Упр.133 Рабочая тетрадь №1 ГДЗ Мерзляк Полонский 6 класс (Математика)

Выполните действия.

1. 1) $$6\frac{4}{15}-2\frac{1}{9}+1\frac{3}{10}$$; 2) $$7\frac{2}{3}-5\frac{5}{36}+3\frac{3}{8}$$; 3) $$10\frac{9}{22}-3\frac{7}{11}-4\frac{8}{33}$$; 4) $$12\frac{17}{42}-\left(3\frac{1}{4}+4\frac{1}{6}\right)$$; 5) $$15-\left(6\frac{4}{35}-2\frac{3}{14}\right)$$.

1) Приведём дробные части к общему знаменателю:

$$6\frac{4}{15}-2\frac{1}{9}+1\frac{3}{10} =6\frac{24}{90}-2\frac{10}{90}+1\frac{27}{90}$$
$$=4\frac{14}{90}+1\frac{27}{90} =5\frac{41}{90}$$

2)
$$7\frac{2}{3}-5\frac{5}{36}+3\frac{3}{8} =7\frac{48}{72}-5\frac{10}{72}+3\frac{27}{72}$$
$$=2\frac{38}{72}+3\frac{27}{72} =5\frac{65}{72}$$

3)
$$10\frac{9}{22}-3\frac{7}{11}-4\frac{8}{33} =10\frac{27}{66}-3\frac{42}{66}-4\frac{16}{66}$$
$$=9\frac{93}{66}-3\frac{42}{66}-4\frac{16}{66} =6\frac{51}{66}-4\frac{16}{66} =2\frac{35}{66}$$

4)
$$12\frac{17}{42}-\left(3\frac{1}{4}+4\frac{1}{6}\right) =12\frac{17}{42}-\left(3\frac{3}{12}+4\frac{2}{12}\right)$$
$$=12\frac{17}{42}-7\frac{5}{12} =12\frac{34}{84}-7\frac{35}{84} =4\frac{83}{84}$$

5)
$$15-\left(6\frac{4}{35}-2\frac{3}{14}\right) =15-6\frac{4}{35}+2\frac{3}{14}$$
$$=8\frac{31}{35}+2\frac{3}{14} =8\frac{62}{70}+2\frac{15}{70} =10\frac{77}{70} =11\frac{1}{10}$$

Ответ: 1) $$5\frac{41}{90}$$; 2) $$5\frac{65}{72}$$; 3) $$2\frac{35}{66}$$; 4) $$4\frac{83}{84}$$; 5) $$11\frac{1}{10}$$.