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Chapter 1—Whole Numbers

 When you complete the work for this section, you should be able to: Add small whole numbers without making any errors. Explain how to use a standard addition table. Explain when and how to use the carry principle in addition. Add columns of whole numbers with 100% accuracy.

Addition is a 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!

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.

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 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, "Six plus five equals eleven." In a manner of speaking, this number sentence shows that 6 + 5 can be more simply expressed as 11.
• 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 = 5In other words, 2 + 3 = 3 + 2

Examples and Exercises

 Adding Single Digits Use these interactive examples and exercises to strengthen your understanding and build your skills:

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. 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.

Example 1 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.

 Note When the sum of a column happens to be 10 or greater, you must carry the tens digit of the sum to the top of the next column.

Example 2 Examples and Exercises

 Adding With Carry Use these interactive examples and exercises to strengthen your understanding and build your skills:

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 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.

Example 3

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  9,672 6,543 6 + 428 16,649 4.     222  876 987 + 877 2740 5.     2233  9,999 9,777 689 + 288 20,753

Examples and Exercises

 Adding Columns of Whole Numbers Use these interactive examples and exercises to strengthen your understanding and build your skills:

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