Реши примеры на применение распределительного свойства умножения, выполни умножение и упрости выражения.

Привет! Давай помогу с математикой. **1. Применение распределительного свойства умножения** а) $(10 - \frac{1}{3}) \cdot 3 = 10 \cdot 3 - \frac{1}{3} \cdot 3 = 30 - 1 = 29$ б) $(\frac{1}{5} + \frac{1}{3}) \cdot 15 = \frac{1}{5} \cdot 15 + \frac{1}{3} \cdot 15 = 3 + 5 = 8$ в) $(\frac{7}{8} - \frac{1}{6}) \cdot 24 = \frac{7}{8} \cdot 24 - \frac{1}{6} \cdot 24 = 21 - 4 = 17$ г) $(3 + 9) \cdot \frac{1}{3} = 3 \cdot \frac{1}{3} + 9 \cdot \frac{1}{3} = 1 + 3 = 4$ д) $(7 - \frac{3}{4}) \cdot \frac{1}{3} = 7 \cdot \frac{1}{3} - \frac{3}{4} \cdot \frac{1}{3} = \frac{7}{3} - \frac{1}{4} = \frac{28}{12} - \frac{3}{12} = \frac{25}{12} = 2\frac{1}{12}$ е) $(\frac{1}{7} + 2) \cdot \frac{7}{9} = \frac{1}{7} \cdot \frac{7}{9} + 2 \cdot \frac{7}{9} = \frac{1}{9} + \frac{14}{9} = \frac{15}{9} = \frac{5}{3} = 1\frac{2}{3}$ **2. Выполните умножение** а) $7\frac{1}{4} \cdot 8 = \frac{29}{4} \cdot 8 = 29 \cdot 2 = 58$ б) $35\frac{2}{5} \cdot 5 = \frac{177}{5} \cdot 5 = 177$ в) $12\frac{1}{5} \cdot \frac{1}{12} = \frac{61}{5} \cdot \frac{1}{12} = \frac{61}{60} = 1\frac{1}{60}$ $5\frac{2}{3} \cdot 6 = \frac{17}{3} \cdot 6 = 17 \cdot 2 = 34$ $9 \cdot 1\frac{1}{18} = 9 \cdot \frac{19}{18} = \frac{19}{2} = 9\frac{1}{2}$ $80 \cdot \frac{1}{5} \cdot \frac{1}{20} = 80 \cdot \frac{1}{100} = \frac{80}{100} = \frac{4}{5}$ $4 \cdot 1\frac{1}{2} = 4 \cdot \frac{3}{2} = 2 \cdot 3 = 6$ $2\frac{1}{3} \cdot 2 = \frac{7}{3} \cdot 2 = \frac{14}{3} = 4\frac{2}{3}$ $16\frac{1}{8} = \frac{129}{8} = 16.125$ $70 \cdot 2\frac{1}{7} = 70 \cdot \frac{15}{7} = 10 \cdot 15 = 150$ $18\frac{1}{4} \cdot \frac{1}{9} = \frac{73}{4} \cdot \frac{1}{9} = \frac{73}{36} = 2\frac{1}{36}$ $32\frac{1}{9} \cdot \frac{1}{8} = \frac{289}{9} \cdot \frac{1}{8} = \frac{289}{72} = 4\frac{1}{72}$ **4. Упростите выражения** а) $\frac{11}{13}x + \frac{2}{13}x = \frac{11+2}{13}x = \frac{13}{13}x = x$ б) $\frac{7}{9}a - \frac{2}{16}a = (\frac{7}{9} - \frac{2}{16})a = (\frac{7 \cdot 16 - 2 \cdot 9}{9 \cdot 16})a = (\frac{112 - 18}{144})a = \frac{94}{144}a = \frac{47}{72}a$ в) $5\frac{2}{3}b - \frac{2}{3}b = (5\frac{2}{3} - \frac{2}{3})b = 5b$ г) $\frac{7}{8}y - 