Question

arrange the following rational numbers in ascending orders 4/5,-3/7,-6/-7​

Answer 1

answer:-

We first write the given rational numbers so that their denominators are positive.

We have,

5−8 = 5×(−1)(−8)×(−1) = −58 and 2−3 = 2×(−1)(−3)×(−1)  = −23

Thus, the given rational numbers with positive denominators are

−710, −58, −23

Now, LCM of the denominators 10, 8 and 3 is 2 × 2 × 2 × 3 × 5 = 120

We now write the numerators so that they have a common denominator 120 as follows:

−710 = (−7)×1210×12 = −84120,

−58 = (−5)×158×15 = −75120 and

−23 = (−2)×403×40 = −80120.

Comparing the numerators of these numbers, we get,

- 84 < -80 < -75

Therefore, −84120 < −80120 < −75120 ⇒ −710 < −23 < −58 ⇒ −710 < 2−3 < 5−8

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

−710, 2−3, 5−8