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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add whole numbers. By the end of this module, students should be able to understand the addition process, add whole numbers, and use the calculator to add one whole number to another.

Section overview

  • Addition
  • Addition Visualized on the Number Line
  • The Addition Process
  • Addition Involving Carrying
  • Calculators


Suppose we have two collections of objects that we combine together to form a third collection. For example,

A group of four dots is combine with a group of three dots to yield seven dots.

We are combining a collection of four objects with a collection of three objects to obtain a collection of seven objects.


The process of combining two or more objects (real or intuitive) to form a third, the total, is called addition .

In addition, the numbers being added are called addends or terms , and the total is called the sum . The plus symbol (+) is used to indicate addition, and the equal symbol (=) is used to represent the word "equal." For example, 4 + 3 = 7 size 12{4+3=7} {} means "four added to three equals seven."

Addition visualized on the number line

Addition is easily visualized on the number line. Let's visualize the addition of 4 and 3 using the number line.

To find 4 + 3 size 12{4+3} {} ,

  1. Start at 0.
  2. Move to the right 4 units. We are now located at 4.
  3. From 4, move to the right 3 units. We are now located at 7.

Thus, 4 + 3 = 7 size 12{4+3=7} {} .

A number line from 0 to 11. An arrow is drawn from 0 to 4, and is labeled 4. An arrow is drawn from 4 to 7 to a dot on the 7, and is labeled 3. There is a plus sign in between the two arrows.

The addition process

We'll study the process of addition by considering the sum of 25 and 43.

25 + 43 ̲ means Vertical math. 2 tens + 5 ones over 4 tens + 3 ones = 6 tens + 8 ones

We write this as 68.

We can suggest the following procedure for adding whole numbers using this example.

The process of adding whole numbers

To add whole numbers ,

The process:

  1. Write the numbers vertically, placing corresponding positions in the same column.

    25 + 43 ̲

  2. Add the digits in each column. Start at the right (in the ones position) and move to the left, placing the sum at the bottom.

    25 + 43 ̲ 68

Confusion and incorrect sums can occur when the numbers are not aligned in columns properly. Avoid writing such additions as
25 + 43 ̲
25 + 43 ̲

Sample set a

Add 276 and 103.

276 + 103 ̲ 379 6 + 3 = 9 . 7 + 0 = 7 . 2 + 1 = 3 . alignl { stack { size 12{6+3=9 "." } {} #size 12{7+0=7 "." } {} # size 12{2+1=3 "." } {}} } {}

Add 1459 and 130

1459 + 130 ̲ 1589 9 + 0 = 9 . 5 + 3 = 8 . 4 + 1 = 5 . 1 + 0 = 1 . alignl { stack { size 12{9+0=9 "." } {} #size 12{5+3=9 "." } {} # size 12{4+1=5 "." } {} #size 12{1+0=1 "." } {} } } {}

In each of these examples, each individual sum does not exceed 9. We will examine individual sums that exceed 9 in the next section.

Practice set a

Perform each addition. Show the expanded form in problems 1 and 2.

Add 63 and 25.


Vertical addition. 6 tens + 3 ones, over 2 tens + 5 ones = 8 tens + 8 ones.

Add 4,026 and 1,501.


Vertical addition. 4 thousands + 0 hundreds + 2 tens + 6 ones, over 1 thousand + 5 hundreds + 0 tens + 1 one = 5 thousands + 5 hundreds + 2 tens + 7 ones.

Add 231,045 and 36,121.


Addition involving carrying

It often happens in addition that the sum of the digits in a column will exceed 9. This happens when we add 18 and 34. We show this in expanded form as follows.

18 + 34 is separated into 1 ten + 8 ones over 3 tens + 4 ones. The sum of the ones column exceeds nine. The sum is 4 tens + 12 ones, which is separated into 4 tens  + 1 ten + 2 ones. This is simplified to 5 tens + 2 ones, which is simplified to 52.

Notice that when we add the 8 ones to the 4 ones we get 12 ones. We then convert the 12 ones to 1 ten and 2 ones. In vertical addition, we show this conversion by carrying the ten to the tens column. We write a 1 at the top of the tens column to indicate the carry. This same example is shown in a shorter form as follows:

18 + 34 = 52. Above the tens column is a carried one. 8 + 4 = 12 Write 2, carry 1 ten to the top of the next column to the left.

Sample set b

Perform the following additions. Use the process of carrying when needed.

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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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