Arrangement of fractions \(\rm \frac{1}{9}, \frac{1}{21}, \frac{3}{7}, \frac{12}{63}\)  in decreasing order is:

Explanation:

Make the Expression's Denominator same

By Taking the LCM of Denominator

lcm(9, 21, 7, 63) = 63

Now Make the Denominator same in Each Case

Multiply and Divide 1/9 by 7 = 7/63

Multiply and Divide 1/21 by 3 = 3/63

Multiply and Divide 3/7 by 9 = 27/63

And as the Denominator of 4th Expression is 63

So, we Kept it same i.e 12/63

Now The Given Expression becomes 7/63, 3/63, 27/63 & 12/63

Now, Arrange the Following Fractions in Descending Order
27/63 > 12/63 > 7/63 > 3/63 = \(\frac{3}{7} > \frac{12}{63} > \frac{1}{9} > \frac{1}{21}\)

Alternate Method

Conversion to Decimal:

• 1/9 = 0.1111...
• 1/21 = 0.0476...
• 3/7 = 0.4286...
• 12/63 = 0.1905...

Descending order:

• 3/7 = 0.4286...
• 12/63 = 0.1905...
• 1/9 = 0.1111...
• 1/21 = 0.0476...

Thus, the correct descending order is 3/7, 12/63, 1/9, 1/21.