Question

Write the properties of rational numbers with suitable example

Answer 1

Properties of rational numbers : There are some properties of rational numbers like closure property, commutative property and associative property.

(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. 

(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

Example : 

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

(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

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