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

Answer

To determine whether the product of two consecutive numbers is always odd or always even, let's analyze the situation step by step.

### Step 1: Define Consecutive Numbers
Consecutive numbers are numbers that follow one another in order. For example, if we take two consecutive numbers, they could be:
- 1 and 2
- 5 and 6
- 10 and 11

### Step 2: Identify the Nature of the Numbers
In any pair of consecutive numbers, one number will always be even and the other will always be odd. This is because even and odd numbers alternate on the number line.

### Step 3: Represent the Numbers Mathematically
Let's represent the first consecutive number as \( n \). Therefore, the next consecutive number will be \( n + 1 \).

### Step 4: Analyze the Product
Now, we will multiply these two consecutive numbers:
\[ n \times (n + 1) \]

### Step 5: Check the Product for Evenness
When we multiply an even number by any integer (even or odd), the result is always even. Since one of the two consecutive numbers is always even, the product \( n \times (n + 1) \) will always be even.

### Conclusion
Thus, the result of multiplying two consecutive numbers is always even.

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