1. Решите уравнение a:1\frac{5}{8}=2\frac{7}{27}:1\frac{29}{36}

Решим уравнение.

$$a : 1\frac{5}{8} = 2\frac{7}{27} : 1\frac{29}{36}$$ $$a : \frac{1 \cdot 8 + 5}{8} = \frac{2 \cdot 27 + 7}{27} : \frac{1 \cdot 36 + 29}{36}$$ $$a : \frac{13}{8} = \frac{61}{27} : \frac{65}{36}$$ $$a : \frac{13}{8} = \frac{61}{27} \cdot \frac{36}{65}$$ $$a : \frac{13}{8} = \frac{61 \cdot 4}{3 \cdot 65}$$ $$a : \frac{13}{8} = \frac{244}{195}$$ $$a = \frac{244}{195} \cdot \frac{13}{8}$$ $$a = \frac{61}{195} \cdot \frac{13}{2}$$ $$a = \frac{61}{15} \cdot \frac{1}{2}$$ $$a = \frac{61}{30}$$ $$a = 2\frac{1}{30}$$

Ответ: $$2\frac{1}{30}$$