Page 55 - ICSE Math 7

4 Rational Numbers

Key Concepts

• Rational Numbers • Comparison of Rational Numbers
• Absolute Value of a Rational Number • Addition and Subtraction of Rational Numbers
• Equivalent Rational Numbers • Multiplication and Division of Rational Numbers
• Representation of Rational Numbers on a Number Line • Decimal Representation of Rational Numbers
• Standard Form of Rational Numbers

We have already studied about natural numbers, whole numbers, integers
and fractions. The need to extend our number system arises when we have
to divide an integer by another integer. Let’s understand this with the help of
5
examples. We can easily represent a hot air balloon flying at the height of km
3 6
above sea level. But how do we represent a whale swimming km below sea
5
level? Can we represent this depth as –3 km which is neither an integer nor a
5
fraction? We have not dealt with such numbers till now. Therefore, to express
such numbers the need to extend our number system arises. Such numbers are
categorized as rational numbers.

Rational Numbers

p
The numbers of the form , where p and q are integers and q ≠ 0, are called rational numbers.
q
4 –7 3
For example, , and are rational numbers.
5 9 4
p
In a rational number , the integer p is the numerator, and the integer (q ≠ 0) is the denominator.
q
3
Thus, in , the numerator is 3 and the denominator is 5.
5
Let learn more about rational number.
• Every natural number is a rational number but a rational number need not be a natural number.
3
2
1
n
We can write 1 = , 2 = , 3 = and so on. Hence, every natural number n can be written as
1 1 1 1
3 4 1
which is always a rational number. But, rational numbers like , , and so on are not natural
numbers. 5 9 3
• Every integer is a rational number but a rational number need not be an integer.

1
2
We know that 1 = , 2 = , –11 = –11 , –31 = –31 and so on. In general, any integer n can be
1
1
1
1
n 3 –5 11
written as n = which is a rational number. But rational numbers like , , are not integers.
1 7 9 –5
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