Rational Numbers-Notes

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