frac12 : 4\frac23 = \frac72 : \frac{14}{3} = \frac72 \cdot \frac3{14} = \frac34$$
$$4\frac23 : 3\frac12 = \frac{14}{3} : \frac72 = \frac{14}{3} \cdot \frac27 = \frac43$$
$$\frac34 + \frac43 = \frac9{12} + \frac{16}{12} = \frac{25}{12}$$
$$4\frac45 = \frac{24}{5}$$
$$\frac{25}{12}\cdot \frac{24}{5} = 10$$

д) $$\left(11\frac5{11} — 8\frac{21}{22}\right) : 1\frac23$$

$$11\frac5{11} = 11\frac{10}{22}$$
$$11\frac{10}{22} — 8\frac{21}{22} = 3 — \frac{11}{22} = 2\frac{11}{22} = 2\frac12$$
$$1\frac23 = \frac53$$
$$2\frac12 : \frac53 = \frac52 \cdot \frac35 = \frac32 = 1\frac12$$

е) $$\left(\left(1\frac12\right)^3 — \frac34\right) : \frac78$$

$$\left(1\frac12\right)^3 = \left(\frac32\right)^3 = \frac{27}{8}$$
$$\frac{27}{8} — \frac34 = \frac{27}{8} — \frac68 = \frac{21}{8}$$
$$\frac{21}{8} : \frac78 = \frac{21}{8}\cdot \frac87 = 3$$