# 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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