Lesson 4 Adding Whole Numbers 
A Note from the Author It is likely that you have already mastered the procedures for adding whole numbers, and have applied them successfully for a long time. However, this review of addition might not be a total waste of your time, because it points out some definitions and underlying principles that need to be more clearly recognized in today's workplaces and learning environments. 
Topic 1
Introduction to Adding Whole Numbers
Addition is a just streamlined version of counting. Hold up two fingers on one hand—that's counting one, two. Then pop up three more—that's one, two, three. Now there is five altogether. Using addition terminology, you have just added 2 plus 3, and you can see the result is 5—two fingers plus three fingers equals five fingers. Simple? Yes. Important? Very!
The plus sign (+) indicates the addition operation. 
Addition problems are sometimes written in a horizontal form such as: 6 + 5 = 11.
This form is also known as a number sentence. It is read as, "Two plus three equals five." In a manner of speaking, this number sentence shows that 2 + 3 can be more simply expressed as 5.

Notes

Topic 2
Adding Pairs of Whole Numbers
When adding pairs of whole numbers that are larger than 9, you must add digits that have the same place values. In other words, you must add the ones digits in both numbers, add the tens digits, add the hundreds digits, and so on. So when you are setting up addition operations in the vertical form, always begin by aligning the place values—ones over ones, tens over tens, hundreds over hundreds, and so on.
For example:  Then add each of the columns from right to left. Write the sum digits under their corresponding place columns. 
Procedure Adding a pair of whole numbers larger than 9:

Topic 3
Adding with "Carry"
When the sum in a column is 10 or greater, write the ones digit of this sum under that column, and then carry the tens digit from the sum to the top of the next column.
It's all about working with place values, each place to the left being ten times the value.
Procedure Adding a pair of whole numbers larger than 9:

Topic 4
Adding Long Columns of Whole Numbers
The procedures for adding longer columns of whole numbers are no different from adding just two numbers. The process simply requires more steps ... and more care.
Summary of the Addition Process

Examples
Confirm the solutions to these problems by working them yourself. Notice that the carry values are shown in green.
1. 1  2. 21  3. 1 11 9,672 6,543 6 + 428 16,649  4. 222 876 987 + 877 2740  5. 22 33 9,999 9,777 689 + 288 20,753 
Use these interactive examples and exercises to strengthen your understanding and build your skills. Do not use a calculator  give those neurons in your brain a good workout.
If would like to see more examples or work on a wider range of exercises, you can go to a more detailed tutorial . 