State if the result is always odd or always even:
Two odd numbers are added

Answer

To determine whether the result of adding two odd numbers is always odd or always even, we can follow these steps:

### Step 1: Understand what odd numbers are.
Odd numbers are integers that cannot be divided evenly by 2. They have a remainder of 1 when divided by 2. Examples of odd numbers include 1, 3, 5, 7, 9, 11, etc.

### Step 2: Add two odd numbers.
Let’s take two odd numbers as examples. For instance, we can choose 9 and 11.

### Step 3: Perform the addition.
Now, we add these two numbers:
\[ 9 + 11 = 20 \]

### Step 4: Determine if the result is odd or even.
The result of the addition is 20. Since 20 can be divided by 2 without a remainder, it is an even number.

### Step 5: Generalize the result.
To confirm that this is true for any two odd numbers, let's represent any odd number as \(2n + 1\), where \(n\) is an integer. If we take two odd numbers:
- First odd number: \(2a + 1\)
- Second odd number: \(2b + 1\)

Now, add these two odd numbers:
\[ (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1) \]

### Step 6: Analyze the final result.
The expression \(2(a + b + 1)\) is clearly divisible by 2, which means it is an even number.

### Conclusion:
Thus, we can conclude that the sum of two odd numbers is always even.

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