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Question

Which of the two rational numbers is greater in the given pair?
(i) 38 or 0
(ii) -29 or 0
(iii) -34 or 14
(iv) -57 or -47
(v) 23 or 34
(vi) -12 or -1

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Solution

We know:
(i) Every positive rational number is greater than 0.
(ii) Every negative rational number is less than 0.

Thus, we have:

(i)38 is a positive rational number.
38>0

(ii)-29 is a negative rational number.
-29<0

(iii) -34 is a negative rational number.
-34<0
Also,
14 is a positive rational number.
14>0
Combining the two inequalities, we get:
-34<14

(iv)Both -57 and -47 have the same denominator, that is, 7.
So, we can directly compare the numerators.

-57<-47

(v)The two rational numbers are 23 and 34.
The LCM of the denominators 3 and 4 is 12.
Now,
23=2×43×4=812
Also,
34=3×34×3=912
Further
812<912

23<34

(vi)The two rational numbers are -12 and -1.
We can write -1=-11.
The LCM of the denominators 2 and 1 is 2.
Now,
-12=-1×12×1=-12
Also,
-11=-1×21×2=-22
-21<-11
-1<-12

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