Yes, the sum of two odd numbers always equals an even number.
To understand why, let's consider what odd and even numbers are:
- Even Numbers: Are integers that are divisible by 2. They can be represented in the form 2n, where n is any integer.
- Odd Numbers: Are integers that are not divisible by 2. They can be represented in the form 2m + 1, where m is any integer.
When you add two odd numbers together, you get:
(2m + 1) + (2k + 1) (where m and k are any integers)
= 2m + 2k + 2
= 2(m + k + 1)
Since m + k + 1 is also an integer, the result can be written in the form 2 times an integer. This means that the sum is divisible by 2, and therefore, is an even number.
Examples:
- 3 + 5 = 8
- 7 + 9 = 16
- 11 + 13 = 24
In all these examples, the sum of the two odd numbers is an even number. The initial reference even provides the example of 5 + 7 = 12.
