 NCERT Solutions for Class 7 Maths Chapter 8 Exercise 8.1 Rational Numbers in Hindi and English Medium for CBSE exams 2023-24. All the chapter 8 ex. 8.1 of 7th math is revised according to new syllabus and latest textbooks issued for academic session 2023-24.

• ## NCERT Class 7 Maths Exercise 8.1 Solution in Hindi and English Medium

 Class: 7 Mathematics Chapter: 8 Exercise: 8.1 Topic Name: Rational Numbers Content: Exercise and Extra Questions Session: CBSE 2023-24 Medium: English and Hindi Medium

### Class 7 Maths Chapter 8 Exercise 8.1 Solution

All the solutions and study material are updated according to latest NCERT Books 2023-24. In class 7 math exercise 8.1, we will learn to compare the rational numbers and plotting a rational number on number line. Finding more rational numbers between two given rational number is also important for next classes.

#### Natural Number

The counting number are called natural numbers. Thus, 1, 2, 3, 4, 5, 6, …, etc., are all natural numbers.

#### Whole Numbers

All natural numbers together with 0 (zero) are called whole numbers. Thus, 0, 1, 2, 3, 4, 5, 6, …., etc., are all whole numbers. Clearly, every natural number is a whole number but 0 is a whole number which is not a natural number.

#### Integers

All natural numbers, 0 and negatives of counting numbers are called integers.
Thus, …., – 5, – 4, – 3, -2, – 1, 0, 1, 2, 3, 4, 5, …, etc., are all integers.
1, 2, 3, 4, 5, 6, …., etc., are all positive integers.
– 1, – 2, – 3, – 4, – 5, – 6, …, etc., are all negative integers.
Zero is an integer which is neither positive nor negative.
Clearly, a positive integer is the same as a natural number

#### Fractions

The numbers of the form, where a and b are natural numbers, are called fractions.
Thus 2/3, 5/8, 3/11, 9/23, etc., are all fractions.

#### Rational Numbers

The numbers of the form p/q, where p and q are integers and q ≠ 0. are called rational numbers.
Examples of rational numbers
1. Each of the number 6/8, 9/12, 6/15, is a rational number.
2. Zero is a rational number, since we can write 0 = 0/1, which is the quotient of two integers with a nonzero denominator.
3. Every natural number is a rational number. We can write.
1 = 1/1, 2 = 2/1, 3 = 3/1, ………
In general, if n is a natural number, then we can write it as, which is a rational number.

4. Every integer is a rational number.
If m is an integer then we can write it as m/1, which is clearly a rational number. Thus, every integer is a rational number.
5. Every integer is a rational number. Let a/b be a fraction. Then, a and b are whole numbers and b ≠ 0. But, every whole number is an integer.
Thus, is the quotient of two integers such that b ≠ 0.
So, a/b is a rational number.
Hence, every fraction is a rational number.

#### Positive Rational Numbers

A rational number is said to be positive if its numerator and denominator are either both positive or both negative.
Example: Each of the number 5/7, 13/8, 17/9 etc.

### How are rational numbers used in everyday life?

Share something among friends: For example: if there are four friends and they want to divide a cake equally among themselves, then the quantity of cake that each friend will get will be one-fourth of the cake, that is a rational number 1/4.

### Is 0 a rational number?

Yes, 0 is a rational number. Since we know, a rational number can be expressed as p/q, where p and q are integers and q is not equal to zero.

### What are not irrational numbers?

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333 (the threes go on forever).

### Express each of the following numbers in standard form: (21/35)

(i) The given numbers is (21/35)
HCF of 21 and 35 is 7
So, we divide its numerator and denominator by 7
So, 21/35 = (21/7)/ (35/7) = 3/5

#### Negative Rational Numbers

A rational number is said to be negative if its numerator and denominator are such that one of them is a positive integer and the other is a negative integer.
Example: Each of the number -3/5, 5/-7, -9/11, is a negative rational number.

##### Three Important Properties of Rational Numbers

Theorem-1 of Rational Numbers:
If p/q is a rational number and m is a nonzero integer. Then = (p/q) x (m/m).
Thus, a rational number remains unchanged. if its numerator and denominator are multiplied by the same nonzero integer.

Theorem-2 of Rational Numbers:
If p/q is a rational number and m is a common divisor of p and q, then p/q = (p/m)/ (q/m).
Thus, on dividing the numerator and denominator of a rational number by a common divisor, it remains unchanged.

##### Equivalent Rational Numbers

On multiplying the numerator and denominator of a given rational number by the same nonzero number, we get a rational number equivalent to the given rational number.
Similarly, on dividing the numerator and denominator of a given rational number by a common divisor, we get a rational number equivalent to the given rational number.

##### Standard form of a Rational Number

A rational number p/q
METHOD: In order to express a given rational number in standard form, we first convert it into a rational number whose denominator is positive and then we divide its numerator and denominator by their HCF. is said to be in standard form, if q is positive, and p and q have no common divisor other than 1.

###### For any two rational a/b and c/d numbers and we have (a x d) = (b x c).

Theorem-3 of Rational Numbers
For any two rational numbers a/b and c/d we have (a x d) = (b x c).      Last Edited: April 20, 2023