- 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.
|
 |
I am very impressed by your explanation and your explanation is very good rational numbers are whole numbers,fractions and decimals these are the numbers we use in our daily lives. They can be written as a ratio of two integers in the form a/b where a and b are integers and b is nonzero.
ReplyDeleteWhat are the Properties of Rational Numbers