Здесь представлены математические примеры, которые нужно решить.

Давай решим эти примеры по порядку!

A

1. \[ \frac{2}{5} + \frac{4}{15} = \frac{6}{15} + \frac{4}{15} = \frac{10}{15} = \frac{2}{3} \]

   \[ \frac{2}{3} : \frac{5}{6} = \frac{2}{3} \cdot \frac{6}{5} = \frac{12}{15} = \frac{4}{5} \]

   Ответ: \( \frac{4}{5} \)

2. \[ 4 : \frac{4}{5} = 4 \cdot \frac{5}{4} = 5 \]

       5
     x 3
     ---
      15
   
      15
    x 5
    ---
      75
   
      75
    -10
    ---
      65
     

   Ответ: 65

3. \[ \frac{1}{3} - \frac{1}{4} = \frac{4}{12} - \frac{3}{12} = \frac{1}{12} \]

   \[ \frac{1}{12} \cdot 6 = \frac{6}{12} = \frac{1}{2} \]

   \[ \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]

   Ответ: \( \frac{3}{4} \)

4. \[ 2 \cdot \frac{6}{7} = \frac{12}{7} \]

   \[ \frac{12}{7} : 4 = \frac{12}{7} \cdot \frac{1}{4} = \frac{12}{28} = \frac{3}{7} \]

   \[ \frac{3}{7} + \frac{5}{14} = \frac{6}{14} + \frac{5}{14} = \frac{11}{14} \]

   Ответ: \( \frac{11}{14} \)

Б

1. \[ 1 \frac{1}{4} + 2 = 3 \frac{1}{4} \]

   \[ 3 \frac{1}{4} : \frac{3}{4} = \frac{13}{4} \cdot \frac{4}{3} = \frac{13}{3} = 4 \frac{1}{3} \]

   \[ 4 \frac{1}{3} : 5 = \frac{13}{3} : 5 = \frac{13}{3} \cdot \frac{1}{5} = \frac{13}{15} \]

   Ответ: \( \frac{13}{15} \)

2. \[ 5 \frac{3}{9} \cdot 5 = \frac{48}{9} \cdot 5 = \frac{240}{9} = 26 \frac{6}{9} = 26 \frac{2}{3} \]

   \[ 26 \frac{2}{3} - 1 \frac{1}{6} = 25 \frac{4}{6} - \frac{1}{6} = 25 \frac{3}{6} = 25 \frac{1}{2} \]

   \[ 25 \frac{1}{2} : 5 = \frac{51}{2} : 5 = \frac{51}{2} \cdot \frac{1}{5} = \frac{51}{10} = 5 \frac{1}{10} \]

   Ответ: \( 5 \frac{1}{10} \)

3. \[ \frac{2}{3} : 6 = \frac{2}{3} \cdot \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \]

   \[ \frac{1}{9} + 1 \frac{1}{3} = \frac{1}{9} + \frac{4}{3} = \frac{1}{9} + \frac{12}{9} = \frac{13}{9} = 1 \frac{4}{9} \]

   \[ 1 \frac{4}{9} + \frac{1}{4} = \frac{13}{9} + \frac{1}{4} = \frac{52}{36} + \frac{9}{36} = \frac{61}{36} = 1 \frac{25}{36} \]

   Ответ: \( 1 \frac{25}{36} \)

4. \[ 1 \frac{1}{3} - \frac{1}{6} = \frac{4}{3} - \frac{1}{6} = \frac{8}{6} - \frac{1}{6} = \frac{7}{6} = 1 \frac{1}{6} \]

   \[ 1 \frac{1}{6} \cdot 2 = \frac{7}{6} \cdot 2 = \frac{14}{6} = \frac{7}{3} = 2 \frac{1}{3} \]

   \[ 2 \frac{1}{3} : 4 = \frac{7}{3} \cdot \frac{1}{4} = \frac{7}{12} \]

   \[ \frac{7}{12} + \frac{4}{9} = \frac{21}{36} + \frac{16}{36} = \frac{37}{36} = 1 \frac{1}{36} \]

   Ответ: \( 1 \frac{1}{36} \)

