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Q: Is it sometimes true when the product of Two rational numbers are rational?

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No, it is always true

It will be rational.

No, it is always true

sometimes true (when the rational numbers are the same)

Yes, that's true.

The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.

Sometimes true.

In any case, being the product of two rational numbers, it will also be rational. It can either be another mixed number, or it may happen to be an integer.

sometimes true

It is always true.

Yes, it is true.

True.

That's a true statement. Another true statement is: All integers are rational numbers.

That's a true statement. Another true statement is: All integers are rational numbers.

It is a rational number.

true

True

Yes. The rational numbers are a closed set with respect to subtraction.

False.

No, it is not true.

No, it is not generally true.

Yes, it is true.

Sometimes true. The LCM of 4 and 9 is 36. The LCM of 4 and 8 is 8.

Yes, that's true.

Sometimes true. (when the numbers are mutually prime) e.g. it's true for 5 and 7, 8 and 3. But it's not true when they have a factor in common e.g. 6 and 8, or 15 and 20.