Solve the following equations: 1) \(\frac{8}{15} \times \frac{25}{12} - 2 \times \frac{2}{3}\) 2) \(\frac{21}{25} \times X - 50 : 2 = 51\)

Решение:

1. \(\frac{8}{15} \times \frac{25}{12} - 2 \times \frac{2}{3}\)
1. Сокращаем дроби: \(\frac{8}{15} \times \frac{25}{12} = \frac{2 \times 4}{3 \times 5} \times \frac{5 \times 5}{3 \times 4} = \frac{2}{3} \times \frac{5}{3} = \frac{10}{9}\)
2. \(2 \times \frac{2}{3} = \frac{4}{3}\)
3. \(\frac{10}{9} - \frac{4}{3} = \frac{10}{9} - \frac{12}{9} = -\frac{2}{9}\)
2. \(\frac{21}{25} \times X - 50 : 2 = 51\)
1. \(50 : 2 = 25\)
2. \(\frac{21}{25} \times X - 25 = 51\)
3. \(\frac{21}{25} \times X = 51 + 25\)
4. \(\frac{21}{25} \times X = 76\)
5. \(X = 76 : \frac{21}{25}\)
6. \(X = 76 \times \frac{25}{21}\)
7. \(X = \frac{1900}{21}\)

Ответ: 1) \(-\frac{2}{9}\) 2) \(X = \frac{1900}{21}\)