Упр.527 ГДЗ Муравин 6 класс (Математика)
Вычислите:
- 1) $$1{,}8\div\left(-1\frac{2}{3}\right)+\left(-15\frac{2}{3}\right)\div1\frac{1}{3}$$; 2) $$3\frac{3}{4}\div0{,}03+4{,}52\div\left(-4\frac{5}{27}\right)$$; 3) $$\left(-3\frac{1}{3}\right)\div\left(-2{,}4\right)+7{,}654-\left(\frac{1}{18}+5{,}654\right)$$; 4) $$\left(1{,}545\div1{,}5-1\right)\cdot\left(-2\frac{2}{3}\right)-0{,}5\cdot\frac{4}{15}$$.
1) $$1{,}8:(-1\tfrac{2}{3})+(-15\tfrac{2}{3}):1\tfrac{1}{3}$$
Преобразуем смешанные числа в неправильные дроби:
$$1{,}8=\frac{18}{10},\quad -1\tfrac{2}{3}=-\frac{5}{3},\quad -15\tfrac{2}{3}=-\frac{47}{3},\quad 1\tfrac{1}{3}=\frac{4}{3}$$
Тогда
$$\frac{18}{10}:\left(-\frac{5}{3}\right)+\left(-\frac{47}{3}\right):\frac{4}{3}$$
$$=\frac{18}{10}\cdot\left(-\frac{3}{5}\right)+\left(-\frac{47}{3}\right)\cdot\frac{3}{4}$$
$$=-\frac{27}{25}-\frac{47}{4}$$
Приведём к общему знаменателю:
$$-\frac{27\cdot 4}{100}-\frac{47\cdot 25}{100}=-\frac{108+1175}{100}=-\frac{1283}{100}=-12{,}83$$
2) $$3\tfrac{3}{4}:0{,}03+4{,}52:(-4\tfrac{5}{27})$$
$$3\tfrac{3}{4}=\frac{15}{4},\quad 0{,}03=\frac{3}{100},\quad 4{,}52=\frac{113}{25},\quad -4\tfrac{5}{27}=-\frac{113}{27}$$
Тогда
$$\frac{15}{4}:\frac{3}{100}+\frac{113}{25}:\left(-\frac{113}{27}\right)$$
$$=\frac{15}{4}\cdot\frac{100}{3}-\frac{113}{25}\cdot\frac{27}{113}$$
$$=125-\frac{27}{25}=125-1\tfrac{2}{25}=123\tfrac{23}{25}$$
3) $$(-3\tfrac{1}{3}):(-2{,}4)+7{,}654-\left(\frac{1}{18}+5{,}654\right)$$
$$-3\tfrac{1}{3}=-\frac{10}{3},\quad -2{,}4=-\frac{12}{5}$$
Тогда
$$\left(-\frac{10}{3}\right):\left(-\frac{12}{5}\right)+7{,}654-\frac{1}{18}-5{,}654$$
$$=\frac{10}{3}\cdot\frac{5}{12}+2-\frac{1}{18}$$
$$=\frac{25}{18}+2-\frac{1}{18}=\frac{24}{18}+2=\frac{4}{3}+2=3\tfrac{1}{3}$$
4) $$(1{,}545:1{,}5-1)\cdot\left(-2\tfrac{2}{3}\right)-0{,}5\cdot\frac{4}{15}$$
$$1{,}545:1{,}5=1{,}03,\quad -2\tfrac{2}{3}=-\frac{8}{3},\quad 0{,}5=\frac{1}{2}$$
Тогда
$$\left(1{,}03-1\right)\cdot\left(-\frac{8}{3}\right)-\frac{1}{2}\cdot\frac{4}{15}$$
$$0{,}03\cdot\left(-\frac{8}{3}\right)-\frac{2}{15}$$
$$=\frac{3}{100}\cdot\left(-\frac{8}{3}\right)-\frac{2}{15}=-\frac{8}{100}-\frac{2}{15}=-\frac{2}{25}-\frac{2}{15}$$
$$=-\frac{6}{75}-\frac{10}{75}=-\frac{16}{75}$$
Ответ
1) $$-12{,}83$$; 2) $$123\tfrac{23}{25}$$; 3) $$3\tfrac{1}{3}$$; 4) $$-\frac{16}{75}$$.
