Упр.1158 ГДЗ Никольский Потапов 6 класс (Математика)

Задача

а) 2/7 :8+5:0,7-3/4 :21;
б) 3:4 1/5+5,4:7,2-2/7 :0,8;
в) 4,5•2/3-1 5/7 :1,2+3 1/5•3 1/8;
г) 6,25:5/3-2,5:1,5+7 1/2-8 1/3.

Подробный ответ

а) $$\frac{2}{7}:8+5:0{,}7-\frac{3}{4}:21$$

$$\frac{2}{7}:8=\frac{2}{7}\cdot\frac{1}{8}=\frac{1}{28}$$
$$5:0{,}7=5:\frac{7}{10}=5\cdot\frac{10}{7}=\frac{50}{7}$$
$$\frac{3}{4}:21=\frac{3}{4}\cdot\frac{1}{21}=\frac{1}{28}$$
$$\frac{1}{28}+\frac{50}{7}-\frac{1}{28}=\frac{50}{7}=7\frac{1}{7}$$

б) $$3:4\frac{1}{5}+5{,}4:7{,}2-\frac{2}{7}:0{,}8$$

$$4\frac{1}{5}=\frac{21}{5},\quad 5{,}4=\frac{54}{10},\quad 7{,}2=\frac{72}{10},\quad 0{,}8=\frac{8}{10}$$
$$3:4\frac{1}{5}=3:\frac{21}{5}=3\cdot\frac{5}{21}=\frac{5}{7}$$
$$5{,}4:7{,}2=\frac{54}{10}:\frac{72}{10}=\frac{54}{72}=\frac{3}{4}$$
$$\frac{2}{7}:0{,}8=\frac{2}{7}:\frac{8}{10}=\frac{2}{7}\cdot\frac{10}{8}=\frac{5}{14}$$
$$\frac{5}{7}+\frac{3}{4}-\frac{5}{14}=\frac{20}{28}+\frac{21}{28}-\frac{10}{28}=\frac{31}{28}=1\frac{3}{28}$$

в) $$4{,}5\cdot\frac{2}{3}-1\frac{5}{7}:1{,}2+3\frac{1}{5}\cdot3\frac{1}{8}$$

$$4{,}5\cdot\frac{2}{3}=\frac{9}{2}\cdot\frac{2}{3}=3$$
$$1\frac{5}{7}:1{,}2=\frac{12}{7}:\frac{12}{10}=\frac{12}{7}\cdot\frac{10}{12}=\frac{10}{7}$$
$$3\frac{1}{5}\cdot3\frac{1}{8}=\frac{16}{5}\cdot\frac{25}{8}=10$$
$$3-\frac{10}{7}+10=13-\frac{10}{7}=11\frac{4}{7}$$

г) $$6{,}25:\frac{5}{3}-2{,}5:1{,}5+7\frac{1}{2}-8\frac{1}{3}$$

$$6{,}25:\frac{5}{3}=\frac{625}{100}:\frac{5}{3}=\frac{25}{4}\cdot\frac{3}{5}=\frac{15}{4}$$
$$2{,}5:1{,}5=\frac{25}{10}:\frac{15}{10}=\frac{25}{15}=\frac{5}{3}$$
$$7\frac{1}{2}-8\frac{1}{3}=\frac{15}{2}-\frac{25}{3}=\frac{45-50}{6}=-\frac{5}{6}$$
$$\frac{15}{4}-\frac{5}{3}-\frac{5}{6}=\frac{45}{12}-\frac{20}{12}-\frac{10}{12}=\frac{15}{12}=\frac{5}{4}=1\frac{1}{4}$$