3. Найдите значение выражений. a)9$$\frac{4}{15}$$+11$$\frac{2}{15}$$; б) 4$$\frac{8}{11}$$+8$$\frac{5}{11}$$; в) 11$$\frac{9}{19}$$-5$$\frac{4}{19}$$; г) 16$$\frac{1}{8}$$-7$$\frac{5}{8}$$; д) $$\frac{7}{12} \cdot \frac{24}{49}$$; e) 3$$\frac{5}{9} \cdot 5$$\frac{1}{4}$$; ж) $$\frac{6}{35}:\frac{18}{25}$$; з) 1$$\frac{7}{8}:2\frac{11}{32}$$

Решение:

a) 9$$\frac{4}{15}$$ + 11$$\frac{2}{15}$$ = (9 + 11) + ($$\frac{4}{15}$$ + $$\frac{2}{15}$$) = 20 + $$\frac{6}{15}$$ = 20$$\frac{6}{15}$$ = 20$$\frac{2}{5}$$

б) 4$$\frac{8}{11}$$ + 8$$\frac{5}{11}$$ = (4 + 8) + ($$\frac{8}{11}$$ + $$\frac{5}{11}$$) = 12 + $$\frac{13}{11}$$ = 12 + 1$$\frac{2}{11}$$ = 13$$\frac{2}{11}$$

в) 11$$\frac{9}{19}$$ - 5$$\frac{4}{19}$$ = (11 - 5) + ($$\frac{9}{19}$$ - $$\frac{4}{19}$$) = 6 + $$\frac{5}{19}$$ = 6$$\frac{5}{19}$$

г) 16$$\frac{1}{8}$$ - 7$$\frac{5}{8}$$ = (16 - 7) + ($$\frac{1}{8}$$ - $$\frac{5}{8}$$) = 9 - $$\frac{4}{8}$$ = 8$$\frac{8}{8}$$ - $$\frac{4}{8}$$ = 8$$\frac{4}{8}$$ = 8$$\frac{1}{2}$$

д) $$\frac{7}{12} \cdot \frac{24}{49}$$ = $$\frac{7 \cdot 24}{12 \cdot 49}$$ = $$\frac{7 \cdot 12 \cdot 2}{12 \cdot 7 \cdot 7}$$ = $$\frac{2}{7}$$

е) 3$$\frac{5}{9} \cdot 5$$\frac{1}{4}$$ = $$\frac{32}{9} \cdot \frac{21}{4}$$ = $$\frac{32 \cdot 21}{9 \cdot 4}$$ = $$\frac{8 \cdot 4 \cdot 7 \cdot 3}{3 \cdot 3 \cdot 4}$$ = $$\frac{8 \cdot 7}{3}$$ = $$\frac{56}{3}$$ = 18$$\frac{2}{3}$$

ж) $$\frac{6}{35}:\frac{18}{25}$$ = $$\frac{6}{35} \cdot \frac{25}{18}$$ = $$\frac{6 \cdot 25}{35 \cdot 18}$$ = $$\frac{6 \cdot 5 \cdot 5}{5 \cdot 7 \cdot 6 \cdot 3}$$ = $$\frac{5}{7 \cdot 3}$$ = $$\frac{5}{21}$$

з) 1$$\frac{7}{8}:2\frac{11}{32}$$ = $$\frac{15}{8}:\frac{75}{32}$$ = $$\frac{15}{8} \cdot \frac{32}{75}$$ = $$\frac{15 \cdot 32}{8 \cdot 75}$$ = $$\frac{15 \cdot 4 \cdot 8}{8 \cdot 15 \cdot 5}$$ = $$\frac{4}{5}$$

Ответ: a) 20$$\frac{2}{5}$$, б) 13$$\frac{2}{11}$$, в) 6$$\frac{5}{19}$$, г) 8$$\frac{1}{2}$$, д) $$\frac{2}{7}$$, е) 18$$\frac{2}{3}$$, ж) $$\frac{5}{21}$$, з) $$\frac{4}{5}$$

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