Page 10 - Maths Skills - 8

8 Maths

INTRODUCTION
In mathematics we come across different situations. For example, an almirah has some books. If we take 7 books
from it, there will be 13 books remaining.
So, we can write x – 7 = 13
We can solve this equation when x = 20, because this value satisfies the given equation. This solution x = 20 is a
natural number.
But for this equation, x + 9 = 9
The solution gives the whole number 0 (zero).

Thus, if we add 0 to the set of natural numbers, it is called the set of whole numbers. But even whole numbers will
not be sufficient to solve equations of type, x + 15 = 3

We see the value x = –12 can satisfy this equation, but x = – 12 is not a whole number. This leads us to think of
integers.

Think of another case, 2x = 3
Can we find the answer of this equation from the integers? No, for this equation we cannot find a solution from
the integers.
3
We find the number solves this equation. This leads us to the collection of rational numbers.
2

RATIONAL NUMBERS
p
A rational number is a number that can be expressed as , where p and q are both integers and q ≠ 0.
q
In other words, a rational number is also the quotient of two integers p and q in the form p where q ≠ 0.
q

Examples of rational numbers are − 3 5 , 4 , − 7 .
,
5 12 −11 − 8
Since the denominator q can be 1, so all integers are rational numbers. If the numerator p and the denominator q
have the same sign, it is a positive rational number, otherwise, it is a negative rational number.

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For example, − 2 = ; + 2 = 2 are positive rational numbers.
− 3 3 + 3 3
2 2 2 2
; are negative rational numbers.
3 3 3 3
Zero is also a rational number which is neither positive nor negative. As per the conditions of a rational number,

0 0
0 can be expressed as , , etc.
1 − 5
The decimal representation of a rational number always ends finitely in digits or repeats the sequence of digits.
If, however the decimal representation continues forever without repeating, it is an irrational number. So, any real
number that is not rational is irrational.

For example, 2 and π. Fact-o-meter

Other examples of irrational numbers are: � π is an irrational number
� The value of 2 is
5 = 2.2360679...... 1.414213562373095...

7 = 2.64575131, etc. and π is 3.1415926535...