Subtraction of rational numbers and its properties
Subtraction of rational numbers: If 
and 
are two rational numbers, then subtracting from means adding additive inverse (negative) of to.
and are two rational numbers, then subtracting from means adding additive inverse (negative) of to.
The subtraction of from is written as - .
from is written as - .
Thus, we have - = + 
[\Additive inverse of is
]
- = + [\Additive inverse of is]
Properties of subtraction of rational numbers:
Closure property: If and are any two rational numbers, then – is also a rational number. The subtraction of rational numbers is closed w.r.t. subtraction.
and are any two rational numbers, then – is also a rational number. The subtraction of rational numbers is closed w.r.t. subtraction.
Commutativity: The subtraction of rational numbers is not always commutative. That is, for any two rational numbers and , we have – ≠ –
and , we have – ≠ –
Associativity: The subtraction of rational numbers is not associative, i.e. for any three rational numbers, and 
, we have 
– ≠ – 
, and , we have – ≠ – 
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