2.193 Выполните действие: a) 1/5 + 1/7; б) 3 + 2/5; г) 8/9 - 2/5; д) 12 + 1/6; e) 3 - 4/15; ж) 19/21 - 11/15; з) 5/42 + 10/63; и) 11/21 + 2/26; к) 24/5 - 7/60;

а) $$ \frac{1}{5} + \frac{1}{7} = \frac{7}{35} + \frac{5}{35} = \frac{7+5}{35} = \frac{12}{35} $$

Ответ: $$ \frac{12}{35} $$

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б) $$ 3 + \frac{2}{5} = \frac{3 \cdot 5}{5} + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{15+2}{5} = \frac{17}{5} = 3\frac{2}{5} $$

Ответ: $$ 3\frac{2}{5} $$

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г) $$ \frac{8}{9} - \frac{2}{5} = \frac{8 \cdot 5}{45} - \frac{2 \cdot 9}{45} = \frac{40}{45} - \frac{18}{45} = \frac{40-18}{45} = \frac{22}{45} $$

Ответ: $$ \frac{22}{45} $$

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д) $$ 12 + \frac{1}{6} = \frac{12 \cdot 6}{6} + \frac{1}{6} = \frac{72}{6} + \frac{1}{6} = \frac{72+1}{6} = \frac{73}{6} = 12 \frac{1}{6} $$

Ответ: $$ 12 \frac{1}{6} $$

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е) $$ 3 - \frac{4}{15} = \frac{3 \cdot 15}{15} - \frac{4}{15} = \frac{45}{15} - \frac{4}{15} = \frac{45-4}{15} = \frac{41}{15} = 2\frac{11}{15} $$

Ответ: $$ 2\frac{11}{15} $$

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ж) $$ \frac{19}{21} - \frac{11}{15} = \frac{19 \cdot 5}{105} - \frac{11 \cdot 7}{105} = \frac{95}{105} - \frac{77}{105} = \frac{95-77}{105} = \frac{18}{105} = \frac{6}{35} $$

Ответ: $$ \frac{6}{35} $$

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з) $$ \frac{5}{42} + \frac{10}{63} = \frac{5 \cdot 3}{126} + \frac{10 \cdot 2}{126} = \frac{15}{126} + \frac{20}{126} = \frac{15+20}{126} = \frac{35}{126} = \frac{5}{18} $$

Ответ: $$ \frac{5}{18} $$

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и) $$ \frac{11}{21} + \frac{2}{26} = \frac{11 \cdot 26}{546} + \frac{2 \cdot 21}{546} = \frac{286}{546} + \frac{42}{546} = \frac{286+42}{546} = \frac{328}{546} = \frac{164}{273} $$

Ответ: $$ \frac{164}{273} $$

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к) $$ \frac{24}{5} - \frac{7}{60} = \frac{24 \cdot 12}{60} - \frac{7}{60} = \frac{288}{60} - \frac{7}{60} = \frac{288-7}{60} = \frac{281}{60} = 4 \frac{41}{60} $$

Ответ: $$ 4 \frac{41}{60} $$