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CBSE - VIII
Properties of Rational Number
- Numbers that can be expressed in the form
,
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
is
,
and the additive inverse of 
. - If
,
then 
is
the reciprocal or multiplicative inverse of 
,
and vice versa. - For all rational numbers, p, q and r,
and
,
is known as the distributive property.
