# Class 7 Maths Chapter 9 Exercise 9.1 Pdf Notes NCERT Solutions

Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1 pdf notes:-

- Exercise 9.2`

**Exercise 9.1** Class 7 maths Chapter 9 Pdf Notes:-

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## Ncert Solution for Class 7 Maths Chapter 9 Rational numbers Exercise 9.1 Tips:

**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.

**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 150

was represented by 150 then a loss of 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.

**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 ≠ 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 ≠ 0.

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 1 2/3 , , 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.

**Try These** **1.**Is the number 2/3 rational? Think about it. **2.** List ten rational numbers.

**Numerator and Denominator**

In p/q , the integer p is the numerator, and the integer q (≠ 0) is the denominator.

Thus, in 3/7, the numerator is –3 and the denominator is 7.

Mention five rational numbers each of whose

(a) Numerator is a negative integer and denominator is a positive integer.

(b) Numerator is a positive integer and denominator is a negative integer.

(c) Numerator and denominator both are negative integers.

(d) Numerator and denominator both are positive integers.

Are integers also rational numbers?

Any integer can be thought of as a rational number. For example, the integer – 5 is a

rational number, because you can write it as 5/1. The integer 0 can also be written as 0 = 0/2 0/7or etc. Hence, it is also a rational number.

Thus, rational numbers include integers and fractions.