2.462 Выполните действия: a) 7 : 4 ; б) 5 : 21 ; в) 1 : 38 ; г) : 1 ; д) 2 : 7 ; е) 6 : 1 ; ж) 2 : 7 ; з) 1 : ; к) 4 : 19 .

a) $$7\frac{2}{4} \div 1\frac{1}{9} = \frac{30}{4} \div \frac{10}{9} = \frac{30}{4} \cdot \frac{9}{10} = \frac{3 \cdot 9}{4} = \frac{27}{4} = 6\frac{3}{4} = 6.75$$

б) $$5\frac{3}{7} \div 21\frac{2}{8} = \frac{38}{7} \div \frac{170}{8} = \frac{38}{7} \cdot \frac{8}{170} = \frac{38 \cdot 8}{7 \cdot 170} = \frac{19 \cdot 8}{7 \cdot 85} = \frac{152}{595} \approx 0.255$$

в) $$11\frac{1}{11} \div \frac{38}{9} \div \frac{5}{17} = \frac{122}{11} \cdot \frac{9}{38} \cdot \frac{17}{5} = \frac{61 \cdot 9 \cdot 17}{11 \cdot 19 \cdot 5} = \frac{9387}{1045} \approx 8.983$$

г) $$\frac{5}{6} \div 11\frac{1}{11} = \frac{5}{6} \div \frac{122}{11} = \frac{5}{6} \cdot \frac{11}{122} = \frac{55}{732} \approx 0.075$$

д) $$2\frac{1}{3} \div 7\frac{1}{14} = \frac{7}{3} \div \frac{99}{14} = \frac{7}{3} \cdot \frac{14}{99} = \frac{98}{297} \approx 0.330$$

e) $$6\frac{5}{11} \div 1\frac{1}{11} = \frac{71}{11} \div \frac{12}{11} = \frac{71}{11} \cdot \frac{11}{12} = \frac{71}{12} = 5\frac{11}{12} \approx 5.917$$

ж) $$2\frac{1}{7} \div 1\frac{3}{14} = \frac{15}{7} \div \frac{17}{14} = \frac{15}{7} \cdot \frac{14}{17} = \frac{15 \cdot 2}{17} = \frac{30}{17} = 1\frac{13}{17} \approx 1.765$$

з) $$1\frac{3}{9} \div 3\frac{1}{3} = \frac{12}{9} \div \frac{10}{3} = \frac{12}{9} \cdot \frac{3}{10} = \frac{4}{3} \cdot \frac{1}{10} = \frac{4}{30} = \frac{2}{15} \approx 0.133$$

к) $$4\frac{17}{36} \div 19\frac{1}{6} = \frac{161}{36} \div \frac{115}{6} = \frac{161}{36} \cdot \frac{6}{115} = \frac{161}{6 \cdot 115} = \frac{161}{690} \approx 0.233$$

Ответ: а) 6.75; б) 0.255; в) 8.983; г) 0.075; д) 0.330; e) 5.917; ж) 1.765; з) 0.133; к) 0.233