Reduce the following fractions to their simplest form:

Краткое пояснение:

Пошаговое решение:

• 1. \( \frac{7}{63} \). НОД(7, 63) = 7. \( \frac{7 \div 7}{63 \div 7} = \frac{1}{9} \).
• 2. \( \frac{2}{5} \). Эта дробь уже несократима, так как НОД(2, 5) = 1.
• 3. \( \frac{8}{48} \). НОД(8, 48) = 8. \( \frac{8 \div 8}{48 \div 8} = \frac{1}{6} \).
• 4. \( \frac{18}{45} \). НОД(18, 45) = 9. \( \frac{18 \div 9}{45 \div 9} = \frac{2}{5} \).
• 5. \( \frac{28}{42} \). НОД(28, 42) = 14. \( \frac{28 \div 14}{42 \div 14} = \frac{2}{3} \).
• 6. \( \frac{52}{91} \). НОД(52, 91) = 13. \( \frac{52 \div 13}{91 \div 13} = \frac{4}{7} \).
• 7. \( \frac{42}{49} \). НОД(42, 49) = 7. \( \frac{42 \div 7}{49 \div 7} = \frac{6}{7} \).
• 8. \( \frac{34}{85} \). НОД(34, 85) = 17. \( \frac{34 \div 17}{85 \div 17} = \frac{2}{5} \).
• 9. \( \frac{27}{57} \). НОД(27, 57) = 3. \( \frac{27 \div 3}{57 \div 3} = \frac{9}{19} \).
• 10. \( \frac{18}{51} \). НОД(18, 51) = 3. \( \frac{18 \div 3}{51 \div 3} = \frac{6}{17} \).
• 11. \( \frac{51}{68} \). НОД(51, 68) = 17. \( \frac{51 \div 17}{68 \div 17} = \frac{3}{4} \).

Ответ:

• 1. \( \frac{1}{9} \)
• 2. \( \frac{2}{5} \)
• 3. \( \frac{1}{6} \)
• 4. \( \frac{2}{5} \)
• 5. \( \frac{2}{3} \)
• 6. \( \frac{4}{7} \)
• 7. \( \frac{6}{7} \)
• 8. \( \frac{2}{5} \)
• 9. \( \frac{9}{19} \)
• 10. \( \frac{6}{17} \)
• 11. \( \frac{3}{4} \)