Question

Order the fractions from largest to smallest: 1, 2/3, 8/9, 16/27, 64/81, 128/243, 512/729, 2048/2187, 4096/6561, 16384/19683, 32768/59049, 131072/177147

Answer 1

For this problem, we need to order the given fractions from largest to smallest.

The fractions are:

`1,(2)/(3),(8)/(9),(16)/(27),(64)/(81),(128)/(243),(512)/(729),(2048)/(2187),(4096)/(6561),(16384)/(19683),(32768)/(59049),(131072)/(177147)`

In order to order these fractions, we need to determine which are the largest, which can be done by looking at the difference between numerator and denominator, the smallest the difference the bigger the fraction. We also need to take a look at the denominator, to determine how the two fractions are related. So we have:

`1,(2048)/(2187),(8)/(9),(16384)/(19683),(64)/(81),(131072)/(177147),(512)/(729),(2)/(3),(4096)/(6561),(16)/(27),(32768)/(59049),(128)/(243)`

The correct order is:

1, 2048/2187, 8/9, 16384/19683, 64/81, 131072/177147, 512/729, 2/3, 4096/6561, 16/27, 32768/59049, 128/243