Упр.8.49 ГДЗ Дорофеев Шарыгин 5 класс (Математика)

Выполните сложение:

• а) $$2\frac{3}{4}+1\frac{2}{3}$$;
• в) $$\frac{7}{20}+8\frac{3}{4}$$;
• д) $$8\frac{5}{6}+2\frac{3}{8}$$;
• б) $$8\frac{3}{5}+1\frac{9}{10}$$;
• г) $$12\frac{5}{6}+\frac{4}{15}$$;
• е) $$1\frac{4}{5}+3\frac{11}{30}$$.

а) $$2\frac{3}{4}+1\frac{2}{3}=(2+1)+\left(\frac{3}{4}+\frac{2}{3}\right)=3+\left(\frac{9}{12}+\frac{8}{12}\right)=3+\frac{17}{12}=3+1\frac{5}{12}=4\frac{5}{12}.$$

б) $$8\frac{3}{5}+1\frac{9}{10}=(8+1)+\left(\frac{3}{5}+\frac{9}{10}\right)=9+\left(\frac{6}{10}+\frac{9}{10}\right)=9+\frac{15}{10}=9+1\frac{1}{2}=10\frac{1}{2}.$$

в) $$\frac{7}{20}+8\frac{3}{4}=8+\left(\frac{7}{20}+\frac{3}{4}\right)=8+\left(\frac{7}{20}+\frac{15}{20}\right)=8+\frac{22}{20}=8+1\frac{1}{10}=9\frac{1}{10}.$$

г) $$12\frac{5}{6}+\frac{4}{15}=12+\left(\frac{5}{6}+\frac{4}{15}\right)=12+\left(\frac{25}{30}+\frac{8}{30}\right)=12+\frac{33}{30}=12+1\frac{1}{10}=13\frac{1}{10}.$$

д) $$8\frac{5}{6}+2\frac{3}{8}=(8+2)+\left(\frac{5}{6}+\frac{3}{8}\right)=10+\left(\frac{20}{24}+\frac{9}{24}\right)=10+\frac{29}{24}=10+1\frac{5}{24}=11\frac{5}{24}.$$

е) $$1\frac{4}{5}+3\frac{11}{30}=(1+3)+\left(\frac{4}{5}+\frac{11}{30}\right)=4+\left(\frac{24}{30}+\frac{11}{30}\right)=4+\frac{35}{30}=4+1\frac{1}{6}=5\frac{1}{6}.$$

Ответ

а) $$4\frac{5}{12}$$; б) $$10\frac{1}{2}$$; в) $$9\frac{1}{10}$$; г) $$13\frac{1}{10}$$; д) $$11\frac{5}{24}$$; е) $$5\frac{1}{6}$$.