2.303 Выполните умножение: a) 3 3 4 5 б) 1 7 в) 1 15 29 г) 8 23 1 1 9 20 34 59 1 3

a) $$3 \frac{3}{4} \cdot 1 \frac{1}{5} = \frac{3 \cdot 4 + 3}{4} \cdot \frac{1 \cdot 5 + 1}{5} = \frac{12 + 3}{4} \cdot \frac{5 + 1}{5} = \frac{15}{4} \cdot \frac{6}{5} = \frac{15 \cdot 6}{4 \cdot 5} = \frac{3 \cdot 5 \cdot 6}{4 \cdot 5} = \frac{3 \cdot 6}{4} = \frac{18}{4} = \frac{9 \cdot 2}{2 \cdot 2} = \frac{9}{2} = 4 \frac{1}{2} $$

б) $$1 \frac{1}{7} \cdot 3 \frac{3}{5} = \frac{1 \cdot 7 + 1}{7} \cdot \frac{3 \cdot 5 + 3}{5} = \frac{7+1}{7} \cdot \frac{15+3}{5} = \frac{8}{7} \cdot \frac{18}{5} = \frac{8 \cdot 18}{7 \cdot 5} = \frac{144}{35} = 4 \frac{4}{35}$$

в) $$1 \frac{15}{29} \cdot 1 \frac{9}{20} = \frac{1 \cdot 29 + 15}{29} \cdot \frac{1 \cdot 20 + 9}{20} = \frac{29 + 15}{29} \cdot \frac{20 + 9}{20} = \frac{44}{29} \cdot \frac{29}{20} = \frac{44 \cdot 29}{29 \cdot 20} = \frac{44}{20} = \frac{11 \cdot 4}{5 \cdot 4} = \frac{11}{5} = 2 \frac{1}{5} $$

г) $$8 \frac{23}{34} \cdot \frac{34}{59} = \frac{8 \cdot 34 + 23}{34} \cdot \frac{34}{59} = \frac{272 + 23}{34} \cdot \frac{34}{59} = \frac{295}{34} \cdot \frac{34}{59} = \frac{295 \cdot 34}{34 \cdot 59} = \frac{295}{59} = \frac{5 \cdot 59}{59} = 5$$

Ответ: а) $$4 \frac{1}{2}$$, б) $$4 \frac{4}{35}$$, в) $$2 \frac{1}{5}$$, г) $$5$$