Q. 123.8( 10 Votes )
(i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?
Answer :
(i) No rational numbers are not always closed under division,
Since, 
which is not a rational number
(ii) No rational numbers are not always commutative under division,
Let 
and 
be two rational numbers.
And
Therefore,
Hence, rational numbers are not always commutative under division
(iii) No rational numbers are not always associative under division,
Let 
, 
and 
be two rational numbers.
And
Therefore,
Hence, rational numbers are not always associative under division.
(iv) No we cannot divide 1 by 0.
Since, 
which is not defined.
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Verify the property: 
by taking:
(i) 
(ii) 
(iii) 
(iv) 
The sum of the two numbers is 
. If one of the numbers is 
, find the other
The sum of two numbers is 
. If one of the numbers is 
, find the other
Tell which property allows you to compare
Find the multiplicative inverse of
(i) 
(ii) 
What number should be addede to
to get
?
