Проверочная работа № 3 1 Найдите разность: a)4/5-3/4; б)3/10-2/7; в)2/3-1/7; г)5/9-1/3; д)5/6-5/12; е)2/13-0. 2 Найдите значение выражения: a)3/14+(2/7+1/2); б)11/56+(6/7-3/8); в)(5/8+1/6)-7/24; г)15/36-(1/3-1/12).

Ответ:

Задание 1

1. а) \[\frac{4}{5} - \frac{3}{4} = \frac{4 \cdot 4}{5 \cdot 4} - \frac{3 \cdot 5}{4 \cdot 5} = \frac{16}{20} - \frac{15}{20} = \frac{16 - 15}{20} = \frac{1}{20}\]
2. б) \[\frac{3}{10} - \frac{2}{7} = \frac{3 \cdot 7}{10 \cdot 7} - \frac{2 \cdot 10}{7 \cdot 10} = \frac{21}{70} - \frac{20}{70} = \frac{21 - 20}{70} = \frac{1}{70}\]
3. в) \[\frac{2}{3} - \frac{1}{7} = \frac{2 \cdot 7}{3 \cdot 7} - \frac{1 \cdot 3}{7 \cdot 3} = \frac{14}{21} - \frac{3}{21} = \frac{14 - 3}{21} = \frac{11}{21}\]
4. г) \[\frac{5}{9} - \frac{1}{3} = \frac{5}{9} - \frac{1 \cdot 3}{3 \cdot 3} = \frac{5}{9} - \frac{3}{9} = \frac{5 - 3}{9} = \frac{2}{9}\]
5. д) \[\frac{5}{6} - \frac{5}{12} = \frac{5 \cdot 2}{6 \cdot 2} - \frac{5}{12} = \frac{10}{12} - \frac{5}{12} = \frac{10 - 5}{12} = \frac{5}{12}\]
6. е) \[\frac{2}{13} - 0 = \frac{2}{13}\]

Задание 2

1. a) \[\frac{3}{14} + (\frac{2}{7} + \frac{1}{2}) = \frac{3}{14} + (\frac{2 \cdot 2}{7 \cdot 2} + \frac{1 \cdot 7}{2 \cdot 7}) = \frac{3}{14} + (\frac{4}{14} + \frac{7}{14}) = \frac{3}{14} + \frac{11}{14} = \frac{3 + 11}{14} = \frac{14}{14} = 1\]
2. б) \[\frac{11}{56} + (\frac{6}{7} - \frac{3}{8}) = \frac{11}{56} + (\frac{6 \cdot 8}{7 \cdot 8} - \frac{3 \cdot 7}{8 \cdot 7}) = \frac{11}{56} + (\frac{48}{56} - \frac{21}{56}) = \frac{11}{56} + \frac{27}{56} = \frac{11 + 27}{56} = \frac{38}{56} = \frac{19}{28}\]
3. в) \[ (\frac{5}{8} + \frac{1}{6}) - \frac{7}{24} = (\frac{5 \cdot 3}{8 \cdot 3} + \frac{1 \cdot 4}{6 \cdot 4}) - \frac{7}{24} = (\frac{15}{24} + \frac{4}{24}) - \frac{7}{24} = \frac{19}{24} - \frac{7}{24} = \frac{19 - 7}{24} = \frac{12}{24} = \frac{1}{2}\]
4. г) \[\frac{15}{36} - (\frac{1}{3} - \frac{1}{12}) = \frac{15}{36} - (\frac{1 \cdot 4}{3 \cdot 4} - \frac{1}{12}) = \frac{15}{36} - (\frac{4}{12} - \frac{1}{12}) = \frac{15}{36} - \frac{3}{12} = \frac{15}{36} - \frac{3 \cdot 3}{12 \cdot 3} = \frac{15}{36} - \frac{9}{36} = \frac{15 - 9}{36} = \frac{6}{36} = \frac{1}{6}\]

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