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Q: The product of rational number and its reciprocal?

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You take its reciprocal, that is you divide 1 by the number. A rational number can be written as a fraction with integer values in both the numerator and denominator, j/k. The multiplicative inverse of a number is what you have to multiply by to get a product of 1. Putting these ideas together, the multiplicative inverse is the reciprocal, or k/j: (j/k) * (k/j) = 1.

No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.

Dividing by a non-zero rational number is the same as multiplying by its reciprocal.

It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.

Related questions

No. 0 is rational and has no reciprocal.

It is another positive rational number. The reciprocal of p/q is q/p.

The product of a number and its reciprocal is always one. That's what reciprocal means.

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The product of a number and its reciprocal is one. A reciprocal is, quite simply, the opposite of the number.

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You can multiply any pair of rational numbers as well as any irrational number and its reciprocal (or a rational multiple of its reciprocal. Thus pi * 3/7*(1/pi) is rational.

Yes.

The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.

The product of any non-zero number and its reciprocal is 1.

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