**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.