Вопрос:

Найдите сумму и разность чисел.

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Ответ ассистента

2.205 Найдите сумму: а) $4\frac{2}{9} + 3\frac{5}{18} = 4 + \frac{2}{9} + 3 + \frac{5}{18} = 7 + \frac{4}{18} + \frac{5}{18} = 7 + \frac{9}{18} = 7 + \frac{1}{2} = \textbf{7\frac{1}{2}}$ б) $3\frac{5}{12} + 4\frac{7}{9} = 3 + \frac{5}{12} + 4 + \frac{7}{9} = 7 + \frac{15}{36} + \frac{28}{36} = 7 + \frac{43}{36} = 7 + 1\frac{7}{36} = \textbf{8\frac{7}{36}}$ в) $7\frac{11}{12} + 1\frac{3}{8} = 7 + \frac{11}{12} + 1 + \frac{3}{8} = 8 + \frac{22}{24} + \frac{9}{24} = 8 + \frac{31}{24} = 8 + 1\frac{7}{24} = \textbf{9\frac{7}{24}}$ г) $4\frac{3}{8} + 2\frac{4}{11} = 4 + \frac{3}{8} + 2 + \frac{4}{11} = 6 + \frac{33}{88} + \frac{32}{88} = 6 + \frac{65}{88} = \textbf{6\frac{65}{88}}$ д) $6\frac{5}{11} + 5 = \textbf{11\frac{5}{11}}$ е) $7\frac{3}{7} + 5\frac{5}{21} = 7 + \frac{3}{7} + 5 + \frac{5}{21} = 12 + \frac{9}{21} + \frac{5}{21} = 12 + \frac{14}{21} = 12 + \frac{2}{3} = \textbf{12\frac{2}{3}}$ ж) $6 + 4\frac{2}{7} = \textbf{10\frac{2}{7}}$ з) $3\frac{3}{7} + 3\frac{4}{5} = 3 + \frac{3}{7} + 3 + \frac{4}{5} = 6 + \frac{15}{35} + \frac{28}{35} = 6 + \frac{43}{35} = 6 + 1\frac{8}{35} = \textbf{7\frac{8}{35}}$ 2.206 Найдите разность: а) $1 - \frac{4}{5} = \frac{5}{5} - \frac{4}{5} = \textbf{\frac{1}{5}}$ б) $2 - \frac{3}{7} = \frac{14}{7} - \frac{3}{7} = \textbf{1\frac{4}{7}}$ в) $7 - \frac{4}{13} = \frac{91}{13} - \frac{4}{13} = \frac{87}{13} = \textbf{6\frac{9}{13}}$ г) $6 - 1\frac{5}{9} = 6 - (1 + \frac{5}{9}) = 6 - 1 - \frac{5}{9} = 5 - \frac{5}{9} = 4 + 1 - \frac{5}{9} = 4 + \frac{9}{9} - \frac{5}{9} = 4 + \frac{4}{9} = \textbf{4\frac{4}{9}}$ д) $9 - 3\frac{4}{7} = 9 - (3 + \frac{4}{7}) = 9 - 3 - \frac{4}{7} = 6 - \frac{4}{7} = 5 + 1 - \frac{4}{7} = 5 + \frac{7}{7} - \frac{4}{7} = 5 + \frac{3}{7} = \textbf{5\frac{3}{7}}$ е) $5 - 4\frac{2}{11} = 5 - (4 + \frac{2}{11}) = 5 - 4 - \frac{2}{11} = 1 - \frac{2}{11} = \frac{11}{11} - \frac{2}{11} = \textbf{\frac{9}{11}}$ 2.207 Выполните вычитание: а) $5\frac{7}{15} - 3\frac{3}{20} = 5 + \frac{7}{15} - 3 - \frac{3}{20} = (5 - 3) + (\frac{7}{15} - \frac{3}{20}) = 2 + (\frac{28}{60} - \frac{9}{60}) = 2 + \frac{19}{60} = \textbf{2\frac{19}{60}}$ б) $4\frac{7}{12} - \frac{2}{9} = 4 + (\frac{7}{12} - \frac{2}{9}) = 4 + (\frac{21}{36} - \frac{8}{36}) = 4 + \frac{13}{36} = \textbf{4\frac{13}{36}}$ в) $6\frac{5}{7} - \frac{3}{14} = 6 + (\frac{5}{7} - \frac{3}{14}) = 6 + (\frac{10}{14} - \frac{3}{14}) = 6 + \frac{7}{14} = 6 + \frac{1}{2} = \textbf{6\frac{1}{2}}$ г) $7\frac{5}{7} - 4\frac{2}{3} = 7 + \frac{5}{7} - 4 - \frac{2}{3} = (7 - 4) + (\frac{5}{7} - \frac{2}{3}) = 3 + (\frac{15}{21} - \frac{14}{21}) = 3 + \frac{1}{21} = \textbf{3\frac{1}{21}}$ д) $3\frac{2}{3} - 3\frac{4}{11} = 3 + \frac{2}{3} - 3 - \frac{4}{11} = (3 - 3) + (\frac{2}{3} - \frac{4}{11}) = 0 + (\frac{22}{33} - \frac{12}{33}) = \frac{10}{33} = \textbf{\frac{10}{33}}$ е) $7\frac{5}{12} - 3\frac{2}{9} = 7 + \frac{5}{12} - 3 - \frac{2}{9} = (7 - 3) + (\frac{5}{12} - \frac{2}{9}) = 4 + (\frac{15}{36} - \frac{8}{36}) = 4 + \frac{7}{36} = \textbf{4\frac{7}{36}}$

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