# 5 Digit Addition: Learn with Solved Examples

Understanding how to add 5-digit numbers is an important math skill that sets the stage for more complex calculations. This lesson will guide you through the process with clear explanations and step-by-step solved examples. By understanding the principles of place value and carrying over, you’ll gain confidence and accuracy in performing these large-number additions. This skill frequently appears on quantitative aptitude sections of exams like the GMAT, GRE, SAT, ACT and various government job entrance exams. Whether you’re a student looking to improve your math skills or someone seeking a refresher, this guide will provide the knowledge and practice you need to excel. Let’s dive in and explore the world of 5-digit addition together.

A five-digit number is a number that ranges from 10,000 to 99,999. These numbers are integral in various real-world contexts, such as statistics, financial calculations, and measurements. Each digit in a five-digit number represents a specific place value, ranging from the units place (rightmost) to the ten-thousands place (leftmost).

For example, in the number 47,823:

• The digit 4 is in the ten-thousands place, representing 40,000.
• The digit 7 is in the thousands place, representing 7,000.
• The digit 8 is in the hundreds place, representing 800.
• The digit 2 is in the tens place, representing 20.
• The digit 3 is in the units place, representing 3.

Understanding the place value of each digit is essential for performing accurate mathematical operations, such as addition, subtraction, multiplication, and division. Working with five-digit numbers often involves carrying over values in addition or borrowing in subtraction, making a solid grasp of these concepts critical for mathematical proficiency.

Addition is one of the fundamental operations in arithmetic and mathematics. It involves combining two or more numbers to get a total or sum. The numbers being added are called addends, and the result is known as the sum. Addition is represented by the plus sign (+).

Some important concepts involved in addition are :

1. Commutative Property: The order of the addends does not affect the sum. For example, 4 + 5 is the same as 5 + 4, both equaling 9.
2. Associative Property: The way in which addends are grouped does not affect the sum. For instance, (2 + 3) + 4 is the same as 2 + (3 + 4), both equaling 9.
3. Identity Property: Adding zero to any number does not change the value of that number. For example, 7 + 0 is still 7.

Important steps involved in doing addition are stated below:

1. Align the Numbers: Write the numbers so that their corresponding place values (units, tens, hundreds, etc.) are aligned vertically.
2. Add Column by Column: Start adding from the rightmost column (units place) and move to the left. If the sum of a column is 10 or more, carry over the extra value to the next column.
3. Write the Sum: After adding all the columns and accounting for any carryovers, write down the final sum.

## What is a 5-digit number?

A five-digit number is a number that ranges from 10,000 to 99,999. These numbers consist of five digits, with each digit holding a specific place value. The place values from left to right are ten-thousands, thousands, hundreds, tens, and units (or ones). The smallest five-digit number is 10,000, and the largest is 99,999.

## Examples of Five-Digit Numbers

Some important examples related to five digit numbers are stated below:

• 10,000: The smallest five-digit number.
• 47,823: A mid-range five-digit number.
• 99,999: The largest five-digit number.

### Place Value in a Five-Digit Number

In the number 47,823, each digit has a specific place value:

• 4 is in the ten-thousands place, representing 40,000.
• 7 is in the thousands place, representing 7,000.
• 8 is in the hundreds place, representing 800.
• 2 is in the tens place, representing 20.
• 3 is in the units (ones) place, representing 3.

## Properties of 5 Digit Addition

When performing addition with five-digit numbers, the process follows the same fundamental properties of addition used with smaller numbers. Here are the key properties of addition, illustrated with five-digit numbers:

### 1. Commutative Property

The order in which two numbers are added does not affect the sum.

• Example:
• 12345+67890=80235
• 67890+12345=80235

### 2. Associative Property

The way in which numbers are grouped when adding does not change the sum.

• Example:
• (12345+67890)+11111=80235+11111=91346
• 12345+(67890+11111)=12345+79001=91346

### 3. Identity Property

Adding zero to any number does not change the value of that number.

• Example:
• 54321+0=54321

Also Read: Questions of Logical Problems Reasoning

## 5 Digit Addition Solved Examples

Here are five solved examples of five-digit addition problems along with their solutions.

Question : Add 12345 and 67890.

Solution:   12345 + 67890 = 80235

Solution:  54321 + 12345 = 66666

Solution:   45987 + 32015 = 78002

Solution:   78901 + 21099 = 100000

Solution:   23456 + 56789 = 80245

## FAQs

What is the importance of place value in five-digit addition?

Place value is important because it determines the value of each digit in a number based on its position. When adding 5-digit numbers, aligning digits according to their place values (units, tens, hundreds, thousands, ten-thousands) ensures that each digit is added to the correct corresponding digit in the other number.

Add the following numbers: 23,456 + 18,721 ?

23456 + 18721 = 42177

What should I do if my sum is more than five digits?

If the sum of your addition results in more than five digits, it simply means the total has overflowed into the next higher place value. This is perfectly fine and should be handled just like any other multi-digit addition. Example, Add 78901 and 21099:  78901 + 21099 = 100000.

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