NCERT Class 8 Maths Chapter 3
A Story of Numbers
NCERT Class 8 Maths Chapter 3 (Ganita Prakash) takes students on a journey through the number system — from natural numbers to integers, fractions, and rational numbers. This CBSE chapter helps students understand the properties of rational numbers, their representation on a number line, and operations on them. The chapter builds a deep conceptual foundation rather than just procedural calculation skills.
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Key Terms
- Rational Number
- A number that can be expressed in the form p/q where p and q are integers and q ≠ 0; includes integers, fractions, terminating decimals, and repeating decimals.
- Irrational Number
- A number that cannot be expressed as a fraction p/q; its decimal expansion is non-terminating and non-repeating; e.g., √2, √3, π.
- Number Line
- A straight line on which every point represents a real number; positive numbers are to the right of zero, negative numbers to the left.
- Additive Inverse
- The additive inverse of a number a is -a, such that a + (-a) = 0; e.g., the additive inverse of 3/4 is -3/4.
- Multiplicative Inverse
- The multiplicative inverse (reciprocal) of a/b is b/a, such that (a/b) × (b/a) = 1; e.g., the reciprocal of 2/3 is 3/2.
- Closure Property
- A set of numbers is closed under an operation if performing that operation on members of the set always produces a member of the same set; rational numbers are closed under +, -, ×, and ÷ (excluding ÷ by 0).
- Density of Rational Numbers
- The property that between any two distinct rational numbers there exist infinitely many other rational numbers.
Frequently Asked Questions
What are rational numbers Class 8 Maths?▾
A rational number is any number that can be written as a fraction p/q, where p and q are integers and q is not zero. Examples include 3/4, -5/2, 7 (=7/1), 0 (=0/1), -3, 1.5 (=3/2). All integers and fractions are rational numbers. NCERT Class 8 Maths Chapter 3 explores their properties extensively.
What is the difference between rational and irrational numbers Class 8?▾
Rational numbers can be expressed as p/q (fraction of integers) and have terminating or repeating decimals (e.g., 1/4 = 0.25; 1/3 = 0.333...). Irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimals (e.g., √2 = 1.41421..., π = 3.14159...). Both types together form the real numbers.
What are the properties of rational numbers Class 8 NCERT?▾
Rational numbers satisfy: (1) Closure under +, -, ×, ÷ (except ÷ 0), (2) Commutativity: a+b = b+a and a×b = b×a, (3) Associativity: (a+b)+c = a+(b+c), (4) Distributivity: a×(b+c) = a×b + a×c, (5) Additive identity: a+0 = a, (6) Multiplicative identity: a×1 = a, (7) Additive and multiplicative inverses exist.
How do you find rational numbers between two numbers Class 8?▾
Method 1 (Mean method): The average (a+b)/2 always lies between a and b. Repeat to find more. Method 2 (Equivalent fractions): Convert both numbers to equivalent fractions with the same denominator, then list integers between them. Example: between 1/3 and 1/2, use 2/6 and 3/6 — so 5/12, 7/24, etc. lie between them.
How are negative rational numbers represented on a number line Class 8?▾
On a number line, positive rational numbers lie to the right of zero and negative rational numbers lie to the left. For example, -3/4 is three-quarters of the way from 0 towards -1. The further left a number is, the smaller its value. Rational numbers are dense on the number line — between any two, there are infinitely many more.
What is the additive inverse of a rational number Class 8?▾
The additive inverse of a rational number a/b is -a/b, because a/b + (-a/b) = 0. For example, the additive inverse of 2/3 is -2/3; the additive inverse of -5/7 is 5/7. Every rational number has an additive inverse. This is different from the multiplicative inverse (reciprocal), which is b/a.
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