Question

if two even numbers are added together, is the sum an even number or an odd number?
choose the correct answer.
a. the sum of two even numbers is an even number.
b. the sum of two even numbers is an odd number.

Explanation:

Step1: Define even numbers

An even number can be written as $2k$ where $k$ is an integer. Let the two even numbers be $2m$ and $2n$, where $m,n$ are integers.

Step2: Calculate their sum

Add the two even numbers:
$$2m + 2n = 2(m + n)$$

Step3: Classify the result

Since $m + n$ is an integer, $2(m + n)$ is a multiple of 2, so it is even.

Answer:

A. The sum of two even numbers is an even number.