NCERT Book Class 7 Maths Rational Numbers

Rational Numbers

9.1 INTRODUCTION

You began your study of numbers by counting objects around you. The numbers used for this purpose were called counting numbers or natural numbers. They are 1, 2, 3, 4, ... By including 0 to natural numbers, we got the whole numbers, i.e., 0, 1, 2, 3, ... The negatives of natural numbers were then put together with whole numbers to make up integers. Integers are ..., –3, –2, –1, 0, 1, 2, 3, .... We, thus, extended the number system, from natural numbers to whole numbers and from whole numbers to integers.

You were also introduced to fractions. These are numbers of the form numerator/denominator,where the numerator is either 0 or a positive integer and the denominator, a positive integer. You compared two fractions, found their equivalent forms and studied all the four basic operations of addition, subtraction, multiplication and division on them. In this Chapter, we shall extend the number system further. We shall introduce the concept of rational numbers alongwith their addition, subtraction, multiplication and division operations.

9.2 NEED FOR RATIONAL NUMBERS

Earlier, we have seen how integers could be used to denote opposite situations involving numbers. For example, if the distance of 3 km to the right of a place was denoted by 3, then the distance of 5 km to the left of the same place could be denoted by –5. If a profit of Rs 150 was represented by 150 then a loss of Rs 100 could be written as –100.

There are many situations similar to the above situations that involve fractional numbers.

You can represent a distance of 750m above sea level as 3/4 km. Can we represent 750m

below sea level in km? Can we denote the distance of 3/4 km below sea level by –3/4 ? We can see –3/4 is neither an integer, nor a fractional number. We need to extend our number system to include such numbers.

9.3 WHAT ARE RATIONAL NUMBERS?

The word ‘rational’ arises from the term ‘ratio’. You know that a ratio like 3:2 can also be written as 3/2

Here, 3 and 2 are natural numbers.

Similarly, the ratio of two integers p and q (q ¹ 0), i.e., p:q can be written in the form p/q . This is the form in which rational numbers are expressed.

A rational number is defined as a number that can be expressed in the form p/q , where p and q are integers and q 

Thus, 4/5 is a rational number. Here, p = 4 and q = 5.

Is –3/4 also a rational number? Yes, because p = – 3 and q = 4 are integers.

You have seen many fractions like 3 /8,4/8,5/3 etc. All fractions are rational numbers. Can you say why?

How about the decimal numbers like 0.5, 2.3, etc.? Each of such numbers can be

written as an ordinary fraction and, hence, are rational numbers. For example, 0.5 = 5/10 ,= 0.333 = 333/1000 etc.

Please refer to attached file for NCERT Class 7 Maths Rational Numbers