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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.
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 is easily visualized on the number line. Let's visualize the addition of 4 and 3 using the number line.
To find $4+3$ ,
Thus, $4+3=7$ .
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.
To add whole numbers ,
The process:
$\begin{array}{c}\hfill 25\\ \hfill \underline{+43}\end{array}$
$\begin{array}{c}\hfill 25\\ \hfill \underline{+43}\\ \hfill 68\end{array}$
Add 276 and 103.
$\begin{array}{c}\hfill 276\\ \hfill \underline{+103}\\ \hfill 379\end{array}\phantom{\rule{16px}{0ex}}\begin{array}{}6+3=9\text{.}\\ 7+0=7\text{.}\\ 2+1=3\text{.}\end{array}$
Add 1459 and 130
$\begin{array}{c}\hfill 1459\\ \hfill \underline{+130}\\ \hfill 1589\end{array}\phantom{\rule{16px}{0ex}}\begin{array}{}9+0=9\text{.}\\ 5+3=8\text{.}\\ 4+1=5\text{.}\\ 1+0=1\text{.}\end{array}$
In each of these examples, each individual sum does not exceed 9. We will examine individual sums that exceed 9 in the next section.
Perform each addition. Show the expanded form in problems 1 and 2.
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.
Perform the following additions. Use the process of carrying when needed.
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