Page 61 - Maths Skills - 7

Rational Numbers 59

INTRODUCTION
Have you ever thought how our life would be without numbers? Numbers define virtually every aspect of our
daily life like our address, phone number, age, size of clothes, quantity of commodities like milk, fruits and
vegetables, etc. Actually our life revolves around numbers in some way or the other.

Numbers which we have already studied are natural numbers, whole numbers, integers and fractions. Let’s
understand with examples the need for extending the number system further. We can easily represent a hot air
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balloon flying at the height of km above sea level. But how do we represent a whale swimming km below
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sea level? Can we represent this depth as −1 km? It is neither an integer nor a fraction. We have not dealt with
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such numbers till now. Therefore, to express such numbers the need to extend our number system arises. Such

numbers are categorized as rational numbers.
p
“A number in the form q , where p and q are integers and q ≠ 0 is called a rational number. ”

A rational number has a numerator and a denominator where denominator is not equal to zero. The set of rational
numbers is denoted by Q.
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Thus, , , , , 0, 9, 3.6, etc. all are rational numbers.
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Rational numbers include all number systems learned till now, i.e. whole numbers, natural numbers, fractions,
integers etc.

SOME IMPORTANT FACTS ABOUT RATIONAL NUMBERS
Fact - 1: Every natural number is a rational number.
3 5
We can write 3 = , 5 = and so on.
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Fact - 2: Zero is a rational number.
0 0 0 0 0
We can write 0 as , , , , and so on. Here, the quotient is zero in each case and the
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denominators are non-zero integers.
Fact - 3: Every fraction is a rational number but every rational number is not a fraction.
Fact - 4: Every integer is a rational number.
1 − 1 − 3 P
We can write 1= , − 1= , −= and so on. Thus, any integer P (say) can be written as which
3
1 1 1 1
is a rational number.

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.

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For example; each of the numbers , , , , is a positive rational number.
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A rational number is said to be negative if its numerator and denominator are such that one of them is a positive
integer and the other is a negative integer.
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For example; each of the numbers , , is a negative rational number.
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