Упр.15.11 ГДЗ Рабочая тетрадь Зубарева Мордкович 6 класс Экзамен (Математика)

а) 1:1/7; 5:5/8; 4:8/9; 120:1/10;
б) 3/7 :9/14; 3/10 :8/11; 7/12 :5/6; 7/8 :3/4;
в) 12:5/8; 1/3 :3; 5/7 :10; 10/11 :5;
г) 1/200 :200; 9/16 :6; 84/121 :63/110.

При делении на дробь умножаем на обратную дробь:

$$a : \frac{b}{c} = a \cdot \frac{c}{b}$$

а)

$$1 : \frac{1}{7} = 1 \cdot \frac{7}{1} = 7$$
$$5 : \frac{5}{8} = 5 \cdot \frac{8}{5} = 8$$
$$4 : \frac{8}{9} = 4 \cdot \frac{9}{8} = \frac{9}{2} = 4\frac{1}{2}$$
$$120 : \frac{1}{10} = 120 \cdot \frac{10}{1} = 1200$$

б)

$$\frac{3}{7} : \frac{9}{14} = \frac{3}{7} \cdot \frac{14}{9} = \frac{3 \cdot 14}{7 \cdot 9} = \frac{2}{3}$$
$$\frac{3}{10} : \frac{8}{11} = \frac{3}{10} \cdot \frac{11}{8} = \frac{33}{80}$$
$$\frac{7}{12} : \frac{5}{6} = \frac{7}{12} \cdot \frac{6}{5} = \frac{7 \cdot 1}{2 \cdot 5} = \frac{7}{10}$$
$$\frac{7}{8} : \frac{3}{4} = \frac{7}{8} \cdot \frac{4}{3} = \frac{7 \cdot 1}{2 \cdot 3} = \frac{7}{6} = 1\frac{1}{6}$$

в)

$$12 : \frac{5}{8} = 12 \cdot \frac{8}{5} = \frac{96}{5} = 19\frac{1}{5}$$
$$\frac{1}{3} : 3 = \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{9}$$
$$\frac{5}{7} : 10 = \frac{5}{7} \cdot \frac{1}{10} = \frac{1}{14}$$
$$\frac{10}{11} : 5 = \frac{10}{11} \cdot \frac{1}{5} = \frac{2}{11}$$

г)

$$\frac{1}{200} : 200 = \frac{1}{200} \cdot \frac{1}{200} = \frac{1}{40000}$$
$$\frac{9}{16} : 6 = \frac{9}{16} \cdot \frac{1}{6} = \frac{9}{96} = \frac{3}{32}$$
$$\frac{84}{121} : \frac{63}{110} = \frac{84}{121} \cdot \frac{110}{63} = \frac{4 \cdot 10}{11 \cdot 3} = \frac{40}{33} = 1\frac{7}{33}$$

Ответ

а) $$7,\ 8,\ 4\frac{1}{2},\ 1200$$;
б) $$\frac{2}{3},\ \frac{33}{80},\ \frac{7}{10},\ 1\frac{1}{6}$$;
в) $$19\frac{1}{5},\ \frac{1}{9},\ \frac{1}{14},\ \frac{2}{11}$$;
г) $$\frac{1}{40000},\ \frac{3}{32},\ 1\frac{7}{33}$$.