Решите пример с дробями.

```\(\text{Дан пример:}\) \ \(\frac{4}{45}\) : \(\left\)\(\frac{12}{25} - \frac{4}{15}\right\) + \(\frac{15}{16}\) - \(\frac{4}{15}\).``` \ \(\text{Решение:}\) \ \(\text{1. Посчитаем выражение в скобках:}\) \ \(\frac{12}{25}\) - \(\frac{4}{15}\). \ \(\text{Приведем к общему знаменателю:}\) \ \(\text{НОК знаменателей 25 и 15 равен 75.}\) \ \(\frac{12}{25}\) = \(\frac{36}{75}\), \ \(\frac{4}{15}\) = \(\frac{20}{75}\). \ \(\text{Вычитаем:}\) \ \(\frac{36}{75}\) - \(\frac{20}{75}\) = \(\frac{16}{75}\). \ \(\text{Итак, }\) \ \(\frac{4}{45}\) : \(\frac{16}{75}\) + \(\frac{15}{16}\) - \(\frac{4}{15}\). \ \(\text{2. Разделим дробь }\) \ \(\frac{4}{45}\) \ \(\text{на }\) \ \(\frac{16}{75}\): \ \(\frac{4}{45}\) : \(\frac{16}{75}\) = \(\frac{4}{45}\) \(\times\) \(\frac{75}{16}\) = \(\frac{4 \cdot 75}{45 \cdot 16}\). \ \(\text{Сократим:}\) \ \(\frac{4 \cdot 75}{45 \cdot 16}\) = \(\frac{1 \cdot 75}{45 \cdot 4}\) = \(\frac{25}{45}\) = \(\frac{5}{9}\). \ \(\text{Теперь выражение:}\) \ \(\frac{5}{9}\) + \(\frac{15}{16}\) - \(\frac{4}{15}\). \ \(\text{3. Приведем все дроби к общему знаменателю. НОК знаменателей 9, 16 и 15 равен 720.}\) \ \(\frac{5}{9}\) = \(\frac{400}{720}\), \ \(\frac{15}{16}\) = \(\frac{675}{720}\), \ \(\frac{4}{15}\) = \(\frac{192}{720}\). \ \(\text{Складываем и вычитаем:}\) \ \(\frac{400}{720}\) + \(\frac{675}{720}\) - \(\frac{192}{720}\) = \(\frac{400 + 675 - 192}{720}\) = \(\frac{883}{720}\). \ \(\text{Ответ: }\) \ \(\frac{883}{720}\).```