To solve the problem of finding two odd numbers whose sum is exactly 500,000, let's delve into it step by step:
### Step 1: Understanding the Properties of Odd Numbers
1. Definition of Odd Numbers:
- Odd numbers are integers that are not divisible by 2. Examples include 1, 3, 5, 7, etc.
2. Sum of Two Odd Numbers:
- The sum of two odd numbers is always even. This is because adding two odd numbers results in (odd + odd = even).
### Step 2: Setting Up the Problem
- We are asked to find two odd numbers such that their sum is 500,000, which is an even number.
### Step 3: Choosing the First Odd Number
- Let's choose an arbitrary odd number that is less than 500,000. To keep things simple, we can start near the midpoint of 500,000, around the 250,000 range.
- Let's choose 249,999 (which is an odd number).
### Step 4: Finding the Second Odd Number
- To find the second odd number, we subtract the first odd number from 500,000:
[tex]\[
\text{Second odd number} = 500,000 - \text{First odd number}
\][/tex]
[tex]\[
\text{Second odd number} = 500,000 - 249,999
\][/tex]
[tex]\[
\text{Second odd number} = 250,001
\][/tex]
### Step 5: Verification
- We need to verify that both numbers are odd and their sum is 500,000:
1. 249,999 is odd because it is not divisible by 2.
2. 250,001 is odd because it is not divisible by 2.
- Their sum should be:
[tex]\[
249,999 + 250,001 = 500,000
\][/tex]
### Conclusion
- Thus, the two odd numbers we have chosen are 249,999 and 250,001. They sum exactly to 500,000.
### Summary
1. Choose an odd number less than 500,000, such as 249,999.
2. Subtract the chosen number from 500,000 to get the second odd number, which is 250,001.
3. Verify that both are odd and their sum is correct.
Hence, the two odd numbers are 249,999 and 250,001.