2\frac{1}{8}y = (\frac{7}{8} - \frac{17}{8})y = -\frac{10}{8}y = -\frac{5}{4}y = -1\frac{1}{4}y$ д) $2\frac{1}{2}x - (1\frac{1}{4}x - \frac{1}{2}x) = \frac{5}{2}x - (\frac{5}{4}x - \frac{1}{2}x) = \frac{5}{2}x - \frac{5}{4}x + \frac{1}{2}x = \frac{10}{4}x - \frac{5}{4}x + \frac{2}{4}x = \frac{7}{4}x = 1\frac{3}{4}x$ е) $3 - x - (2\frac{1}{2}x - 1\frac{1}{5}x) = 3 - x - (\frac{5}{2}x - \frac{6}{5}x) = 3 - x - \frac{5}{2}x + \frac{6}{5}x = 3 - \frac{10}{10}x - \frac{25}{10}x + \frac{12}{10}x = 3 - \frac{23}{10}x = 3 - 2\frac{3}{10}x$ ж) $3\frac{7}{15}x - (2\frac{1}{2}x - 1\frac{8}{15}x) = \frac{52}{15}x - (\frac{5}{2}x - \frac{23}{15}x) = \frac{52}{15}x - \frac{5}{2}x + \frac{23}{15}x = \frac{104}{30}x - \frac{75}{30}x + \frac{46}{30}x = \frac{75}{30}x = \frac{5}{2}x = 2\frac{1}{2}x$ з) $4\frac{7}{32}x - (3\frac{3}{4}x - 1\frac{7}{32}x) = \frac{135}{32}x - (\frac{15}{4}x - \frac{39}{32}x) = \frac{135}{32}x - \frac{15}{4}x + \frac{39}{32}x = \frac{135}{32}x - \frac{120}{32}x + \frac{39}{32}x = \frac{54}{32}x = \frac{27}{16}x = 1\frac{11}{16}x$ **5. Найдите значение выражения** а) $(7\frac{1}{2} + 3\frac{2}{3}) \cdot 6 = (\frac{15}{2} + \frac{11}{3}) \cdot 6 = (\frac{45}{6} + \frac{22}{6}) \cdot 6 = \frac{67}{6} \cdot 6 = 67$ б) $(9 - 1\frac{1}{7}) \cdot 7 = (9 - \frac{8}{7}) \cdot 7 = 9 \cdot 7 - \frac{8}{7} \cdot 7 = 63 - 8 = 55$ в) $(6 + 1\frac{1}{2}) \cdot 30 = (6 + \frac{3}{2}) \cdot 30 = 6 \cdot 30 + \frac{3}{2} \cdot 30 = 180 + 45 = 225$ г) $7\frac{3}{11} \cdot \frac{3}{5} + 7\frac{7}{11} \cdot \frac{3}{5} = \frac{3}{5} \cdot (7\frac{3}{11} + 7\frac{7}{11}) = \frac{3}{5} \cdot (14\frac{10}{11}) = \frac{3}{5} \cdot \frac{164}{11} = \frac{492}{55} = 8\frac{52}{55}$ д) $5\frac{3}{7} \cdot \frac{5}{4} + 3\frac{5}{7} \cdot \frac{1}{4} = \frac{5}{4} \cdot \frac{38}{7} + \frac{1}{4} \cdot \frac{26}{7} = \frac{190}{28} + \frac{26}{28} = \frac{216}{28} = \frac{54}{7} = 7\frac{5}{7}$ е) $8\frac{3}{4} \cdot 6 - 1\frac{1}{8} \cdot \frac{3}{5} = \frac{35}{4} \cdot 6 - \frac{9}{8} \cdot \frac{3}{5} = \frac{210}{4} - \frac{27}{40} = \frac{2100}{40} - \frac{27}{40} = \frac{2073}{40} = 51\frac{33}{40}$ 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) = \frac{115}{11} \cdot 10 = \frac{1150}{11} = 104\frac{6}{11}