# What are all the properties of real numbers? (multiplication and addition please)

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Properties of real numbers with respct to addition and multiplication

1. Addition

(i) Closed

if a and b are real numbers then a+b is also real number.

(ii) Commutative

if a and b are real number .

a+b=b+a

(iii) Associative

if a ,b and c are real numbers then

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

(iv) Identity element Zero

a is real number then

a+0=0+a=a

(v) Additive inverse

a is real number then there exist real number b such that

a+b=0

a=-b

i.e b=-a

2. Multiplication

(i) Closed

if a and b are real numbers then axb is also real number.

(ii) Commutative

if a and b are real number .

a x b=b x a

(iii) Associative

if a ,b and c are real numbers then

a x (b x c)=(a x b) x c

(iv) Identity element one

a is real number then

a x 1=1 x a=a

(v) Multplicative inverse

a is real number then there exist real number b such that

a x b= 1

a=1/b

i.e b=1 / a

3. Distributive property over addition

If a,b and c are real numbers then

a x (b+c)= a x b+ a x c