30.01.26 Классная работа a) \(\frac{\left(9\frac{1}{4}-7\frac{2}{5}\right) \cdot 2\frac{1}{2}-1\frac{1}{2}}{\left(3\frac{1}{8}+4\frac{3}{20}-1\frac{5}{48}-5\frac{2}{5}\right): 3\frac{1}{12}}+\frac{6-4 \cdot \frac{1}{10}}{7+1:\frac{3}{7}}=\)

a) Решим пример по действиям:

1) \(9\frac{1}{4}-7\frac{2}{5}=\frac{37}{4}-\frac{37}{5}=\frac{37 \cdot 5 - 37 \cdot 4}{20}=\frac{37 \cdot (5-4)}{20}=\frac{37 \cdot 1}{20}=\frac{37}{20}=1\frac{17}{20}\)

2) \(1\frac{17}{20} \cdot 2\frac{1}{2}=\frac{37}{20} \cdot \frac{5}{2}=\frac{37 \cdot 5}{20 \cdot 2}=\frac{37 \cdot \cancel{5}}{4 \cdot \cancel{5} \cdot 2}=\frac{37}{8}=4\frac{5}{8}\)

3) \(4\frac{5}{8}-1\frac{1}{2}=4\frac{5}{8}-1\frac{4}{8}=3\frac{1}{8}=\frac{25}{8}\)

4) \(3\frac{1}{8}+4\frac{3}{20}-1\frac{5}{48}-5\frac{2}{5}=\frac{25}{8}+\frac{83}{20}-\frac{53}{48}-\frac{27}{5}=\frac{25 \cdot 300 + 83 \cdot 120 - 53 \cdot 50 - 27 \cdot 480}{12000}=\frac{7500+9960-2650-12960}{12000}=\frac{14850}{12000}=\frac{99}{80}=1\frac{19}{80}\)

5) \(1\frac{19}{80}: 3\frac{1}{12}=\frac{99}{80}: \frac{37}{12}=\frac{99}{80} \cdot \frac{12}{37}=\frac{99 \cdot 12}{80 \cdot 37}=\frac{99 \cdot 3}{20 \cdot 37}=\frac{297}{740}\)

6) \(6-4 \cdot \frac{1}{10}=6-\frac{4}{10}=6-\frac{2}{5}=\frac{30-2}{5}=\frac{28}{5}=5\frac{3}{5}\)

7) \(7+1:\frac{3}{7}=7+1 \cdot \frac{7}{3}=7+\frac{7}{3}=\frac{21+7}{3}=\frac{28}{3}=9\frac{1}{3}\)

8) \(\frac{5\frac{3}{5}}{9\frac{1}{3}}=\frac{\frac{28}{5}}{\frac{28}{3}}=\frac{28}{5} \cdot \frac{3}{28}=\frac{\cancel{28} \cdot 3}{5 \cdot \cancel{28}}=\frac{3}{5}\)

9) \(\frac{25}{8}:\frac{297}{740}=\frac{25}{8} \cdot \frac{740}{297}=\frac{25 \cdot 740}{8 \cdot 297}=\frac{25 \cdot 185}{2 \cdot 297}=\frac{4625}{594}\)

10) \(\frac{4625}{594}+\frac{3}{5}=\frac{4625 \cdot 5+3 \cdot 594}{2970}=\frac{23125+1782}{2970}=\frac{24907}{2970}=8\frac{1063}{2970}\)

Ответ: \(8\frac{1063}{2970}\)