B-1 al) B-2 al) 2 Решите уравнение: 1) 2) 3)

B-1

a) \[ \frac{3}{4} : \frac{5}{7} = \frac{3}{4} \cdot \frac{7}{5} = \frac{3 \cdot 7}{4 \cdot 5} = \frac{21}{20} = 1 \frac{1}{20} \]

б) \[ \frac{5}{18} : \frac{25}{27} = \frac{5}{18} \cdot \frac{27}{25} = \frac{5 \cdot 27}{18 \cdot 25} = \frac{1 \cdot 3}{2 \cdot 5} = \frac{3}{10} \]

№2 Решите уравнение:

1) \[ \frac{6}{5} x = \frac{3}{5} \]

\[ x = \frac{3}{5} : \frac{6}{5} \]

\[ x = \frac{3}{5} \cdot \frac{5}{6} \]

\[ x = \frac{3 \cdot 5}{5 \cdot 6} \]

\[ x = \frac{1 \cdot 1}{1 \cdot 2} \]

\[ x = \frac{1}{2} \]

2) \[ \frac{3}{4} x = 12 \]

\[ x = 12 : \frac{3}{4} \]

\[ x = 12 \cdot \frac{4}{3} \]

\[ x = \frac{12 \cdot 4}{3} \]

\[ x = \frac{4 \cdot 4}{1} \]

\[ x = 16 \]

3) \[ x : \frac{7}{15} = \frac{15}{28} \]

\[ x = \frac{15}{28} \cdot \frac{7}{15} \]

\[ x = \frac{15 \cdot 7}{28 \cdot 15} \]

\[ x = \frac{1 \cdot 1}{4 \cdot 1} \]

\[ x = \frac{1}{4} \]

B-2

a) \[ \frac{9}{16} : \frac{3}{64} = \frac{9}{16} \cdot \frac{64}{3} = \frac{9 \cdot 64}{16 \cdot 3} = \frac{3 \cdot 4}{1 \cdot 1} = 12 \]

б) \[ \frac{25}{72} : \frac{45}{63} = \frac{25}{72} \cdot \frac{63}{45} = \frac{25 \cdot 63}{72 \cdot 45} = \frac{5 \cdot 7}{8 \cdot 9} = \frac{35}{72} \]

Решите уравнение:

1) \[ \frac{4}{7} x = 1 \]

\[ x = 1 : \frac{4}{7} \]

\[ x = 1 \cdot \frac{7}{4} \]

\[ x = \frac{7}{4} = 1 \frac{3}{4} \]

2) \[ 3 \cdot x = \frac{2}{3} \]

\[ x = \frac{2}{3} : 3 \]

\[ x = \frac{2}{3} : \frac{3}{1} \]

\[ x = \frac{2}{3} \cdot \frac{1}{3} \]

\[ x = \frac{2}{9} \]

3) \[ 5 \frac{1}{4} : x = \frac{7}{8} \]

\[ \frac{21}{4} : x = \frac{7}{8} \]

\[ x = \frac{21}{4} : \frac{7}{8} \]

\[ x = \frac{21}{4} \cdot \frac{8}{7} \]

\[ x = \frac{21 \cdot 8}{4 \cdot 7} \]

\[ x = \frac{3 \cdot 2}{1 \cdot 1} \]

\[ x = 6 \]