The reciprocal of x is 1/x. It's the inverse. The number when multiplied by the original number equals 1.

x * 1/x = 1

For a fraction: x/y * y/x (its reciprocal) = 1.
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
The reciprocal is a number that, when multiplied by the original number, yields 1.
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In simplest terms, the reciprocal of the number 'x' is 1/x.
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The reciprocal of a fraction is the fraction "upside" down.
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Say you have a fraction 'a/b'. The reciprocal is 'b/a'.
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As you can imagine, reciprocals can be defined for functions, too.
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Let's say you have 'x +1'. The reciprocal is 1/(x+1).
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The reciprocal also is defined by exponents.
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Given you have 'x', that is the same as saying you have 'x^1' because any number to the power 1 = itself.
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We also know that any number raised to the 0th power = 1.
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When we multiply the same number raised to powers you add the exponents.
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As noted above, x = x^1
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In general,
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So you probably can guess the reciprocal of 'x^1'.
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'y' has to = -1
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This definition of the reciprocal also reveals that negative exponents can be shown as fractions.
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That's a lot to cover in one answer, but I hope it gives you feel for the definition and usefulness of the reciprocal.
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