Упр.1015 ГДЗ Никольский Потапов 5 класс (Математика)

1. Вычислите: а) $$2\frac{13}{30}-\left(1\frac{1}{10}+\frac{1}{5}\right)$$; б) $$2\frac{8}{15}-\left(1\frac{3}{10}+\frac{2}{5}\right)$$; в) $$4\frac{14}{45}-1\frac{7}{15}-\frac{3}{5}$$; г) $$4\frac{11}{30}-2\frac{9}{20}-\frac{1}{10}$$.

а) Приведём дроби в скобках к общему знаменателю:

$$2\frac{13}{30}-\left(1\frac{1}{10}+\frac{1}{5}\right) =2\frac{13}{30}-\left(1\frac{1}{10}+\frac{2}{10}\right) =2\frac{13}{30}-1\frac{3}{10}$$

$$2\frac{13}{30}-1\frac{3}{10} =2\frac{13}{30}-1\frac{9}{30} =1\frac{4}{30} =1\frac{2}{15}$$

б)

$$2\frac{8}{15}-\left(1\frac{3}{10}+\frac{2}{5}\right) =2\frac{8}{15}-\left(1\frac{3}{10}+\frac{4}{10}\right) =2\frac{8}{15}-1\frac{7}{10}$$

$$2\frac{8}{15}-1\frac{7}{10} =2\frac{16}{30}-1\frac{21}{30} =1\frac{46}{30}-1\frac{21}{30} =\frac{25}{30} =\frac{5}{6}$$

в)

$$4\frac{14}{45}-1\frac{7}{15}-\frac{3}{5} =4\frac{14}{45}-1\frac{21}{45}-\frac{27}{45}$$

$$4\frac{14}{45}-1\frac{21}{45} =3\frac{59}{45}-\frac{27}{45} =2\frac{38}{45}-\frac{27}{45} =2\frac{11}{45}$$

г)

$$4\frac{11}{30}-2\frac{9}{20}-\frac{1}{10} =4\frac{22}{60}-2\frac{27}{60}-\frac{6}{60}$$

$$4\frac{22}{60}-2\frac{27}{60} =3\frac{82}{60}-2\frac{27}{60} =1\frac{55}{60}$$

$$1\frac{55}{60}-\frac{6}{60} =1\frac{49}{60}$$

Ответ

а) $$1\frac{2}{15}$$; б) $$\frac{5}{6}$$; в) $$2\frac{11}{45}$$; г) $$1\frac{49}{60}$$.