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Explanations:

If we can write a number as a ratio (or fraction) of two whole numbers, then that number is considered rational. The denominator can never be 0. In the case of 6/4, this is a rational number. Therefore, the statement "6/4 is irrational" is false. This is a true statement. We cannot write sqrt(2) as a fraction of two integers. The proof of this is fairly lengthy, but one way is to use a proof by contradiction to show that sqrt(2) = a/b is impossible. Since we cannot make sqrt(2) into a ratio of two integers, we consider it irrational.This is a true statement. Any terminating decimal is always rational. In this case, 1.3 = 13/10.This is false. Any repeating decimal can be converted to a fraction through a bit of work. It turns out that 17.979797... = 1780/99 which makes the value to be rational.Any integer is rational. We can write the integer over 1. So something like -16 is the same as -16/1, showing how it is rational. So that's why this statement is true.This statement is false because we found true statements earlier.