Question

$\frac{1}{2}\times (1+\frac{1}{4})\times (1+\frac{2}{4})\times (1+\frac{3}{4})\times (1+\frac{5}{4})$ is equal to:

• A. 44/256
• B. 948/255
• C. 255/948
• D. 945/256

Answer 1

Answer: (C), (D)

The correct options are
C

255/948

D

945/256

Given,
$\frac{1}{2}\times (1+\frac{1}{4})\times (1+\frac{2}{4})\times (1+\frac{3}{4})\times (1+\frac{5}{4})$
= $\frac{1}{2}\times \frac{5}{4}\times \frac{6}{4}\times \frac{7}{4}\times \frac{9}{4}$ (Using BODMAS)
[$\because$ Product of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ is equal to $\frac{a\times c}{b\times d}$]
= $\frac{1890}{512}$
= $\frac{945}{256}$ [Dividing numerator and denominator by largest possible number such that both remain whole number.]