Ordering Rational Numbers

Arrange the following rational numbers ascendingly:

−23, 34, −712, 56, −1

Solution

∵ Since L.C.M of the denominators is 12

, then −23 = −812, 34 = 912, 56 = 1012, −1 = −1212

, then the numbers after converting their denominators are:

−812, 912, −712, 1012, −1212

Since −12 < −8 < −7 < 9 < 10, then:

−1212 < −812 < −712 < 912 < 1012

∴ i.e. −1 < −23 < −712 < 34 < 56

Created with Mr. Ayman Hassan for Math Egypt Lovers