Question

The value of $\overline{1.285714} \div \overline{1.714285} =$

• A. $\frac{3}{4}$
• B. $\frac{7}{8}$
• C. $\frac{7}{12}$
• D. $\frac{3}{7}$

Answer 1

Answer: (A)

$\frac{3}{4}$

Answer 2

1. Recognize that:

   • $\overline{1.285714} = 1.285714285714\ldots = \frac{9}{7}$
     (since $\frac{9}{7} \approx 1.285714\ldots$)
   • $\overline{1.714285} = 1.714285714285\ldots = \frac{12}{7}$
     (since $\frac{12}{7} \approx 1.714285\ldots$)

2. Compute the division:

   $\frac{\frac{9}{7}}{\frac{12}{7}} = \frac{9}{7} \times \frac{7}{12} = \frac{9}{12} = \frac{3}{4}$