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Q: What numbers will produce a rational number when multiplied by?

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Every rational number does.

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.

Yes.

A mixed number is a rational number. Mixed numbers are not a rational number but many of them.

At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.

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Any number will be a rational number when multiplied.0 multiplied by any real number is rational and so it will produce a rational number when multiplied.If x is any non-zero number (rational or not), then since it is non-zero, 1/x is defined and x*(1/x) = 1 which is rational. So any non-zero number will produce a rational number when multiplied.Thus any number will produce a rational number when multiplied.

Any irrational number multiplied by 0.5 will remain irrational. Any rational number multiplied by 0.5 will remain rational.

Yes. Since 0.555 and 0.5 are both rational numbers, their product will be rational.

Every rational number does.

The product of two rational numbers is a rational number. All decimal numbers that terminate or end with a repeating sequence of digits are rational numbers. As both 0.54732814 (as written) and 0.5 are terminating decimals, they are both rational numbers. As 0.54732814 is a rational number and 0.5 is a rational number, their product will also be a rational number.

Please don't write "the following" if you don't provide a list. Any rational number will work in this case. Any irrational number will not.

Any and every rational number.

Any other rational number.

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.

Every irrational number, when multiplied by 0.5 will produce an irrational number.

Any other rational number.

Every irrational number, when multiplied by 0.4 will produce an irrational number.

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