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Q: Is the product of a rational number and its multiplicative inverse always one?

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If the multiplicative inverse exists then, by definition, the product is 1 which is rational.

it means reciprocal, the number that multiplies by the original number to get a product of 1. The multiplicative inverse is always 1/x; x=5, then the multiplicative inverse is 1/5. If x=1/2 or .5, the multiplicative inverse is 1/.5, which is also 2.

multiplicative inverse of a number 'p' = 1/p

The multiplicative inverse is also known as the reciprocal. The multiplicative inverse of a number "x" can be expressed as 1/x. In the case of a fraction, exchange numerator and denominator to get the multiplicative inverse.

Always, unless the original number is zero. This does not have an inverse.

Yes.

The product of two rational number is always rational.

The product of two rational numbers is always a rational number.

It is always rational.

Sometimes. Also, when depends on what you mean by "opposite": the additive inverse or the multiplicative inverse.

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

Yes, it is.

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