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Place value is a fundamental concept in mathematics. It refers to the value of the digit depending on its position within a number.

In the number 15,382, each digit holds a different place value:

- The digit '1' is in the ten-thousands place and represents 10,000.
- The digit '5' is in the thousands place and represents 5,000.
- The digit '3' is in the hundreds place and represents 300.
- The digit '8' is in the tens place and represents 80.
- Lastly, the digit '2' is in the units place and represents 2.

Understanding place value helps break down and simplify the addition of large numbers.

Vertical addition is a method where numbers are written one below the other, aligning the digits by their place values. This arrangement helps easily add each column of digits.

Steps to perform vertical addition:
1. **Write the numbers:** Place one number directly above the other with digits aligned in columns.

\[\begin{array}{r} 15382 \ +00001\end{array}\]

2. **Add from the right**: Start adding the digits from the rightmost column (units place). If the sum of a column is greater than 9, carry over the extra value to the next left column.
3. **Write the result:** After adding all columns, the final number is written below the line.

Vertical addition is simple and helps in reducing errors, especially with larger numbers. This method ensures that each place value is correctly considered.

Let's break down the given problem step-by-step to grasp vertical addition better:

1. **Identify the operation:** We determined that we need to add two numbers: 15,382 and 1.
2. **Set up the addition:** We align the numbers vertically by their digits.

\[\begin{array}{r} 15382 \ +00001\end{array}\]

3. **Perform the addition:** We add the digits starting from the right (units place). Here's how it goes:

- Units place: 2 + 1 = 3
- Tens place: 8 + 0 = 8
- Hundreds place: 3 + 0 = 3
- Thousands place: 5 + 0 = 5
- Ten-thousands place: 1 + 0 = 1

Adding all columns, we get 15,383.

This breakdown simplifies the addition process, ensuring each digit is correctly added and the place values are maintained.