Yes, two thirds is a rational number. This is because it a is recurring decimal and can be expressed as a fraction. All fractions are rational numbers and all recurring decimals are rational numbers.
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Yes.
2/3 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
It would be 21 and two thirds, so it can be expressed as a fraction and is therefore rational.
Every time. The sum of two rational numbers MUST be a 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.