ANSWER:

First we express the given rational numbers in the form so that their denominators are positive.

We have,

−7−12 = (−7)×(−1)(−12)×(−1), [Multiplying the NUMERATOR and denominator by -1]

⇒ −7−12 = 712

and 11−24 = 11×(−1)(−24)×(−1) = −1124

Thus, given rational numbers are:

49, −56, 712, −1124

Now, we find the LCM of 9, 6, 12 and 24.

Required LCM = 2 × 2 × 2 × 3 × 3 = 72.

We now write the rational numbers so that they have a common denominator 72.

We have,

49 = 4×89×8, [Multiplying the numerator and denominator by 72 ÷ 9 = 8]

⇒ 49 = 3272

−56 = −5×126×12, [Multiplying the numerator and denominator by 72 ÷ 6 = 12]

⇒ −56 = −6072

712 = 7×612×6, [Multiplying the numerator and denominator by 72 ÷ 12 = 6]

⇒ 712 = 4272

−1124 = −11×324×3, [Multiplying the numerator and denominator by 72 ÷ 24 = 3]

⇒ −1124 = −3372

Arranging the numerators of these rational numbers in descending order, we have

42 > 32 > -33 > -60

⇒ 4272 > 3272 > −3372 > −6072 ⇒ −7−12 > 49 > 11−24 > −56

Hence, the given numbers when arranged in descending order are:

−7−12, 49, 11−24, −56.

Explanation: