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Because "opposite" doesn't mean anything with respect to numbers, or rather, it doesn't have a unique and definite meaning with respect to numbers.

Q: Why is the reciprocal of a nonzero number is not the same as the opposite of the number?

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For numbers with ordinary multiplication defined on them, they are the same.

The property of the reciprocal of the opposite of a number is: Reciprocals of inverse values are themselves inverse values. i.e. for b = (-1)a , the reciprocal 1/b = (-1) 1/a The negative or positive status of a reciprocal is the same as that of the original number.

A whole number is any number that is not a fraction, decimal, or mixed number. A nonzero whole number is the same, except that it doesn't equal zero.

The cosecant is the reciprocal of the sine function. Now, the reciprocal of a positive number is positive, and the reciprocal of a negative number is negative.

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Related questions

What is the inverse reciprocal of 0.01

For numbers with ordinary multiplication defined on them, they are the same.

The property of the reciprocal of the opposite of a number is: Reciprocals of inverse values are themselves inverse values. i.e. for b = (-1)a , the reciprocal 1/b = (-1) 1/a The negative or positive status of a reciprocal is the same as that of the original number.

Actually it IS. perpendicular lines have opposite reciprocal slopes and parallel lines have the same slope.

That depends what you mean with "opposite". Two important math concepts are:a) The additive inverse. That's the same number, with a minus in front of it (a number plus its additive inverse = 0).b) The multiplicative inverse, also called the reciprocal. One divide by the number. For a fraction, you can simply exchange numerator and denominator to get the reciprocal. (A number times its reciprocal = 1.)

The additive opposite of a positive is a negative, and the opposite of a negative is a positive. If you reverse the sign twice (opposite of opposite) you have the original number. The same applies to an inverse (multiplicative opposite): the inverse of any inverse for a nonzero number is the original number. n (1/n)(n) = n

That is the definition of reciprocal.

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A mathematical element that when added to another numeral makes the same numeral

A whole number is any number that is not a fraction, decimal, or mixed number. A nonzero whole number is the same, except that it doesn't equal zero.

The cosecant is the reciprocal of the sine function. Now, the reciprocal of a positive number is positive, and the reciprocal of a negative number is negative.

1