# 4 Digit Addition: Learn with Solved Examples

Learning to 4 digit addition numbers can seem challenging at first, but with practice and the right approach, it becomes an easy and enjoyable task. This guide will walk you through the process step-by-step, starting with basic concepts and progressing to more complex examples. By working through solved examples, you’ll gain confidence and develop a solid understanding of 4 digit addition. 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 brushing up on basic arithmetic, this introduction will set you on the path to mastering four-digit addition.

A four-digit number is any number that has four digits, ranging from 1000 to 9999. These numbers are significant in various contexts, such as counting, calculations, and real-life applications like currency, population data, and more. Understanding four-digit numbers is a crucial step in mathematics, as it lays the foundation for more advanced arithmetic operations, including addition, subtraction, multiplication, and division.

Examples of Four-Digit Numbers:

1. 1000: The smallest four-digit number.
2. 2024: The current year.
3. 5768: A random four-digit number.
4. 9999: The largest four-digit number.

Properties of Four-Digit Numbers:

1. Place Value: Each digit in a four-digit number has a specific place value. From left to right, the place values are thousands, hundreds, tens, and ones.
• For example, in the number 5768:
• 5 is in the thousands place (5000)
• 7 is in the hundreds place (700)
• 6 is in the tens place (60)
• 8 is in the ones place (8)
2. Range: Four-digit numbers range from 1000 to 9999.
• The number just before 1000 is 999 (a three-digit number).
• The number just after 9999 is 10000 (a five-digit number).
3. Even and Odd: Four-digit numbers can be even or odd.
• An even four-digit number ends in 0, 2, 4, 6, or 8 (e.g., 2024, 5780).
• An odd four-digit number ends in 1, 3, 5, 7, or 9 (e.g., 2021, 5769).
4. Divisibility: Four-digit numbers can be checked for divisibility by various rules.
• A number is divisible by 2 if its last digit is even.
• A number is divisible by 5 if its last digit is 0 or 5.
• A number is divisible by 10 if its last digit is 0.

Also Read: Questions of Logical Problems Reasoning

Addition is a basic arithmetic operation that involves combining two or more numbers to find their total. When adding four-digit numbers, the process follows the same principles as adding smaller numbers but requires careful attention to place value and carrying over digits when necessary.

### Steps for Adding Four-Digit Numbers

Some important steps related to adding four digit numbers are stated below:

1. Align the Numbers: Write the numbers to be added in a column, aligning them by place value (thousands, hundreds, tens, and ones).
2. Add the One’s Place: Start by adding the digits in the one’s place. If the sum is 10 or greater, write down the one’s digit and carry over the tens digit to the next column.
3. Add the Tens Place: Move to the tens place, and add the digits along with any carryover from the one’s place. Again, if the sum is 10 or greater, write down the ones digit and carry over the tens digit.
4. Add the Hundreds Place: Repeat the process for the hundreds place, adding any carryover from the tens place.
5. Add the Thousands Place: Finally, add the digits in the thousands place along with any carryover from the hundreds place. Write down the entire sum since there are no more digits to carry over to.

## Properties of 4 Digit Addition

When performing the addition of four-digit numbers, several key properties and concepts come into play. Understanding these properties helps in grasping the fundamental aspects of addition and ensures accurate calculations.

Important properties related to 4 digit addition are mentioned below:

1. Commutative Property:
• The order in which you add the numbers does not affect the sum.
• For example: 1234+5678=5678+1234
2. Associative Property:
• The way in which numbers are grouped when adding does not change the sum.
• For example: (1234+5678)+4321=1234+(5678+4321)
3. Identity Property:
• Adding zero to any number does not change the value of that number.
• For example: 5678+0=5678
4. Carrying Over:
• When the sum of digits in a particular place value column is 10 or more, you carry over the extra value to the next higher place value.
• For example: When adding 3765 and 4897:   3765 + 4897 = 8662.
5. Place Value Importance:
• Each digit in a number has a specific place value (ones, tens, hundreds, thousands). When adding, it’s crucial to align the digits according to their place values.
• For example: Adding 2345 and 6789 requires aligning as follows:   2345 + 6789 = 9134.
6. Distributive Property (although more relevant in multiplication, it can aid in breaking down complex additions):
• Breaking down numbers into smaller parts to make addition easier.
• For example: Adding 3456 and 1234 can be seen as adding 3000 + 1000, 400 + 200, 50 + 30, and 6 + 4 separately, then combining the results.

## 4 Digit Addition Solved Examples

Example 1: Adding 1234 and 5678

Solution:   1234 + 5678 = 6912

• Ones Place: 4 + 8 = 12 (write 2, carry over 1)
• Tens Place: 3 + 7 + 1 (carry over) = 11 (write 1, carry over 1)
• Hundreds Place: 2 + 6 + 1 (carry over) = 9 (write 9)
• Thousands Place: 1 + 5 = 6 (write 6)

Example 2: Adding 3456 and 7890

Solution:   3456 + 7890 = 11346

• Ones Place: 6 + 0 = 6 (write 6)
• Tens Place: 5 + 9 = 14 (write 4, carry over 1)
• Hundreds Place: 4 + 8 + 1 (carry over) = 13 (write 3, carry over 1)
• Thousands Place: 3 + 7 + 1 (carry over) = 11 (write 11)

Example 3: Adding 4321 and 8765

Solution:   4321 + 8765 = 13086

• Ones Place: 1 + 5 = 6 (write 6)
• Tens Place: 2 + 6 = 8 (write 8)
• Hundreds Place: 3 + 7 = 10 (write 0, carry over 1)
• Thousands Place: 4 + 8 + 1 (carry over) = 13 (write 13)

Example 4: Adding 5678 and 1234

Solution:   5678 + 1234 = 6912

• Ones Place: 8 + 4 = 12 (write 2, carry over 1)
• Tens Place: 7 + 3 + 1 (carry over) = 11 (write 1, carry over 1)
• Hundreds Place: 6 + 2 + 1 (carry over) = 9 (write 9)
• Thousands Place: 5 + 1 = 6 (write 6)

Example 5: Adding 9876 and 5432

Solution:   9876 + 5432 = 15308

• Ones Place: 6 + 2 = 8 (write 8)
• Tens Place: 7 + 3 = 10 (write 0, carry over 1)
• Hundreds Place: 8 + 4 + 1 (carry over) = 13 (write 3, carry over 1)
• Thousands Place: 9 + 5 + 1 (carry over) = 15 (write 15)

## FAQs

What is 2345 + 6789?

2345 + 6789 = 9134.

How do you handle a carry-over in four-digit addition?

When the sum of digits in a column is 10 or more, write down the units digit and carry over the tens digit to the next column on the left.

What is the sum of 4071 and 5892?

4071 + 5892 = 9963.

How do you handle a carry-over in four-digit addition?

When the sum of digits in a column is 10 or more, write down the units digit and carry over the tens digit to the next column on the left.

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