Примени распределительное свойство умножения и выполни умножение, записав результаты.

Решаю примеры из твоего задания. **Задание 1** a) $\left(1 + \frac{1}{2}\right) \cdot 6 = 1 \cdot 6 + \frac{1}{2} \cdot 6 = 6 + 3 = 9$ б) $\left(10 - \frac{1}{3}\right) \cdot 3 = 10 \cdot 3 - \frac{1}{3} \cdot 3 = 30 - 1 = 29$ в) $\left(\frac{1}{5} + \frac{1}{3}\right) \cdot 15 = \frac{1}{5} \cdot 15 + \frac{1}{3} \cdot 15 = 3 + 5 = 8$ г) $\left(\frac{7}{8} - \frac{1}{6}\right) \cdot 24 = \frac{7}{8} \cdot 24 - \frac{1}{6} \cdot 24 = 21 - 4 = 17$ д) $(3 + 9) \cdot \frac{1}{3} = 3 \cdot \frac{1}{3} + 9 \cdot \frac{1}{3} = 1 + 3 = 4$ e) $\left(7 - \frac{3}{4}\right) \cdot \frac{1}{3} = 7 \cdot \frac{1}{3} - \frac{3}{4} \cdot \frac{1}{3} = \frac{7}{3} - \frac{1}{4} = \frac{28 - 3}{12} = \frac{25}{12} = 2\frac{1}{12}$ ж) $\left(1 + 2\right) \cdot \frac{7}{9} = 1 \cdot \frac{7}{9} + 2 \cdot \frac{7}{9} = \frac{7}{9} + \frac{14}{9} = \frac{21}{9} = \frac{7}{3} = 2\frac{1}{3}$ **Задание 2** a) $7\frac{1}{4} \cdot 8 = \frac{29}{4} \cdot 8 = 29 \cdot 2 = 58$ б) $5\frac{2}{3} \cdot 6 = \frac{17}{3} \cdot 6 = 17 \cdot 2 = 34$ в) $4 \cdot 1\frac{1}{2} = 4 \cdot \frac{3}{2} = 2 \cdot 3 = 6$ г) $70 \cdot 2\frac{1}{7} = 70 \cdot \frac{15}{7} = 10 \cdot 15 = 150$ д) $35\frac{2}{5} \cdot 5 = \frac{177}{5} \cdot 5 = 177$ e) $9 \cdot 1\frac{1}{18} = 9 \cdot \frac{19}{18} = \frac{19}{2} = 9\frac{1}{2}$ ж) $2\frac{1}{3} \cdot 2 = \frac{7}{3} \cdot 2 = \frac{14}{3} = 4\frac{2}{3}$ з) $18\frac{1}{4} \cdot 9 = \frac{73}{4} \cdot 9 = \frac{657}{4} = 164\frac{1}{4}$ и) $12\frac{1}{5} \cdot \frac{1}{12} = \frac{61}{5} \cdot \frac{1}{12} = \frac{61}{60}$ к) $80\frac{1}{5} \cdot \frac{1}{20} = \frac{401}{5} \cdot \frac{1}{20} = \frac{401}{100} = 4\frac{1}{100}$ л) $16\frac{1}{8} = \frac{129}{8}$ м) $32\frac{1}{9} \cdot \frac{1}{8} = \frac{289}{9} \cdot \frac{1}{8} = \frac{289}{72}$ **Задание 4** a) $\frac{11}{13}x + \frac{2}{13}x = \frac{11+2}{13}x = \frac{13}{13}x = x$ б) $\frac{7}{8}a - \frac{9}{16}a = \frac{14}{16}a - \frac{9}{16}a = \frac{14-9}{16}a = \frac{5}{16}a$ в) $5\frac{2}{3}b - 2b = \frac{17}{3}b - \frac{6}{3}b = \frac{17-6}{3}b = \frac{11}{3}b = 3\frac{2}{3}b$ г) $\frac{7}{8}y - 2\frac{1}{2}y = \frac{7}{8}y - \frac{5}{2}y = \frac{7}{8}y - \frac{20}{8}y = -\frac{13}{8}y$ д) $9\frac{1}{2}x - \frac{1}{4} \cdot (2x - 1\frac{1}{2}x) = \frac{19}{2}x - \frac{1}{4} \cdot (2x - \frac{3}{2}x) = \frac{19}{2}x - \frac{1}{4} \cdot (\frac{4}{2}x - \frac{3}{2}x) = \frac{19}{2}x - \frac{1}{4} \cdot \frac{1}{2}x = \frac{19}{2}x - \frac{1}{8}x = \frac{76}{8}x - \frac{1}{8}x = \frac{75}{8}x$ e) $3\frac{2}{5}x - \frac{3}{4} \cdot (2x - 1\frac{1}{5}x) = \frac{17}{5}x - \frac{3}{4} \cdot (2x - \frac{6}{5}x) = \frac{17}{5}x - \frac{3}{4} \cdot (\frac{10}{5}x - \frac{6}{5}x) = \frac{17}{5}x - \frac{3}{4} \cdot \frac{4}{5}x = \frac{17}{5}x - \frac{3}{5}x = \frac{14}{5}x$ ж) $3\frac{7}{15}x - \frac{1}{2} \cdot (2\frac{1}{2}x - 1\frac{3}{15}x) = \frac{52}{15}x - \frac{1}{2} \cdot (\frac{5}{2}x - \frac{18}{15}x) = \frac{52}{15}x - \frac{1}{2} \cdot (\frac{75}{30}x - \frac{36}{30}x) = \frac{52}{15}x - \frac{1}{2} \cdot \frac{39}{30}x = \frac{52}{15}x - \frac{39}{60}x = \frac{208}{60}x - \frac{39}{60}x = \frac{169}{60}x$ з) $4\frac{7}{32}x - \frac{3}{4} \cdot (3\frac{1}{2}x - 1\frac{7}{32}x) = \frac{135}{32}x - \frac{3}{4} \cdot (\frac{7}{2}x - \frac{39}{32}x) = \frac{135}{32}x - \frac{3}{4} \cdot (\frac{112}{32}x - \frac{39}{32}x) = \frac{135}{32}x - \frac{3}{4} \cdot \frac{73}{32}x = \frac{135}{32}x - \frac{219}{128}x = \frac{540}{128}x - \frac{219}{128}x = \frac{321}{128}x$ **Задание 5** a) $\left(7\frac{1}{4} + 3\frac{2}{3}\right) \cdot 6 = \left(\frac{29}{4} + \frac{11}{3}\right) \cdot 6 = \left(\frac{87}{12} + \frac{44}{12}\right) \cdot 6 = \frac{131}{12} \cdot 6 = \frac{131}{2} = 65\frac{1}{2}$ б) $\left(9 - 1\frac{1}{7}\right) \cdot 7 = \left(9 - \frac{8}{7}\right) \cdot 7 = 9 \cdot 7 - \frac{8}{7} \cdot 7 = 63 - 8 = 55$ в) $\left(6 + 1\frac{1}{2}\right) \cdot 30 = \left(6 + \frac{3}{2}\right) \cdot 30 = 6 \cdot 30 + \frac{3}{2} \cdot 30 = 180 + 45 = 225$ г) $7\frac{3}{11} \cdot \frac{2}{5} + 7\frac{3}{11} \cdot \frac{7}{5} = 7\frac{3}{11} \cdot \left(\frac{2}{5} + \frac{7}{5}\right) = 7\frac{3}{11} \cdot \frac{9}{5} = \frac{80}{11} \cdot \frac{9}{5} = \frac{16}{11} \cdot 9 = \frac{144}{11}$ д) $5\frac{3}{4} \cdot \frac{5}{7} + 3\frac{5}{7} \cdot 1\frac{1}{4} = \frac{23}{4} \cdot \frac{5}{7} + \frac{26}{7} \cdot \frac{5}{4} = \frac{115}{28} + \frac{130}{28} = \frac{245}{28} = \frac{35}{4}$ e) $8\frac{3}{7} \cdot 6 - 1\frac{1}{8} \cdot \frac{3}{5} = \frac{59}{7} \cdot 6 - \frac{9}{8} \cdot \frac{3}{5} = \frac{354}{7} - \frac{27}{40} = \frac{14160}{280} - \frac{189}{280} = \frac{13971}{280}$ ж) $15\frac{3}{8} \cdot 4 - 4 \cdot 15\frac{3}{8} = 0$ з) $10\frac{5}{11} \cdot 4 + 10\frac{5}{11} \cdot 6 = 10\frac{5}{11} \cdot (4+6) = 10\frac{5}{11} \cdot 10 = \frac{115}{11} \cdot 10 = \frac{1150}{11}