Discussion
Arrangement of fractions \(\frac{1}{9}, \frac{1}{21}, \frac{3}{7}, \frac{12}{63}\) in decreasing order is :
Answer: B
The decreasing order is \(\frac{3}{7}, \frac{12}{63}, \frac{1}{9}, \frac{1}{21}\).
Convert each fraction to the common denominator 63:
\[ \begin{aligned} \tfrac{3}{7} &= \tfrac{27}{63}, \quad \tfrac{12}{63} = \tfrac{12}{63} \\ \tfrac{1}{9} &= \tfrac{7}{63}, \quad \tfrac{1}{21} = \tfrac{3}{63} \end{aligned} \]
So \(27 \gt 12 \gt 7 \gt 3\) gives the order above. Option 1 puts \(\frac{1}{9}\) above \(\frac{12}{63}\), option 3 starts with \(\frac{12}{63}\), and option 4 repeats \(\frac{1}{9}\) and is in increasing order.
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