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−5 2 1 8
Example 6: Arrange the following rational numbers in ascending order: ,, ,
9 5 −3 −15
Solution: To arrange the given rational numbers in ascending order, first convert the given rational
numbers into their standard form, if any. And express each of the rational numbers to an equivalent
rational number with the denominator equal to the LCM.
−5 2 −1 −8
The rational numbers with positive denominators are: ,, ,
9 5 3 15
Now, LCM of 9, 5, 3 and 15 is 45.
−5 5 −25 2 9 18
\ × = , × =
9 5 45 5 9 45
−1 × 15 = −15 , −8 × 3 = −24

3 15 45 15 3 45
Q –25< – 24 < – 15 < 18
−25 −24 −15 18
\ < < <
45 45 45 45
Thus, the ascending order of the given rational numbers is: −5 < −8 < −1 < 2
9 15 3 5
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MAths connect

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Parliament, as well as elected members of the Legislative Assemblies of States and Union Territories.
The vote weightage of each MLA is not equal to that of each MP, and the vote weightage of each state's
MLA varies depending on the state's population. The vote weightage of an MLA is calculated by dividing
the state's population by the number of MLAs, and this value is then adjusted using the 1971 census as a
standard reference. Search online to collect data on the number of MLAs in various states, the population
from the 1971 census, and calculate the vote weightage of MLAs from different states. Identify which state's
MLAs have more weightage in presidential elections.

Rational Numbers Between Two Rational Numbers

Let us find the integers between two integers, e.g., –4 and –3 or 2 and 6.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
Clearly, there is no integer between –4 and –3, and there are 3 integers between 2 and 6.

Hence, we can say that there are finite or limited number of integers between two integers.

But, we can always find infinitely many rational numbers between any two rational numbers.
−1 2
Let us find some rational numbers between and .
2 3
Write the equivalent rational numbers for the given numbers. As the LCM of 2 and 3 is 6, we have,

−×13 = −3 and 22 = 4
×
23 6 32 6
×
×
61 Rational Numbers