# CBSE Class 8 Math, Rational Numbers

Notes on Rational Numbers
▪  Rational Number- Any Number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is known as rational number. The collection or group of rational numbers is denoted by Q.
Properties of a Rational Number
▪  Closure- Rational numbers are closed under addition, subtraction and multiplication. For eg.- If p and q are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number. This is known as the closure law
▪  Commutativity- Rational numbers are commutative under addition and multiplication. If p and q are two rational numbers, then:
Commutative law under addition says- p + q = q + p.
Commutative law under multiplication says p x q = q x p.
Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.
▪  Associativity- Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:
Associative property under addition: p + (q + r) = (p + q) + r
Associative property under multiplication: p(qr) = (pq)r
▪  Role of zero and one- 0 is the additive identity for rational numbers. 1 is the multiplicative identity for rational numbers.
▪  Multiplicative inverse- If the product of two rational numbers is 1, then they are called multiplicative inverse of each other.
Eg. 4/9 * 9/4 = 1