The product of a number and its reciprocal is always ##1##. Let ##a## be a

The product of a number and its reciprocal is always ##1##.
Let ##a## be any number.
Assume that ##x##is the reciprocal of ##a##.
From definition,
##a####xx####x=1##
So, ##x=1/a##
Hence, the reciprocal of ##a## is ##1/a##.
The reciprocal of ##5## is ##1/5##. The reciprocal of ##-2## is ##-1/2##. Incidentally, the reciprocals of ##1## and ##-1## are ##1## and ##-1## themselves. The reciprocal of ##0## does not exist.
The opposite of a number may be defined in multiple ways.
The numbers which have equal magnitudes but opposite signs are called opposite numbers.
##OR##
The numbers that are equidistant from ##0## on a number line are called opposite numbers of each other.
The product of opposite numbers is always negative of the square of one of the numbers.
Let ##b## is a number.
Let ##y## be its opposite number.
By definition,
##bxxy=-b^2##
So, ##y=-b^2/b=-b##
Hence, for a number ##b## the opposite number is ##-b##
The opposite of ##2## is ##-2## and vice versa.

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