1.4 Addition of whole numbers

Section overview

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

Addition

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

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

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, $4+3=7$ 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 $4+3$ ,

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, $4+3=7$ .

The addition process

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

$\begin{array}{cc}\begin{array}{c}\hfill 25\\ \hfill \underline{+43}\end{array}& \text{means}\end{array}$

We write this as 68.

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

Sample set a

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.

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.

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:

$8+4=12$ 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.