Question

Arrange the following rational number in the descending order.
$\frac{4}{9} \frac{ - 4}{3} \frac{ - 7}{ - 12} \frac{ - 11}{24}$
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Answer 1

Question

Arrange the following rational number in the descending order.

$\frac{4}{9} \frac{ - 4}{3} \frac{ - 7}{ - 12} \frac{ - 11}{24}$

Answer

$\large \bf \frac{4}{9} \: \: \: \frac{ (- 4)}{ \: 3} \: \: \: \frac{ (- 7)}{( - 12)} \: \: \: \frac{( - 11)}{ \: 24}$

The LCM of the given numbers is (-72).

Let's calculate each term,

$\tt \mapsto \frac{4}{9} = \frac{4 \times ( - 8)}{ - 72} = \frac{( - 32)}{ - 72} = \frac{ \cancel - 32}{ \cancel - 72} = \bf \frac{32}{72}$

$\tt \mapsto \frac{( - 4)}{3} = \frac{4 \times ( - 24)}{ - 72} = \frac{( - 96)}{ - 72} = \frac{ \cancel - 96}{ \cancel - 72} = \bf \frac{96}{72}$

$\tt \mapsto \frac{( - 7)}{( - 12)} = \frac{( - 7)\times 6}{ - 72} = \frac{( - 42)}{ - 72} = \frac{ \cancel - 42}{ \cancel - 72} = \bf\frac{42}{72}$

$\tt \mapsto \frac{( - 11)}{( - 24)} = \frac{( - 11)\times 3}{ - 72} = \frac{( - 33)}{ - 72} = \frac{ \cancel - 33}{ \cancel - 72} = \bf\frac{33}{72}$

The numerator are 32,96,42 and 33

Here,we find that 32<33<42<96.

Therefore the descending order are:-

$\large \rm\frac{4}{9} < \: \: \:\frac{( - 11)}{ \: 24} < \: \: \: \frac{ (- 7)}{( - 12)} < \: \: \: \frac{ (- 4)}{ \: 3}$