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Yes, it is.

Q: Is a rational number multiplied a rational number rational?

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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.

Any rational number will do.

Yes, it is possible only if an irrational number is multiplied with 0.

Maybe. It depends on the number that you are multiplying. Pi multiplied by (1 / 4pi) = 1/4. A quarter is definitely rational.

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Only if the rational number is 0.

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.

Every rational number does.

Every rational number does.

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

Yes, unless the rational number is 0.

Any and every rational number.

It is the square of the rational number.

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

Any already 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.

rational * irrational = irrational.