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Chapter 1 Whole Numbers 1-4 Adding Whole Numbers Addition is a souped-up 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! Introduction to Adding Whole Numbers | Here is a standard addition table. It shows the results of adding all possible combinations of two digits, from 0 + 0 = 0 through 9 + 9 = 18. Study the table carefully, and see if you can figure out how it works. 
Addition Table | | | Addition facts | Definitions - 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. | Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: | | 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.
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| Examples - 1 + 2 = 3
- 3 + 6 = 9
- 4 + 0 = 4
- 5 + 7 = 12
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Adding Pairs of Whole Numbers | When you are setting up addition operations in the vertical form, always begin by aligning the place values—ones over ones, tens over tends, 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. For example: |  | Example 
If 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. [Don't worry, this is easier done than said.] Example 
Examples/Exercises Confirm the solutions to these problems by working them yourself.The carry values are shown in green. 1. 1
68
+ 8
76 | 2. 1
22
+ 99
121 | 3. 111
9672
+ 428
10100 | 4. 111
876
+ 877
1753 | 5. 111
1999
+ 888
2887 | Summary of the Addition Process - 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.
- Add the digits in each column, beginning from the right (ones place) column.
- 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.
| 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 | | 1-4.3 Adding Columns of Whole Numbers Examples/Exercises 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. 111
9672
6543
6
+ 428
16649 | 4. 222
876
987
+ 877
2740 | 5. 2233
9999
9777
689
+ 288
20755 |
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