11. Выполните деление, рассуждая, как в предыдущем примере: a) 16:8= 9 34:2= 9 35:5= 8 в) 6416:4= 21 386:2= 11 100 50:25 = 109 6) 1200:3= 7 17.7 14-:7= 13 26 8:2= 11 г) 4914 :7 = 15 84-42:42 = 271 75 100 : 25 = 647

a) $$16\frac{4}{9}:8=(16+\frac{4}{9}):8=16:8+\frac{4}{9}:8=2+\frac{4}{9}:\frac{8}{1}=2+\frac{4}{9} \cdot \frac{1}{8}=2+\frac{4 \cdot 1}{9 \cdot 8}=2+\frac{4}{72}=2+\frac{1}{18}=2\frac{1}{18}$$

$$34\frac{4}{9}:2=(34+\frac{4}{9}):2=34:2+\frac{4}{9}:2=17+\frac{4}{9}:\frac{2}{1}=17+\frac{4}{9} \cdot \frac{1}{2}=17+\frac{4 \cdot 1}{9 \cdot 2}=17+\frac{4}{18}=17+\frac{2}{9}=17\frac{2}{9}$$

$$35\frac{5}{8}:5=(35+\frac{5}{8}):5=35:5+\frac{5}{8}:5=7+\frac{5}{8}:\frac{5}{1}=7+\frac{5}{8} \cdot \frac{1}{5}=7+\frac{5 \cdot 1}{8 \cdot 5}=7+\frac{5}{40}=7+\frac{1}{8}=7\frac{1}{8}$$

б) $$120\frac{6}{7}:3=(120+\frac{6}{7}):3=120:3+\frac{6}{7}:3=40+\frac{6}{7}:\frac{3}{1}=40+\frac{6}{7} \cdot \frac{1}{3}=40+\frac{6 \cdot 1}{7 \cdot 3}=40+\frac{6}{21}=40+\frac{2}{7}=40\frac{2}{7}$$

$$14\frac{7}{13}:7=(14+\frac{7}{13}):7=14:7+\frac{7}{13}:7=2+\frac{7}{13}:\frac{7}{1}=2+\frac{7}{13} \cdot \frac{1}{7}=2+\frac{7 \cdot 1}{13 \cdot 7}=2+\frac{7}{91}=2+\frac{1}{13}=2\frac{1}{13}$$

$$26\frac{8}{11}:2=(26+\frac{8}{11}):2=26:2+\frac{8}{11}:2=13+\frac{8}{11}:\frac{2}{1}=13+\frac{8}{11} \cdot \frac{1}{2}=13+\frac{8 \cdot 1}{11 \cdot 2}=13+\frac{8}{22}=13+\frac{4}{11}=13\frac{4}{11}$$

в) $$64\frac{16}{21}:4=(64+\frac{16}{21}):4=64:4+\frac{16}{21}:4=16+\frac{16}{21}:\frac{4}{1}=16+\frac{16}{21} \cdot \frac{1}{4}=16+\frac{16 \cdot 1}{21 \cdot 4}=16+\frac{16}{84}=16+\frac{4}{21}=16\frac{4}{21}$$

$$38\frac{6}{11}:2=(38+\frac{6}{11}):2=38:2+\frac{6}{11}:2=19+\frac{6}{11}:\frac{2}{1}=19+\frac{6}{11} \cdot \frac{1}{2}=19+\frac{6 \cdot 1}{11 \cdot 2}=19+\frac{6}{22}=19+\frac{3}{11}=19\frac{3}{11}$$

$$100\frac{50}{109}:25=(100+\frac{50}{109}):25=100:25+\frac{50}{109}:25=4+\frac{50}{109}:\frac{25}{1}=4+\frac{50}{109} \cdot \frac{1}{25}=4+\frac{50 \cdot 1}{109 \cdot 25}=4+\frac{50}{2725}=4+\frac{2}{109}=4\frac{2}{109}$$

г) $$49\frac{14}{15}:7=(49+\frac{14}{15}):7=49:7+\frac{14}{15}:7=7+\frac{14}{15}:\frac{7}{1}=7+\frac{14}{15} \cdot \frac{1}{7}=7+\frac{14 \cdot 1}{15 \cdot 7}=7+\frac{14}{105}=7+\frac{2}{15}=7\frac{2}{15}$$

$$84\frac{42}{271}:42=(84+\frac{42}{271}):42=84:42+\frac{42}{271}:42=2+\frac{42}{271}:\frac{42}{1}=2+\frac{42}{271} \cdot \frac{1}{42}=2+\frac{42 \cdot 1}{271 \cdot 42}=2+\frac{42}{11382}=2+\frac{1}{271}=2\frac{1}{271}$$

$$100\frac{75}{647}:25=(100+\frac{75}{647}):25=100:25+\frac{75}{647}:25=4+\frac{75}{647}:\frac{25}{1}=4+\frac{75}{647} \cdot \frac{1}{25}=4+\frac{75 \cdot 1}{647 \cdot 25}=4+\frac{75}{16175}=4+\frac{3}{647}=4\frac{3}{647}$$

Ответ: a) $$16\frac{4}{9}:8=2\frac{1}{18}$$, $$34\frac{4}{9}:2=17\frac{2}{9}$$, $$35\frac{5}{8}:5=7\frac{1}{8}$$; б) $$120\frac{6}{7}:3=40\frac{2}{7}$$, $$14\frac{7}{13}:7=2\frac{1}{13}$$, $$26\frac{8}{11}:2=13\frac{4}{11}$$; в) $$64\frac{16}{21}:4=16\frac{4}{21}$$, $$38\frac{6}{11}:2=19\frac{3}{11}$$, $$100\frac{50}{109}:25=4\frac{2}{109}$$; г) $$49\frac{14}{15}:7=7\frac{2}{15}$$, $$84\frac{42}{271}:42=2\frac{1}{271}$$, $$100\frac{75}{647}:25=4\frac{3}{647}$$