Properties of Division Of Integers Video Lecture | Advance Learner Course: Mathematics (Maths) Class 6

let us now learn about some of the
properties of division for integers we
have seen earlier that if any two
integers are added the result is an
integer if one integer is subtracted
from any other integer the result is
again an integer
similarly if any two integers are
multiplied the result is an integer now
let us see if an integer is divided by a
nonzero integer will the quotient be
always an integer we know that minus 8
divided by 4 is equal to minus 2 and
minus 16 divided by minus 4 is equal to
4 here the quotients -2 and 4 in both
the cases are integers but when an
integer is divided by another nonzero
integer it is not always possible that
the quotient is an integer
for example minus 5 divided by 3 is not
an integer
hence we draw property one which states
that the collection of integers is not
closed under division property 2 if a a
is not equal to zero is any integer then
a divided by a is equal to 1 a divided
by 1 is equal to a for example 5 divided
by 5 is equal to 1 and minus 7 divided
by 1 is equal to minus 7 property 3 if a
a not equal to 0 is any integer then a
divided by minus a is equal to minus 1
minus a divided by a is equal to minus 1
a divided by minus 1 is equal to minus a
for example 5 divided by minus 5 is
equal to minus 1 and
eight divided by minus one is equal to
eight property for if zero is divided by
any nonzero integer the result is always
zero
for example zero divided by minus nine
is equal to zero hence if a a not equal
to zero is any integer then zero divided
by a always gives the result as zero the
mathematical statements are simplified
in order of