5. $$\left(2\frac{13}{48} + 2\frac{5}{12}\right) : 3\frac{3}{4} - 9\frac{3}{4} : 12$$

INSIGHT

Решение:

1. \(2\frac{13}{48} = \frac{2 \cdot 48 + 13}{48} = \frac{96 + 13}{48} = \frac{109}{48}\)
2. \(2\frac{5}{12} = \frac{2 \cdot 12 + 5}{12} = \frac{24 + 5}{12} = \frac{29}{12}\)
3. \(\frac{109}{48} + \frac{29}{12} = \frac{109}{48} + \frac{29 \cdot 4}{12 \cdot 4} = \frac{109 + 116}{48} = \frac{225}{48}\)
4. \(3\frac{3}{4} = \frac{3 \cdot 4 + 3}{4} = \frac{15}{4}\)
5. \(\frac{225}{48} : \frac{15}{4} = \frac{225}{48} \cdot \frac{4}{15} = \frac{225 \cdot 4}{48 \cdot 15} = \frac{15 \cdot 1}{12 \cdot 1} = \frac{15}{12} = \frac{5}{4}\)
6. \(9\frac{3}{4} = \frac{9 \cdot 4 + 3}{4} = \frac{39}{4}\)
7. \(\frac{39}{4} : 12 = \frac{39}{4} \cdot \frac{1}{12} = \frac{39}{48} = \frac{13}{16}\)
8. \(\frac{5}{4} - \frac{13}{16} = \frac{5 \cdot 4}{4 \cdot 4} - \frac{13}{16} = \frac{20 - 13}{16} = \frac{7}{16}\)

Ответ: \(\frac{7}{16}\)