Rules for Adding & Multiplying etc Odd & Even Numbers

Rules for Adding & Multiplying etc Odd & Even Numbers

Addition / Subtraction:
even +/- even = even;
even +/- odd = odd;
odd +/- odd = even.

Multiplication:
even * even = even;
even * odd = even;
odd * odd = odd.

Division of two integers can result into an even/odd integer or a fraction.
Odd/Odd could be Odd or a Fraction (CANNOT be even). For example: 7/1 = 7 = odd and 7/3 = non-integer.
Odd/even is ALWAYS a Fraction. For example: 7/2 = 3.5 = odd and 7/3 = non-integer.
Even/Odd could be Even or a Fraction (CANNOT be odd). For example: 6/3 = 2 = even and 6/13 = non-integer.
Even/Even could be Even, Odd or a Fraction. For example: 4/2 = 2 = even, 6/2 = 3 = odd and 6/12 = non-integer.

Exponents:
(Positive Even Integer)^(Positive Even Integer) = Even
(Positive Even Integer)^(Positive Odd Integer) = Even
(Positive Odd Integer)^(Positive Even Integer) = Odd
(Positive Odd Integer)^(Positive Odd Integer) = Odd

Notice here that if the exponent is not positive then these rules break. For example, \(2^{(-2)} = \frac{1}{4}\), \(3^{(-1)} = \frac{1}{3}\), \(2^0 = 1\), ...