Вопрос:

2. Вычислите: 1) $$8\frac{3}{8}+9\frac{4}{9}$$; 2) $$12\frac{7}{12}-8\frac{3}{8}$$; 3) $$2\frac{5}{8}+1\frac{3}{10}$$; 4) $$6\frac{6}{10}-4\frac{5}{12}$$; 5) $$3\frac{2}{5}\div 3\frac{9}{10}$$; 6) $$5\frac{3}{5}\div 1\frac{9}{26}$$; 7) $$\frac{24}{35}\div \frac{6}{7}$$.

Смотреть решения всех заданий с листа

Ответ:

1) $$8\frac{3}{8}+9\frac{4}{9} = 8 + 9 + \frac{3}{8} + \frac{4}{9} = 17 + \frac{3\cdot 9 + 4 \cdot 8}{72} = 17 + \frac{27 + 32}{72} = 17 + \frac{59}{72} = 17\frac{59}{72}$$

2) $$12\frac{7}{12}-8\frac{3}{8} = 12 - 8 + \frac{7}{12} - \frac{3}{8} = 4 + \frac{7\cdot 2 - 3 \cdot 3}{24} = 4 + \frac{14 - 9}{24} = 4 + \frac{5}{24} = 4\frac{5}{24}$$

3) $$2\frac{5}{8}+1\frac{3}{10} = 2 + 1 + \frac{5}{8} + \frac{3}{10} = 3 + \frac{5\cdot 5 + 3 \cdot 4}{40} = 3 + \frac{25 + 12}{40} = 3 + \frac{37}{40} = 3\frac{37}{40}$$

4) $$6\frac{6}{10}-4\frac{5}{12} = 6 - 4 + \frac{6}{10} - \frac{5}{12} = 2 + \frac{6\cdot 6 - 5 \cdot 5}{60} = 2 + \frac{36 - 25}{60} = 2 + \frac{11}{60} = 2\frac{11}{60}$$

5) $$3\frac{2}{5}\div 3\frac{9}{10} = \frac{3\cdot 5 + 2}{5} \div \frac{3\cdot 10 + 9}{10} = \frac{17}{5} \div \frac{39}{10} = \frac{17}{5} \cdot \frac{10}{39} = \frac{17 \cdot 2}{39} = \frac{34}{39}$$

6) $$5\frac{3}{5}\div 1\frac{9}{26} = \frac{5\cdot 5 + 3}{5} \div \frac{1 \cdot 26 + 9}{26} = \frac{28}{5} \div \frac{35}{26} = \frac{28}{5} \cdot \frac{26}{35} = \frac{4}{5} \cdot \frac{26}{5} = \frac{4 \cdot 26}{5 \cdot 5} = \frac{104}{25} = 4\frac{4}{25}$$

7) $$\frac{24}{35}\div \frac{6}{7} = \frac{24}{35} \cdot \frac{7}{6} = \frac{4}{5} \cdot \frac{1}{1} = \frac{4}{5}$$

Ответ: 1) $$17\frac{59}{72}$$; 2) $$4\frac{5}{24}$$; 3) $$3\frac{37}{40}$$; 4) $$2\frac{11}{60}$$; 5) $$\frac{34}{39}$$; 6) $$4\frac{4}{25}$$; 7) $$\frac{4}{5}$$.

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