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 numbers to be added are called the addends.
  • The result of the addition operation is called the sum.

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.
  • The plus sign (+) indicates the addition operation.
  • The equal sign (=) expresses the equality of the two parts of the sentence.

Notes

Zero added to any value is equal to the original value. Example: 2 + 0 = 2
   
It makes no difference in which order two whole numbers are added. (This is known as the commutative law of addition) Example:
2 + 3 = 5 and 3 + 2 = 5

In other words,
2 + 3 = 3 + 2


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:

Step 1: Align the addends vertically so that the places values line up vertically — ones line up in the first column, tens line up in the second column, hundreds in the third column, and so on.
Step 2: Add the digits in each column, beginning from the right (ones place) column.

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:

Step 1: Align the addends vertically so that the places values line up vertically — ones line up in the first column, tens line up in the second column, hundreds in the third column, and so on.
Step 2: Add the digits in each column, beginning from the right (ones place) column.
Step 3: When the sum for a column is 10 or greater, write the ones digit and carry the tens digit to the next column of digits.

 


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

  1. Align the addends vertically so that corresponding places values line up vertically — ones line up in the first column, tens line up in the second column, hundreds in the third column, and so on.

  2. Add the digits in each column, beginning from the right (ones place) column.

  3. When the sum for a column is 10 or greater, write the ones digit and carry the tens digit to the next column of digits.

Examples

Confirm the solutions to these problems by working them yourself. Notice that the carry values are shown in green.

1.          1     
68
22
+  8
98

2.     21     
22
186
+ 99
307

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 .