Задание 9. Выполните действие: 1) 6/25 * 5/12 2) 15/22 * 11/20 3) 7/4 * 12/35 4) 18/5 * 40/9 5) 2/15 * 3/8 6) 6/11 * 15/8 * 22/5 7) 3/10 * 35/36 * 24/7 8) 20/3 * 9/28 * 14/75 9) 30/19 * 13/100 * 20/39 10) 16/5 * 15/14 * 63/24 11) (3/a) * (2a/15) 12) (9c/8) * (56/3c) 13) (1/13b) * (26/3) 14) (4k/9) * (27/20) 15) (15b/8) * (2/35b) 16) (3x/2) * (6/x^2) 17) (y^2/5) * (2/y) 18) (32a^3/9) * (18/12a^2) 19) (10/x^3) * (6x/25) * (x/9) 20) (3/a) * (a^2/12) * (8/a^3) 21) 1/(a-b) * 1/(a+b) 22) 1/(2(c-3)) * 1/(c-3) 23) (3+c)/4 * 9/(2(3+c)) 24) (5(x+y))/63 * 7/(3(x+y)) 25) ((b-2)^2)/a * 8/(b-2) 26) (4c^3)/(x-y) * ((x-y)^2)/(40c) 27) (3b/a) * 2/a 28) 5x/4 * 8 29) (12a^2/5) * 15a 30) (9/16m) * 48m^2

Выполним указанные действия: 1) $$rac{6}{25} \cdot \frac{5}{12} = \frac{6 \cdot 5}{25 \cdot 12} = \frac{30}{300} = \frac{1}{10}$$ 2) $$rac{15}{22} \cdot \frac{11}{20} = \frac{15 \cdot 11}{22 \cdot 20} = \frac{165}{440} = \frac{3 \cdot 5 \cdot 11}{4 \cdot 5 \cdot 11 \cdot 2} = \frac{3}{8}$$ 3) $$rac{7}{4} \cdot \frac{12}{35} = \frac{7 \cdot 12}{4 \cdot 35} = \frac{84}{140} = \frac{3 \cdot 4 \cdot 7}{5 \cdot 4 \cdot 7} = \frac{3}{5}$$ 4) $$rac{18}{5} \cdot \frac{40}{9} = \frac{18 \cdot 40}{5 \cdot 9} = \frac{720}{45} = \frac{2 \cdot 9 \cdot 5 \cdot 8}{5 \cdot 9} = 16$$ 5) $$rac{2}{15} \cdot \frac{3}{8} = \frac{2 \cdot 3}{15 \cdot 8} = \frac{6}{120} = \frac{1}{20}$$ 6) $$rac{6}{11} \cdot \frac{15}{8} \cdot \frac{22}{5} = \frac{6 \cdot 15 \cdot 22}{11 \cdot 8 \cdot 5} = \frac{1980}{440} = \frac{2 \cdot 3 \cdot 3 \cdot 5 \cdot 2 \cdot 11}{2 \cdot 2 \cdot 2 \cdot 11 \cdot 5} = \frac{9}{2} = 4.5$$ 7) $$rac{3}{10} \cdot \frac{35}{36} \cdot \frac{24}{7} = \frac{3 \cdot 35 \cdot 24}{10 \cdot 36 \cdot 7} = \frac{2520}{2520} = 1$$ 8) $$rac{20}{3} \cdot \frac{9}{28} \cdot \frac{14}{75} = \frac{20 \cdot 9 \cdot 14}{3 \cdot 28 \cdot 75} = \frac{2520}{6300} = \frac{2 \cdot 2 \cdot 5 \cdot 3 \cdot 3 \cdot 2 \cdot 7}{3 \cdot 4 \cdot 7 \cdot 3 \cdot 5 \cdot 5} = \frac{2}{5} $$ 9) $$rac{30}{19} \cdot \frac{13}{100} \cdot \frac{20}{39} = \frac{30 \cdot 13 \cdot 20}{19 \cdot 100 \cdot 39} = \frac{7800}{74100} = \frac{2 \cdot 3 \cdot 5 \cdot 2 \cdot 5 \cdot 13}{19 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 3 \cdot 13} = \frac{2}{19}$$ 10) $$rac{16}{5} \cdot \frac{15}{14} \cdot \frac{63}{24} = \frac{16 \cdot 15 \cdot 63}{5 \cdot 14 \cdot 24} = \frac{15120}{1680} = 9$$ 11) $$rac{3}{a} \cdot \frac{2a}{15} = \frac{3 \cdot 2a}{a \cdot 15} = \frac{6a}{15a} = \frac{2}{5}$$ 12) $$rac{9c}{8} \cdot \frac{56}{3c} = \frac{9c \cdot 56}{8 \cdot 3c} = \frac{504c}{24c} = 21$$ 13) $$rac{1}{13b} \cdot \frac{26}{3} = \frac{1 \cdot 26}{13b \cdot 3} = \frac{26}{39b} = \frac{2 \cdot 13}{3 \cdot 13 \cdot b} = \frac{2}{3b}$$ 14) $$rac{4k}{9} \cdot \frac{27}{20} = \frac{4k \cdot 27}{9 \cdot 20} = \frac{108k}{180} = \frac{3k}{5}$$ 15) $$rac{15b}{8} \cdot \frac{2}{35b} = \frac{15b \cdot 2}{8 \cdot 35b} = \frac{30b}{280b} = \frac{3}{28}$$ 16) $$rac{3x}{2} \cdot \frac{6}{x^2} = \frac{3x \cdot 6}{2 \cdot x^2} = \frac{18x}{2x^2} = \frac{9}{x}$$ 17) $$rac{y^2}{5} \cdot \frac{2}{y} = \frac{y^2 \cdot 2}{5 \cdot y} = \frac{2y^2}{5y} = \frac{2y}{5}$$ 18) $$rac{32a^3}{9} \cdot \frac{18}{12a^2} = \frac{32a^3 \cdot 18}{9 \cdot 12a^2} = \frac{576a^3}{108a^2} = \frac{16a}{3}$$ 19) $$rac{10}{x^3} \cdot \frac{6x}{25} \cdot \frac{x}{9} = \frac{10 \cdot 6x \cdot x}{x^3 \cdot 25 \cdot 9} = \frac{60x^2}{225x^3} = \frac{4}{15x}$$ 20) $$rac{3}{a} \cdot \frac{a^2}{12} \cdot \frac{8}{a^3} = \frac{3 \cdot a^2 \cdot 8}{a \cdot 12 \cdot a^3} = \frac{24a^2}{12a^4} = \frac{2}{a^2}$$ 21) $$rac{1}{a-b} \cdot \frac{1}{a+b} = \frac{1}{(a-b)(a+b)} = \frac{1}{a^2 - b^2}$$ 22) $$rac{1}{2(c-3)} \cdot \frac{1}{c-3} = \frac{1}{2(c-3)(c-3)} = \frac{1}{2(c-3)^2}$$ 23) $$rac{3+c}{4} \cdot \frac{9}{2(3+c)} = \frac{(3+c) \cdot 9}{4 \cdot 2(3+c)} = \frac{9}{8}$$ 24) $$rac{5(x+y)}{63} \cdot \frac{7}{3(x+y)} = \frac{5(x+y) \cdot 7}{63 \cdot 3(x+y)} = \frac{35(x+y)}{189(x+y)} = \frac{5}{27}$$ 25) $$rac{(b-2)^2}{a} \cdot \frac{8}{b-2} = \frac{(b-2)^2 \cdot 8}{a \cdot (b-2)} = \frac{8(b-2)}{a}$$ 26) $$rac{4c^3}{x-y} \cdot \frac{(x-y)^2}{40c} = \frac{4c^3 \cdot (x-y)^2}{(x-y) \cdot 40c} = \frac{c^2 (x-y)}{10}$$ 27) $$rac{3b}{a} \cdot \frac{2}{a} = \frac{3b \cdot 2}{a \cdot a} = \frac{6b}{a^2}$$ 28) $$rac{5x}{4} \cdot 8 = \frac{5x \cdot 8}{4} = \frac{40x}{4} = 10x$$ 29) $$rac{12a^2}{5} \cdot 15a = \frac{12a^2 \cdot 15a}{5} = \frac{180a^3}{5} = 36a^3$$ 30) $$rac{9}{16m} \cdot 48m^2 = \frac{9 \cdot 48m^2}{16m} = \frac{432m^2}{16m} = 27m$$