2.419 Вычислите значение частного: a) 5 1/4 : 4/5; в) 2 4/7 : 1 3/10; д) 5 1/4 : 1 3/4; ж) 0 : 10 7/15; б) 2/13 : 2 2/13; г) 10 3/5 : 3 3/5; е) 5 3/7 : 3; з) 5 1/16 : 1.

a) $$ 5 \frac{1}{4} : \frac{4}{5} = \frac{21}{4} : \frac{4}{5} = \frac{21}{4} \cdot \frac{5}{4} = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16} = 6 \frac{9}{16} $$

в) $$ 2 \frac{4}{7} : 1 \frac{3}{10} = \frac{18}{7} : \frac{13}{10} = \frac{18}{7} \cdot \frac{10}{13} = \frac{18 \cdot 10}{7 \cdot 13} = \frac{180}{91} = 1 \frac{89}{91} $$

д) $$ 5 \frac{1}{4} : 1 \frac{3}{4} = \frac{21}{4} : \frac{7}{4} = \frac{21}{4} \cdot \frac{4}{7} = \frac{21 \cdot 4}{4 \cdot 7} = \frac{3 \cdot 1}{1 \cdot 1} = 3 $$

ж) $$ 0 : 10 \frac{7}{15} = 0 $$

б) $$ \frac{2}{13} : 2 \frac{2}{13} = \frac{2}{13} : \frac{28}{13} = \frac{2}{13} \cdot \frac{13}{28} = \frac{2 \cdot 13}{13 \cdot 28} = \frac{1 \cdot 1}{1 \cdot 14} = \frac{1}{14} $$

г) $$ 10 \frac{3}{5} : 3 \frac{3}{5} = \frac{53}{5} : \frac{18}{5} = \frac{53}{5} \cdot \frac{5}{18} = \frac{53 \cdot 5}{5 \cdot 18} = \frac{53 \cdot 1}{1 \cdot 18} = \frac{53}{18} = 2 \frac{17}{18} $$

е) $$ 5 \frac{3}{7} : 3 = \frac{38}{7} : 3 = \frac{38}{7} \cdot \frac{1}{3} = \frac{38 \cdot 1}{7 \cdot 3} = \frac{38}{21} = 1 \frac{17}{21} $$

з) $$ 5 \frac{1}{16} : 1 = \frac{81}{16} : 1 = \frac{81}{16} \cdot 1 = \frac{81}{16} = 5 \frac{1}{16} $$

Ответ: a) 6 9/16, в) 1 89/91, д) 3, ж) 0, б) 1/14, г) 2 17/18, е) 1 17/21, з) 5 1/16