The Smallest Number to Make the Sum an Odd Number

To find the smallest number that when added to an even number makes the sum an odd number, we need to understand some basic concepts in mathematics. Let's break down the solution into several steps:

Understanding Even and Odd Numbers:
- Even numbers are those that can be divided evenly by 2, leaving no remainder.
- Odd numbers are those that cannot be divided evenly by 2, leaving a remainder of 1.

Identifying the Problem:
In this problem, we are given an even number and we need to find the smallest number to add to it so that the sum becomes an odd number.

Step 1: Understanding the Properties of Even and Odd Numbers:
- When we add two even numbers, the sum is always an even number.
- When we add two odd numbers, the sum is always an even number.
- When we add an even number and an odd number, the sum is always an odd number.

Step 2: Finding the Solution:
Since we are given an even number and need to make the sum an odd number, we can conclude that the number we need to add must be an odd number.

However, we are looking for the smallest number, so we need to find the smallest odd number. The smallest odd number is 1.

Step 3: Checking the Solution:
Let's test our solution with an example:
- Suppose we have the even number 6.
- If we add 1 to 6, the sum is 7, which is an odd number.

Therefore, the smallest number that when added to an even number makes the sum an odd number is 1.

In conclusion, when we have an even number, adding 1 to it will always result in an odd number. This is because odd numbers are obtained by adding an odd number to an even number. Therefore, the smallest number to add to an even number to make the sum an odd number is 1.