NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

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Chapter 9 : Rational Numbers

INTRODUCTION :
In Previous classes, the students have learned the different types of numbers including natural numbers, whole numbers, integers, etc. Now, In this Chapter of Class 7 the students will understand about rational numbers. This chapter explains almost all the concepts that a student of Class 7 has to learn about the rational numbers. this chapter of Class 7 also describes the method of representing a rational number on a number line as well as the method of finding rational numbers between 2 rational numbers.
This Chapter contains 2 exercises, and The Content available on this page provides Brief Explanation of this Chapter and solutions for the questions present in the NCERT Exercises. Now, let's look at some of the concepts which we will discussed in this chapter.
1. Introduction to Numbers 
2. Equivalent Rational Numbers
3. Positive and Negative Rational Numbers
4. Rational Number On Number Line
5. Rational Numbers in Standard Form
6. Comparison of Rational Number
7. Rational Numbers b/w Two rational Number
8. Operations on Rational numbers.

CHAPTER OVERVIEW :
# A number which can be written in the form p/q, where p and q are integers and q ≠ 0 is called a rational number. 

# All integers and fractions are rational numbers.

# A rational number p/q is said to be in the (lowest form / simplest form / standard form) if p and q have no common factor other than 1, Where q ≠ 0.

# If the numerator and denominator of a rational number are multiplied or divided by a non-zero integer, we get a rational number which is said to be equivalent to the given rational number. 

For example :-

                             OR         

** Here -6/14 is the equivalent form of -3/7.

# Addition, subtraction, multiplication and division of rational numbers are done in the same way as we do for fractions.

* Two rational numbers with the same denominator can be added by adding their numerators, keeping the denominator same. Two rational numbers with different denominators are added by first taking the LCM of the two denominators and then converting both the rational numbers to their equivalent forms having the LCM as the denominator. 

For example :-

** Here LCM of 3 and 8 is 24.

* While subtracting two rational numbers, we add the additive inverse of the rational number to be subtracted to the other rational number.

For example :-


* To multiply two rational numbers, we multiply their numerators and denominators separately, and write the product as  -

* To divide one rational number by the other non-zero rational number, we multiply the rational number by the reciprocal of the other. 

For example :-


# Rational numbers are classified as positive, zero or negative rational numbers. When the numerator and denominator both are positive integers or both are negative integers, it is a positive rational number. When either the numerator or the denominator is a negative integer, it is a negative rational number.

# The number 0 is neither a positive nor a negative rational number

# Rational numbers can be represented on a number line.

# Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.

NCERT EXERCISE WISE SOLUTIONS :

NCERT Solutions for Class 7 Math Chapter 9 : Rational Numbers are available here. we have prepared step by step solutions with detailed video explanations. We advise students who want's to score good marks in Mathematics, to go through these solutions and strengthen their knowledge.

- Exercise 9.1 Solutions -

Question 1... Class 7 Math Ex.9.1
List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii) -4/5 & -2/3
(iv) -1/2 and 2/3

Click here for more Solutions....
- Exercise 9.2 Solutions -
Question 1... Class 7 Math Ex.9.2
Find the sum:

- Extra Questions -
# Practice Questions
Question 1...
Write each of the following rational numbers with positive denominators: 
 5/–8 , 15/–28 , –17/–13.
Question 2...
Express 3/4 as a rational number with denominator:
(i) 36 
(ii) – 80
Question 3...
Reduce each of the following rational numbers in its lowest form:
(i) – 60/ 72
(ii) 91/ – 364


# Fill in the Blanks
Q1) 2/3 and -5/4 are ___rational____  numbers.
Q2) The _____additive________  inverse of a/f is -a/f .
Q3) The addition and multiplication of whole numbers, integers and rational numbers is ___________.


# True - False
Q1) Every natural number is a rational number but every rational number need not be a natural number.
Q2) Zero is a rational number.
Q3) Every integer is a rational number but every rational number need not be an integer.


# MCQ's
Q1) Which of the following rational numbers is equivalent to 2/3 ?
a) 3/2
b) 4/9
c) 4/6
d) 9/4
Q2) Which of the following rational numbers is in standard form?
a) 20/30
b) 10/4
c) 1/2
d) 1/-3
Q3) The Sum of -3/2 and 1/2 is 
a) -1
b) -2
c) 4
d) 3


# Self Evaluation Test -
This is a quiz based test which is consist of 20 Multiple Choice Questions to test your Understanding about this Chapter...


Chapter 9 : Rational Numbers
RELATED LINKS :-
Chapter 7   : Linear Equations In One Variable
Chapter 8   : Understanding Quadrilaterals
Chapter 9   : Rational Numbers
Chapter 10 : Practical Geometry
Chapter 11 : Data Handling

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