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Before we start investigating real numbers, it is important to first understand one of their close relatives - rational numbers. In a world full of numbers and uncertainty, rational numbers provide insight that everything can actually be divided logically and fairly. With rational numbers, it even begins to help to make sense of fractions, providing clarity where there was confusion. This is possible because rational numbers are numbers that can be written as
Rational numbers provide us with the understanding of sharing, measuring and balancing in the world of numbers. Rational numbers are everywhere and impact our lives daily, when sharing a bill, baking a cake, sharing a pizza, or solving an equation. In previous classes, students have already studied real numbers, whole numbers, natural numbers, and integers. So, these NCERT solutions for class 8 Maths on Rational Numbers Class 8 will complete the learning of the number system like a cherry on the cake. For quick access to your syllabus, notes, and PDFs, head over to the following link: NCERT.
Students who wish to access the NCERT solutions for class 8, chapter 1, Rational Numbers, can click on the link below to download the entire solution in PDF.
Try These Questions: Closure Property Page Number: 4 |
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | Yes | Yes | ... | No |
Integers | ... | Yes | ... | No |
Whole Numbers | ... | ... | Yes | ... |
Natural Numbers | ... | No | ... | ... |
Answer:
It can be seen that rational numbers, integers, whole numbers, and natural numbers are not closed under division because Zero is included in these numbers. Any number divided by zero is not defined.
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | Yes | Yes | Yes | No |
Integers | Yes | Yes | Yes | No |
Whole Numbers | Yes | No | Yes | No |
Natural Numbers | Yes | No | Yes | Yes |
Try These Questions: Commutative Property Page Number: 6 |
Commutative for
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | Yes | .. | ... | ... |
Integers | ... | No | ... | ... |
Whole Numbers | ... | ... | Yes | ... |
Natural Numbers | ... | ... | ... | No |
Answer:
In rational numbers, a ÷ b ≠ b ÷ a
also a-b ≠ b-a
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | Yes | No | Yes | No |
Integers | Yes | No | Yes | No |
Whole Numbers | Yes | No | Yes | No |
Natural Numbers | Yes | No | Yes | No |
Try These Questions: Associative Property Page Number: 9 |
Associative for
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | ... | ... | ... | No |
Integers | ... | ... | Yes | ... |
Whole Numbers | Yes | ... | ... | ... |
Natural Numbers | ... | No | ... | ... |
Answer:
For associative in multiplication:- a × (b × c) = (a × b) × c
Addition | Subtraction | Multiplication | Division | |
Rational Numbers | Yes | No | Yes | No |
Integers | Yes | No | Yes | No |
Whole Numbers | Yes | No | Yes | No |
Natural Numbers | Yes | No | Yes | No |
Try These Questions: Distributivity Page Number: 12 |
Find using distributivity.
(i)
(ii)
Answer:
(i)
(ii)
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers: Exercise: 1.1 Total Questions: 3 Page Number: 12 |
Question 1: Name the property under multiplication used in each of the following.
(i)
(ii)
(iii)
Answer:
(i) Multiplying any number by 1, we get the same number back.
i.e., a × 1 = 1 × a = a
Hence, 1 is the multiplicative identity for rational numbers.
(ii) Commutativity property states that a × b = b × a
(iii) Here Multiplicative Inverse Property is used.
Each number has an inverse (reciprocal), and the product of a number and its inverse is 1.
In this case,
Question 2: Tell what property allows you to compute
Answer:
By the Associativity property for multiplication, we know that a × (b × c) = (a × b) × c.
Thus property used here is associativity.
Question 3: The product of two rational numbers is always a _______.
Answer:
Rational number. We know that if p and q are 2 rational numbers, then pq is also a rational number.
The topics discussed in the NCERT Solutions for class 8, chapter 1, Rational numbers, are:
Properties Of Rational Numbers
Representation Of Rational Numbers On The Number Line
Rational Numbers Between Rational Numbers
Here are some important formulas that will help students to solve problems related to rational numbers.
Property | Formula |
---|---|
Additive Identity | |
Multiplicative Identity | |
Additive Inverse | |
Multiplicative Inverse | |
Closure (Addition) | |
Closure (Subtraction) | |
Closure (Multiplication) | |
Closure (Division) | Not closed under division |
Commutative (Addition) | |
Commutative (Multiplication) | |
Associative (Addition) | |
Associative (Multiplication) | |
Distributive Property |
For students' preparation, Careers360 has gathered all Class 8 Maths NCERT solutions here for quick and convenient access.
Careers360 also provides well-structured and well-explained solutions for other subjects. The following links can be used for those purposes.
Students can use the following links to download the latest version of the CBSE syllabus and some other reference books for class 8.
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