В

1. \[ \frac{5}{7} : 5 = \frac{5}{7} \cdot \frac{1}{5} = \frac{1}{7} \]

   \[ \frac{1}{7} \cdot 1 \frac{2}{3} = \frac{1}{7} \cdot \frac{5}{3} = \frac{5}{21} \]

   \[ \frac{5}{21} + \frac{3}{7} = \frac{5}{21} + \frac{9}{21} = \frac{14}{21} = \frac{2}{3} \]

   Ответ: \( \frac{2}{3} \)

2. \[ 2 \frac{1}{3} - \frac{1}{9} = \frac{7}{3} - \frac{1}{9} = \frac{21}{9} - \frac{1}{9} = \frac{20}{9} \]

   \[ \frac{20}{9} \cdot \frac{1}{5} = \frac{20}{45} = \frac{4}{9} \]

   \[ \frac{4}{9} + \frac{2}{9} = \frac{6}{9} = \frac{2}{3} \]

   Ответ: \( \frac{2}{3} \)

3. \[ 1 \frac{1}{4} \cdot 2 = \frac{5}{4} \cdot 2 = \frac{10}{4} = \frac{5}{2} = 2 \frac{1}{2} \]

   \[ 2 \frac{1}{2} : 3 = \frac{5}{2} \cdot \frac{1}{3} = \frac{5}{6} \]

   \[ \frac{5}{6} + 1 \frac{1}{3} = \frac{5}{6} + \frac{4}{3} = \frac{5}{6} + \frac{8}{6} = \frac{13}{6} = 2 \frac{1}{6} \]

   \[ 2 \frac{1}{6} : 4 = \frac{13}{6} \cdot \frac{1}{4} = \frac{13}{24} \]

   Ответ: \( \frac{13}{24} \)

4. \[ 1 \frac{1}{6} + \frac{1}{12} = \frac{7}{6} + \frac{1}{12} = \frac{14}{12} + \frac{1}{12} = \frac{15}{12} = \frac{5}{4} = 1 \frac{1}{4} \]

   \[ 1 \frac{1}{4} : 2 = \frac{5}{4} \cdot \frac{1}{2} = \frac{5}{8} \]

   \[ \frac{5}{8} \cdot 3 = \frac{15}{8} = 1 \frac{7}{8} \]

   Ответ: \( 1 \frac{7}{8} \)

Г

1. \[ 7 \frac{4}{8} : 7 = \frac{60}{8} : 7 = \frac{60}{8} \cdot \frac{1}{7} = \frac{60}{56} = \frac{15}{14} = 1 \frac{1}{14} \]

   \[ 1 \frac{1}{14} \cdot 1 \frac{1}{4} = \frac{15}{14} \cdot \frac{5}{4} = \frac{75}{56} = 1 \frac{19}{56} \]

   Ответ: \( 1 \frac{19}{56} \)

2. \[ 1 \frac{3}{8} + \frac{4}{7} = \frac{11}{8} + \frac{4}{7} = \frac{77}{56} + \frac{32}{56} = \frac{109}{56} = 1 \frac{53}{56} \]

   \[ 1 \frac{53}{56} : 5 = \frac{109}{56} \cdot \frac{1}{5} = \frac{109}{280} \]

   Ответ: \( \frac{109}{280} \)

3. \[ \frac{7}{9} - \frac{2}{3} = \frac{7}{9} - \frac{6}{9} = \frac{1}{9} \]

     1
     ---
     7
   x18
    ---
    126
   
    126
   +10
    ---
    136
     

   \[ \frac{1}{9} : \frac{136}{7} = \frac{1}{9} \cdot \frac{7}{136} = \frac{7}{1224} = \frac{7}{1224} \]

   Ответ: \( \frac{7}{1224} \)

4. \[ \frac{2}{9} : 1 = \frac{2}{9} \]

   \[ \frac{2}{9} \cdot \frac{1}{2} = \frac{2}{18} = \frac{1}{9} \]

   \[ \frac{1}{9} + \frac{1}{12} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36} \]

   Ответ: \( \frac{7}{36} \)

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