**1. Additive Properties (Properties due to Addition): Properties of Rational Numbers**

** a) Closure Property of Addition: **The Set of Rational Numbers is closed with respect to the operation of Addition. In general, it means that the sum of Rational Numbers is always a Rational Number.

** b) Commutative Law of Addition**: If **a **and **b** are two Rational Numbers, then

** a** + **b** = **b** + **a**.

This is know as Commutative Law of Addition in the Set of Rational Numbers.

** c) Associative Law of Addition**: If a, b and c are three Rational Numbers, then

** a** + (**b** + **c**) = (**a** + **b**) + **c**

This is know as the Associative Law of Addition in the Set of Rational Number.

** d) Existence of Additive Identity: **For every Rational Number **a, **there exist a unique Rational Number **0 (Zero)** such that

** 0** + **a = a** + **0 = a**

** 0 (Zero)** is called the Additive Identity in the Set of Rational Numbers** **

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** e) Existence of Additive Inverse: **For every Rational Numbers **a, **there exist a unique Rational Number **–a **such that

** a** + (–**a) = **–**a** + **a = 0**

** a** is called the Additive Inverse of –**a **and vice-versa in the Set of Rational Numbers** **

** 2. Multiplicative Properties (Properties due to Multiplications)**:

** a) Closure Property of Multiplication**: The Set of Rational Numbers is closed with respect to the operation

of Multiplication. In general, it means that the Product of Rational Numbers is always a Rational Number.

This is know as the Close Property of Multiplication in the Set of Rational Numbers.

** b) Commutative Law of Multiplication**: If **a **and **b** are two Rational Numbers, then

** a** × **b** = **b** × **a**.

This is know as the Commutative Law of Multiplication in the Set of Rational Numbers

** c) Associative Law of Multiplication**: If a, b and c are three Rational Numbers, then

** a** × (**b** × **c**) = (**a** × **b**) × **c**

This is know as the Associative Law of Multiplication in the Set of Rational Numbers.

** d) Existence of Multiplicative Identity**: For every Rational Number **a**, there exist a unique Rational Number **1 (one) **such that

** a **× **1 = 1 **× **a** = **a**

**1 (one)** is call the Multiplicative Identity in the Set of Rational Numbers

**Fast Fact:-**

**(i)** ** The Set of Rational Numbers is close with respect to the operation of Subtraction.** The Difference of two Rational numbers is always a Rational Number.

*Illustrate yourself with suitable example.*

* (ii)The Set of Rational Numbers is close with respect to the operation of Division. The Quotient of two Rational Numbers is always a Rational Number.*

*Illustrate yourself with suitable example.*

* (iii) All Natural Numbers, Whole Number and Integers are Rational Numbers. Illustrate yourself with suitable example.*

### Factors and Multiples -Factors, Common Factors, Highest Common Factors (H.C.F.)

**Enquiry related to SBI Balance Enquiry and Mini Statement of SBI Account**

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