RBSE Class 8 Maths Notes Chapter 1 Rational Numbers

These comprehensive RBSE Class 8 Maths Notes Chapter 1 Rational Numbers will give a brief overview of all the concepts.

RBSE Class 8 Maths Chapter 1 Notes Rational Numbers

→ Natural Numbers: The counting numbers 1, 2, 3, .............. are called natural numbers.

→ Whole Numbers: All natural numbers together with 0, i.e. 0, 1, 2, 3, ... are called whole numbers.

→ Integers: The whole numbers together with the negative of counting numbers are known as integers, i.e. .............. - 3, - 2, - 1, 0, 1, 2, 3, .............

→ Rational Numbers: Rational number is the quotient of two integers provided the denominator is a non zero integer, i.e.
Rational number = \(\frac{p}{q}\), where p and q are integers and q ≠ 0.

→ Rational numbers are closed under addition, subtraction and multiplication. Rational numbers are not closed under division.

→ Commutative property of addition and multiplication for any rational numbers are true i.e. a + b = b + a and a × b = b × a for any two rational numbers a and b.

→ Associativity: If a, b and c are three rational numbers, then

• a + (b + c) = (a + b) + c (Associative Property of Addition)
• a × (b × o = (a × b) × c (Associative Property of Multiplication).

→ Subtraction and division are not commutative and associative for rational numbers.

→ Zero is called the identity for the addition of rational numbers. It is the additive identity for rational numbers.
a + 0 = 0 + a = a for any rational number.

→ 1 is the multiplicative identity for rational numbers.
1 × a = a × 1 = a, for any rational number a.

→ \(\left(\frac{-a}{b}\right)\) is the additive inverse of \(\frac{a}{b}\) and \(\frac{a}{b}\) is the additive inverse of \(\left(\frac{-a}{b}\right)\)

→ If \(\frac{a}{b} \times \frac{c}{d}\) = 1, then \(\frac{c}{d}\) is called the reciprocal or multiplicative inverse of \frac{a}{b}. Zero has no reciprocal.

→ For all rational numbers a, b and c

• a (b + c) = ab + ac
• a (b - c) = ab - ac

This is called distributivity of multiplication over addition and subtraction.

→ Between two rational numbers x and y, there is a rational number \(\frac{x+y}{2}\)

→ We can find as many rational numbers between x and y as we want.