Why is an even number minus an even number an even number?

In math, even is just another way of saying divisible by 2.

If you add or subtract two numbers that share a divisor, the resulting number will also share that divisor. So the sum or difference of a pair of even numbers will (always and also) be divisible by two.

In algebraic terms:

• If a/2 results in a whole number, then a must be even. Likewise, b/2.

• a/2 - b/2 = (a-b)/2.

• So if both a/2 and b/2 are whole numbers, then their difference must be, as well.