## Properties of Rational Number

1. Summary

- 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**.

3. Activities & Simulations

4. Teacher Solved Exercises

6. Related Concepts

8. Contributors