ДКО_Подготовка_Задание 2 «ДРОБИ»_6 класс ПО ВАРИАНТАМ – Обыкновенные дроби Вариант 1. Вычислите: 1. ( 8 - 1 ) ⋅ 5 7 3 4 2. ( 7 - 1 ) ⋅ 4 8 4 5 3. ( 12 - 1 ) ⋅ 4 13 26 3 4. ( 9 + 1 - 3 ) : 5 8 4 16 3 Вариант 2. Вычислите: 1. ( 9 + 1 ) ⋅ 2 10 5 3 3 2 2. ( - ) ⋅ 9 5 15 8 3. ( 3 + 1 ) ⋅ 7 4 8 9 4. ( 11 - 1 + 1 ) : 2 12 3 6 5

Задание 1:

\[\left(\frac{8}{7} - \frac{1}{3}\right) \cdot \frac{5}{4} = \left(\frac{24}{21} - \frac{7}{21}\right) \cdot \frac{5}{4} = \frac{17}{21} \cdot \frac{5}{4} = \frac{17 \cdot 5}{21 \cdot 4} = \frac{85}{84}\]

Задание 2:

\[\left(\frac{7}{8} - \frac{1}{4}\right) \cdot \frac{4}{5} = \left(\frac{7}{8} - \frac{2}{8}\right) \cdot \frac{4}{5} = \frac{5}{8} \cdot \frac{4}{5} = \frac{5 \cdot 4}{8 \cdot 5} = \frac{20}{40} = \frac{1}{2}\]

Задание 3:

\[\left(\frac{12}{13} - \frac{1}{26}\right) \cdot \frac{4}{3} = \left(\frac{24}{26} - \frac{1}{26}\right) \cdot \frac{4}{3} = \frac{23}{26} \cdot \frac{4}{3} = \frac{23 \cdot 4}{26 \cdot 3} = \frac{92}{78} = \frac{46}{39}\]

Задание 4:

\[\left(\frac{9}{8} + \frac{1}{4} - \frac{3}{16}\right) : \frac{5}{3} = \left(\frac{18}{16} + \frac{4}{16} - \frac{3}{16}\right) : \frac{5}{3} = \frac{19}{16} : \frac{5}{3} = \frac{19}{16} \cdot \frac{3}{5} = \frac{19 \cdot 3}{16 \cdot 5} = \frac{57}{80}\]

Задание 1:

\[\left(\frac{9}{10} + \frac{1}{5}\right) \cdot \frac{2}{3} = \left(\frac{9}{10} + \frac{2}{10}\right) \cdot \frac{2}{3} = \frac{11}{10} \cdot \frac{2}{3} = \frac{11 \cdot 2}{10 \cdot 3} = \frac{22}{30} = \frac{11}{15}\]

Задание 2:

\[\left(\frac{3}{5} - \frac{2}{15}\right) \cdot \frac{9}{8} = \left(\frac{9}{15} - \frac{2}{15}\right) \cdot \frac{9}{8} = \frac{7}{15} \cdot \frac{9}{8} = \frac{7 \cdot 9}{15 \cdot 8} = \frac{63}{120} = \frac{21}{40}\]

Задание 3:

\[\left(\frac{3}{4} + \frac{1}{8}\right) \cdot \frac{7}{9} = \left(\frac{6}{8} + \frac{1}{8}\right) \cdot \frac{7}{9} = \frac{7}{8} \cdot \frac{7}{9} = \frac{7 \cdot 7}{8 \cdot 9} = \frac{49}{72}\]

Задание 4:

\[\left(\frac{11}{12} - \frac{1}{3} + \frac{1}{6}\right) : \frac{2}{5} = \left(\frac{11}{12} - \frac{4}{12} + \frac{2}{12}\right) : \frac{2}{5} = \frac{9}{12} : \frac{2}{5} = \frac{3}{4} \cdot \frac{5}{2} = \frac{3 \cdot 5}{4 \cdot 2} = \frac{15}{8}\]