Упр.454 ГДЗ Ткачёва 6 класс (Математика)

Задача

Вычислить:
1) $$1\frac{32}{49}:\left(4\frac{15}{49}-2\frac{13}{14}\right)+\frac{2}{3}\cdot\left(4{,}354-1{,}134:0{,}28\right)+1{,}114$$
2) $$4{,}58-\left(1{,}295+1{,}936:3\frac{1}{5}\right)\cdot1\frac{16}{19}+3\frac{5}{51}:\left(4\frac{5}{34}-3\frac{19}{51}\right)$$

Подробный ответ

1) Вычислим по действиям:

$$1\frac{32}{49} : \left(4\frac{15}{49} — 2\frac{13}{14}\right) + \frac{2}{3}\cdot(4{,}254 — 1{,}134 : 0{,}28) + 1{,}114$$

$$4\frac{15}{49} — 2\frac{13}{14} = 4\frac{30}{98} — 2\frac{91}{98} = 3\frac{128}{98} — 2\frac{91}{98} = 1\frac{37}{98}$$

$$1{,}134 : 0{,}28 = 113{,}4 : 28 = 4{,}05$$

$$4{,}254 — 4{,}05 = 0{,}204$$

$$1\frac{32}{49} : 1\frac{37}{98} = \frac{81}{49} : \frac{135}{98} = \frac{81}{49}\cdot\frac{98}{135} = \frac{3\cdot 2}{1\cdot 5} = \frac{6}{5} = 1{,}2$$

$$\frac{2}{3}\cdot 0{,}204 = 2\cdot 0{,}068 = 0{,}136$$

$$1{,}2 + 0{,}136 + 1{,}114 = 1{,}336 + 1{,}114 = 2{,}45$$

2) Аналогично:

$$4{,}58 — \left(1{,}295 + 1{,}936 : 3\frac{1}{5}\right)\cdot 1\frac{16}{19} + 3\frac{5}{51} : \left(4\frac{5}{34} — 3\frac{19}{51}\right)$$

$$1{,}936 : 3\frac{1}{5} = 1{,}936 : 3{,}2 = 19{,}36 : 32 = 0{,}605$$

$$1{,}295 + 0{,}605 = 1{,}9$$

$$4\frac{5}{34} — 3\frac{19}{51} = 4\frac{15}{102} — 3\frac{38}{102} = 3\frac{117}{102} — 3\frac{38}{102} = \frac{79}{102}$$

$$1{,}9\cdot 1\frac{16}{19} = 1{,}9\cdot \frac{35}{19} = \frac{35}{10}\cdot\frac{35}{19} = 3{,}5$$

$$3\frac{5}{51} : \frac{79}{102} = \frac{158}{51} : \frac{79}{102} = \frac{158}{51}\cdot\frac{102}{79} = 4$$

$$4{,}58 — 3{,}5 + 4 = 1{,}08 + 4 = 5{,}08$$