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

Answer 1

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.