Class 8 Maths- Rational Number

Rational number – basics

Rational number: A number which is already in the form or a number which can be expressed in the form, such that the following two conditions hold true -

a.    p and q are integers and

b.    q ¹ 0

Example: is a rational number because 2 and 3 are integers. Similarly  and  are rational numbers as -5, 7, 5, -9 are all integers.

Let’s revisit what we already know about numbers.

Number system was in response to the need to measure and express the quantity of things in our day to day life such as the number of family members, number of cattles, count of money, height and weight of things, time, month and year of the day, number of trees in a garden or fruits gathered in a day.

Interestingly, the things that are part of the nature are all ‘full’ i.e. 1, 2, 3, 4 … 100, 999, 99999, 67655479, 888888888 etc. and these ‘full numbers’ are therefore called ‘Natural numbers’. There are no ‘half’ (e.g. no half tree) or ‘zero’ (e.g. no ‘0 kg’ stone) in nature.

Also note that all natural numbers are positive only (i.e. greater than zero) because in nature things cannot exist in any form other than what we can see, touch or feel.

However, in the world of man-made things and numeric calculations we come across –

a.    things which are a part of full (e.g. pieces of a birthday cake)

b.    zero (e.g. 0 marks in exams)

c.    negative numbers (e.g. loan from someone)

d.    greater-than-one (>1) ‘non-full’ numbers (e.g. 54.5% marks in an exam)

To sum, rational numbers are the numbers of the type ‘a’, ‘c’ and‘d’. And numbers of the type ‘b’ and ‘c’ together with natural numbers are called integers.

Rational numbers are in between two successive integers i.e. between two successive positive or negative integers.

In other words, Rational number = ‘Integer + fraction’ i.e. a ‘positive or negative whole number’ plus a fraction makes a rational number.