Выполни действия с дробями.

Выполняю действия с дробями: a) $$\frac{4}{5} \times \frac{2}{5} = \frac{4 \times 2}{5 \times 5} = \frac{8}{25}$$ b) $$\frac{2}{5} \times \frac{1}{7} = \frac{2 \times 1}{5 \times 7} = \frac{2}{35}$$ c) $$\frac{5}{9} \times \frac{31}{35} = \frac{5 \times 31}{9 \times 35} = \frac{155}{315}$$. Можно сократить дробь на 5: $$\frac{155:5}{315:5} = \frac{31}{63}$$ d) $$\frac{1}{8} \times \frac{4}{15} = \frac{1 \times 4}{8 \times 15} = \frac{4}{120}$$. Можно сократить дробь на 4: $$\frac{4:4}{120:4} = \frac{1}{30}$$ a) $$3 \frac{1}{3} + 2 \frac{2}{5} = \frac{3 \times 3 + 1}{3} + \frac{2 \times 5 + 2}{5} = \frac{10}{3} + \frac{12}{5} = \frac{10 \times 5 + 12 \times 3}{15} = \frac{50 + 36}{15} = \frac{86}{15} = 5 \frac{11}{15}$$ b) $$4 \frac{5}{6} + 5 \frac{3}{4} = \frac{4 \times 6 + 5}{6} + \frac{5 \times 4 + 3}{4} = \frac{29}{6} + \frac{23}{4} = \frac{29 \times 2 + 23 \times 3}{12} = \frac{58 + 69}{12} = \frac{127}{12} = 10 \frac{7}{12}$$ c) $$1 \frac{1}{24} + 5 \frac{5}{8} = \frac{1 \times 24 + 1}{24} + \frac{5 \times 8 + 5}{8} = \frac{25}{24} + \frac{45}{8} = \frac{25 + 45 \times 3}{24} = \frac{25 + 135}{24} = \frac{160}{24} = \frac{20}{3} = 6 \frac{2}{3}$$ d) $$3 \frac{2}{9} + 1 \frac{5}{12} = \frac{3 \times 9 + 2}{9} + \frac{1 \times 12 + 5}{12} = \frac{29}{9} + \frac{17}{12} = \frac{29 \times 4 + 17 \times 3}{36} = \frac{116 + 51}{36} = \frac{167}{36} = 4 \frac{23}{36}$$ b) $$\frac{1}{5} + 3 \frac{3}{5} = \frac{1}{5} + \frac{3 \times 5 + 3}{5} = \frac{1}{5} + \frac{18}{5} = \frac{1 + 18}{5} = \frac{19}{5} = 3 \frac{4}{5}$$ c) $$2 \frac{1}{6} + 1 \frac{5}{12} = \frac{2 \times 6 + 1}{6} + \frac{1 \times 12 + 5}{12} = \frac{13}{6} + \frac{17}{12} = \frac{13 \times 2 + 17}{12} = \frac{26 + 17}{12} = \frac{43}{12} = 3 \frac{7}{12}$$ d) $$3 \frac{5}{7} + 1 \frac{3}{14} = \frac{3 \times 7 + 5}{7} + \frac{1 \times 14 + 3}{14} = \frac{26}{7} + \frac{17}{14} = \frac{26 \times 2 + 17}{14} = \frac{52 + 17}{14} = \frac{69}{14} = 4 \frac{13}{14}$$