Question

Write all the properties of rational numbers in maths

Answer 1

i) Closure property :

The sum of any two rational numbers is always a rational number. This is called ‘Closure property of addition’ of rational numbers. Thus, Q is closed under addition

If a/b and c/d are any two rational numbers, then (a/b) + (c/d) is also a rational number.

Example :

2/9 + 4/9 = 6/9 = 2/3 is a rational number.

(ii) Commutative property :

Addition of two rational numbers is commutative.

If a/b and c/d are any two rational numbers,

then (a/b) + (c/d) = (c/d) + (a/b)

Example :

2/9 + 4/9 = 6/9 = 2/3

4/9 + 2/9 = 6/9 = 2/3

Hence, 2/9 + 4/9 = 4/9 + 2/9

(iii) Associative property :

Addition of rational numbers is associative.

If a/b, c/d and e/f are any three rational numbers,

then a/b + (c/d + e/f) = (a/b + c/d) + e/f

Example :

2/9 + (4/9 + 1/9) = 2/9 + 5/9 = 7/9

(2/9 + 4/9) + 1/9 = 6/9 + 1/9 = 7/9

Hence, 2/9 + (4/9 + 1/9) = (2/9 + 4/9) + 1/9

(iv) Additive identity :

The sum of any rational number and zero is the rational number itself.

If a/b is any rational number,

then a/b + 0 = 0 + a/b = a/b

Zero is the additive identity for rational numbers.

Example :

2/7 + 0 = 0 + 2/7 = 27

v) Additive inverse :

(- a/b) is the negative or additive inverse of (a/b)

If a/b is a rational number,then there exists a rational number (-a/b) such that a/b + (-a/b) = (-a/b) + a/b = 0

Example :

Additive inverse of 3/5 is (-3/5)

Additive inverse of (-3/5) is 3/5

Additive inverse of 0 is 0 itself.