19 Jun The product of a number and its reciprocal is always ##1##.
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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