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Important Facts about Rational Numbers

Raunak, Ruhi, Neha, and Rehan are playing the "Galaxy of Numbers" game. In the game the

numbers are categories are as follows:
Universe for rational numbers, the Milky Way for integers, the Solar System for whole numbers,

and Earth for natural numbers.
Raunak starts by saying '1' and Ruhi responds with "Earth." Neha follows with "Solar System" and
Rehan says "Milky Way."

−3
Next Rehan says "Milky Way" for and he loses. Think and Answer
5
Do you know why? • Is 0 a rational number? Can you
−7 write it in the form of p ?
Suppose integer –7 can be written as 1 , where –7 and 1 q
both are integers and 1 ≠ 0. • Can you figure out why he lost?

So, it is also a rational number.

3 − 2 11
But the rational numbers such as , , , ... are not integers.
7 9 − 13

• All integers are rational numbers, but all rational numbers are Rational numbers
not integers. – 1 3
2 Integers 5
• Also, all fractions are rational numbers but all rational numbers 5 –11 –5 3
are not necessarily fractions. – 9 Whole numbers 2 7
0
Natural
−3 numbers
For example: is a rational number, but it is not a fraction, 1, 2, 3,...
4
because the numerator of this number, i.e., –3 is not a whole

number.

Hence, the rational numbers can be in the form of integers, whole Remember
numbers, natural numbers, and fractions, but the converse is not Mixed fractions are also
rational numbers.
always true.

Positive and Negative Rational Numbers

A rational number is said to be positive if its numerator and denominator are either both positive

or both negative.
2 9 − 13
For example: , , , etc., are the positive rational numbers.
5 11 − 17
A rational number is said to be negative if either of its numerator
0 is also a rational
or denominator is negative. Note: number which is neither
−3 7 −11 positive nor negative.
For example: , , , etc., are the negative rational numbers.
4 −12 13

55 Rational Numbers