There are a few properties that are applicable while dealing with the Subtraction of Rational Numbers. Check out the Closure, Commutative, Distributive and Associative Properties of Rational Numbers under Subtraction Operation. To help you understand each and every property we have taken enough examples and explained all of them step by step.
Closure Property of Subtraction of Rational Numbers
The Difference between any Two Rational Numbers always results in a Rational Number. Let a/b, c/d be two Rational Numbers then (a/b -c/d) will also result in a Rational Number.
Example
Consider two rational numbers 5/9 and 3/9 then
Subtraction of 5/9-3/9
= 2/9
Therefore, 5/9-3/9 = 2/9 is also a Rational Number.
Commutative Property of Subtraction of Rational Numbers
Subtraction of Two Rational Numbers doesn’t obey Commutative Property. Let us consider a/b, c/d be two rational numbers then (a/b)-(c/d)≠(c/d)-(a/b). Have a look at the Example stated below and verify whether the commutative property is applicable or not.
Example
Consider the rational Numbers 5/8 and 2/8 then
= 5/8 – 2/8
= 3/8
2/8 – 5/8
= -3/8
5/8-2/8≠ 2/8-5/8
Therefore, Commutative Property isn’t applicable for Subtraction.
Associative Property of Subtraction of Rational Numbers
Subtraction of Rational Numbers is not Associative. Let us consider three Rational Numbers a/b, c/d, e/f then (a/b-(c/d -e/f)) ≠ (a/b – c/d) – e/f.
Example
2/8-(4/8-1/8) = 2/8-(3/8)
= -1/8
(2/8-4/8)-1/8 = (-2/8)-1/8
= -3/8
Therefore, 2/8-(4/8-1/8) ≠(2/8-4/8)-1/8.
Distributive Property of Subtraction of Rational Numbers
Multiplication of Rational Numbers is Distributive Over Subtraction. Consider three Rational Numbers then a/b*(c/d-e/f) = a/b*c/d-a/b*e/f.
Example
Consider three Rational Numbers 1/2, 2/3, 4/5 then
1/2(2/3-4/5) = (1/2*2/3 – 1/2*4/5)
= (2/6-4/10)
= (2*5/6*5 – 4*3/10*3)
= (10/30 -12/30)
= -2/30
= 1/2*2/3 – 1/2*4/5
= 2/6-4/10
= -2/30
Therefore, 1/2*(2/3-4/5) = 1/2*2/3 – 1/2*4/5