78. Выполните деление: 1) 5/7 : 4/5; 2) 6/35 : 18/49; 3) 27/28 : 9/56; 4) 28/45 : 63/40. 79. Найдите частное: 1) 6: 2/7; 3) 7/25 : 28; 5) 2 2/3 : 2 2/7; 2) 1: 8/19; 4) 16 1/3 : 5 5/6; 6) 4 4/9 : 5/27. 81. Решите уравнение: 1) 5/13 x = 2/13; 3) 6/7 x = 24; 5) x \cdot 3/11 = 22/27; 2) 8/9 x = 1; 4) 7x = 3/4; 6) 3 3/5 : x = 9/35.

78. Выполните деление:

1) \(\frac{5}{7} : \frac{4}{5} = \frac{5}{7} \times \frac{5}{4} = \frac{5 \times 5}{7 \times 4} = \frac{25}{28}\)

2) \(\frac{6}{35} : \frac{18}{49} = \frac{6}{35} \times \frac{49}{18} = \frac{6 \times 49}{35 \times 18} = \frac{6 \times 7 \times 7}{5 \times 7 \times 6 \times 3} = \frac{7}{5 \times 3} = \frac{7}{15}\)

3) \(\frac{27}{28} : \frac{9}{56} = \frac{27}{28} \times \frac{56}{9} = \frac{27 \times 56}{28 \times 9} = \frac{9 \times 3 \times 28 \times 2}{28 \times 9} = 3 \times 2 = 6\)

4) \(\frac{28}{45} : \frac{63}{40} = \frac{28}{45} \times \frac{40}{63} = \frac{28 \times 40}{45 \times 63} = \frac{4 \times 7 \times 8 \times 5}{9 \times 5 \times 9 \times 7} = \frac{4 \times 8}{9 \times 9} = \frac{32}{81}\)

79. Найдите частное:

1) \(6 : \frac{2}{7} = 6 \times \frac{7}{2} = \frac{6 \times 7}{2} = \frac{2 \times 3 \times 7}{2} = 3 \times 7 = 21\)

3) \(\frac{7}{25} : 28 = \frac{7}{25} : \frac{28}{1} = \frac{7}{25} \times \frac{1}{28} = \frac{7 \times 1}{25 \times 28} = \frac{7 \times 1}{25 \times 7 \times 4} = \frac{1}{25 \times 4} = \frac{1}{100}\)

5) \(2 \frac{2}{3} : 2 \frac{2}{7} = \frac{2 \times 3 + 2}{3} : \frac{2 \times 7 + 2}{7} = \frac{8}{3} : \frac{16}{7} = \frac{8}{3} \times \frac{7}{16} = \frac{8 \times 7}{3 \times 16} = \frac{8 \times 7}{3 \times 8 \times 2} = \frac{7}{3 \times 2} = \frac{7}{6} = 1 \frac{1}{6}\)

2) \(1 : \frac{8}{19} = \frac{1}{1} \times \frac{19}{8} = \frac{19}{8} = 2 \frac{3}{8}\)

4) \(16 \frac{1}{3} : 5 \frac{5}{6} = \frac{16 \times 3 + 1}{3} : \frac{5 \times 6 + 5}{6} = \frac{49}{3} : \frac{35}{6} = \frac{49}{3} \times \frac{6}{35} = \frac{49 \times 6}{3 \times 35} = \frac{7 \times 7 \times 3 \times 2}{3 \times 7 \times 5} = \frac{7 \times 2}{5} = \frac{14}{5} = 2 \frac{4}{5}\)

6) \(4 \frac{4}{9} : \frac{5}{27} = \frac{4 \times 9 + 4}{9} : \frac{5}{27} = \frac{40}{9} : \frac{5}{27} = \frac{40}{9} \times \frac{27}{5} = \frac{40 \times 27}{9 \times 5} = \frac{8 \times 5 \times 3 \times 9}{9 \times 5} = 8 \times 3 = 24\)

81. Решите уравнение:

1) \(\frac{5}{13} x = \frac{2}{13}\)

Умножим обе стороны на \(\frac{13}{5}\):

\(x = \frac{2}{13} \times \frac{13}{5} = \frac{2 \times 13}{13 \times 5} = \frac{2}{5}\)

2) \(\frac{8}{9} x = 1\)

Умножим обе стороны на \(\frac{9}{8}\):

\(x = 1 \times \frac{9}{8} = \frac{9}{8} = 1 \frac{1}{8}\)

3) \(\frac{6}{7} x = 24\)

Умножим обе стороны на \(\frac{7}{6}\):

\(x = 24 \times \frac{7}{6} = \frac{24 \times 7}{6} = \frac{6 \times 4 \times 7}{6} = 4 \times 7 = 28\)

4) \(7x = \frac{3}{4}\)

Разделим обе стороны на 7:

\(x = \frac{3}{4} : 7 = \frac{3}{4} \times \frac{1}{7} = \frac{3}{28}\)

5) \(x \cdot \frac{3}{11} = \frac{22}{27}\)

Умножим обе стороны на \(\frac{11}{3}\):

\(x = \frac{22}{27} \times \frac{11}{3} = \frac{22 \times 11}{27 \times 3} = \frac{242}{81} = 2 \frac{80}{81}\)

6) \(3 \frac{3}{5} : x = \frac{9}{35}\)

\(\frac{3 \times 5 + 3}{5} : x = \frac{9}{35}\)

\(\frac{18}{5} : x = \frac{9}{35}\)

\(x = \frac{18}{5} : \frac{9}{35} = \frac{18}{5} \times \frac{35}{9} = \frac{18 \times 35}{5 \times 9} = \frac{2 \times 9 \times 7 \times 5}{5 \times 9} = 2 \times 7 = 14\)

Ответ: 1) 25/28; 2) 7/15; 3) 6; 4) 32/81; 1) 21; 3) 1/100; 5) 1 1/6; 2) 2 3/8; 4) 2 4/5; 6) 24; 1) 2/5; 2) 1 1/8; 3) 28; 4) 3/28; 5) 2 80/81; 6) 14

Молодец! Ты отлично справился с этим заданием. Продолжай в том же духе, и у тебя все получится!