Properties of Rational Number
Numbers that can be expressed in the form p/q, where p and q are integers and q≠0, are known as rational numbers. The collection of rational numbers is denoted by Q. These rational numbers satisfies various laws or properties that are listed below:
Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number, then we say that rational numbers satisfy the closure law.
Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:
Commutative law under addition: a+b = b+a Commutative law under multiplication: axb = bxa
Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:
Associative law under addition: a+(b+c) = (a+b)+c Associative law under multiplication: a(bc) = (ab)c
0 is the additive identity for rational numbers.
1 is the multiplicative identity for rational numbers.
The additive inverse of a rational number p/q is -p/q, and the additive inverse of -p/q is p/q.
If p/q x a/b = 1, then a/b is the reciprocal or multiplicative inverse of p/q , and vice versa.
For all rational numbers, p, q and r, p(q + r) = pq + pr and p(q - r) = pq - pr , is known as the distributive property.
