Question:
Simplify: \(\frac{\frac{7}{2} \div \frac{3}{2} \times \frac{5}{2}}{8 \div \frac{5}{2} \text{ of } \frac{1}{2}} \div \frac{25}{8}\)
सरल बनाएं: \(\frac{\frac{7}{2} \div \frac{3}{2} \times \frac{5}{2}}{8 \div \frac{5}{2} \text{ of } \frac{1}{2}} \div \frac{25}{8}\)
Options :
- a) \(\frac{11}{24}\)
- b) \(\frac{7}{24}\)
- c) \(\frac{5}{24}\)
- d) \(\frac{13}{24}\)
- a) \(\frac{11}{24}\)
- b) \(\frac{7}{24}\)
- c) \(\frac{5}{24}\)
- d) \(\frac{13}{24}\)
correct answer : b)
Explanation :
Numerator: (7/2) ÷ (3/2) × (5/2) = (7/3) × (5/2) = 35/6.
Denominator: 8 ÷ ((5/2) × (1/2)) = 8 ÷ (5/4) = 8 × (4/5) = 32/5.
Main fraction = (35/6) / (32/5) = (35 × 5) / (6 × 32) = 175 / 192.
Dividing by 25/8: (175 / 192) × (8 / 25) = (7 / 24).
अंश: (7/2) ÷ (3/2) × (5/2) = (7/3) × (5/2) = 35/6.
हर: 8 ÷ ((5/2) × (1/2)) = 8 ÷ (5/4) = 8 × (4/5) = 32/5.
मुख्य अंश = (35/6) / (32/5) = (35 × 5) / (6 × 32) = 175 / 192.
25/8 से विभाजित करना: (175/192) × (8/25) = (7/24)।