Jonah is assistant coach to the boys' soccer team at his school. Every practice session, he has to carry 38 soccer balls out to the field. However, Jonah just started an additional assistant position with the girls' soccer team, which has practice on the same days, meaning he will have to carry out an additional 64 soccer balls. How can he figure out how many balls he has to bring out in total?

In this concept, you will learn how to add whole numbers.

### Adding Whole Numbers

Adding whole numbers is probably very familiar to you. You have been adding whole numbers almost as long as you have been in school. Here is a problem that probably looks familiar.

\begin{align*}4 + 5 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

In this problem, you are adding four and five. You have four whole things plus five whole things, which is a total of nine whole things. The numbers that you are adding are called **addends**. The answer to an addition problem is the **sum**.

This first problem was written horizontally. In the past, you may have seen addition problems written vertically. Now that your understanding is growing, you will need to write the problems vertically on your own.

You can add whole numbers by writing them vertically according to place value. **Place value** refers to the units that a number represents, based on its place in a larger number. Below is a place value chart for the number 1,453,221.

Millions |
Hundred Thousands |
Ten Thousands |
Thousands |
Hundreds |
Tens |
Ones |
---|---|---|---|---|---|---|

1 |
4 |
5 |
3 |
2 |
2 |
1 |

When you add whole numbers, it can be less confusing to write them vertically according to place value. Think about the first example.

\begin{align*}4+5=9\end{align*}

If you wrote that vertically, first you would line up the numbers. They both belong in the Ones column.

\begin{align*} \quad 4\\
\ \underline{+ \ 5}\\
\quad 9\end{align*}

When you have more digits, write the problem vertically by lining up each digit according to place value.

\begin{align*}456 + 27 = \underline{\;\;\;\;\;\;\;\;}\end{align*}

\begin{align*} \quad 456\\
\ \underline{+ \ \ \ 27}\end{align*}

Then add the columns. Remember to regroup (carry) if the numbers sum to more than 9.

\begin{align*}_1 \, \ \ &\\
\quad {4}56&\\
\underline{+ \ \ \ \ 27}&\\
483&\\\end{align*}

### Examples

#### Example 1

Earlier, you were given a problem about Jonah and all his sports equipment.

Jonah already carries 38 soccer balls to the field, and now he will have to carry 64 more.

To figure out the sum total of balls, he has to add the two numbers together.

\begin{align*}38+64\end{align*}

First, write the problem vertically.

\begin{align*}38&\\
\underline {+64}\end{align*}

Next, add the ones column, regrouping as needed.

\begin{align*}_1 \ \ &\\
38\\
\underline {+6 4}&\\
\ \ \ \ 2&\\\end{align*}

Then add the tens column.

\begin{align*}_1 \ \ &\\
38\\
\underline {+6 4}&\\
102&\\\end{align*}

The sum is 102.

The total number of soccer balls for Jonah to carry is 102.

#### Example 2

Add together the whole numbers 675 and 587.

First, line up the columns vertically according to place value.

\begin{align*}\quad 675\\
\ \underline {+587}\end{align*}

Then add the columns, regrouping as needed.

\begin{align*}_1 \, _1 \ \ & \\
675&\\
\underline{+ \ \ \ \ \ 587}&\\
1262&\\\end{align*}

#### Example 3

Find the sum.

\begin{align*}3,456 + 87 =\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up numbers by place value.\begin{align*}3456&\\
\underline{+ \ \ \ 87}&\\\end{align*}

Then add each column from right to left, regrouping as needed.

The answer is 3,453.

#### Example 4

Find the sum.

\begin{align*}56, 321 + 7, 600 =\underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up numbers by place value.

\begin{align*}56321&\\
\underline{+ \ 7600}&\\\end{align*}

\begin{align*}_{1}\quad \ \ \ \, &\\
56321&\\
\underline{+ \ 7600}&\\
63921&\\\end{align*}

The answer is 63,921

#### Example 5

Find the sum.

\begin{align*}203,890 + 12, 201 = \underline{\;\;\;\;\;\;\;\;\;\;}\end{align*}

First, rewrite the problem vertically, lining up the numbers by place value.

\begin{align*}203890&\\
\underline{+ \ 12201}&\\\end{align*}

Then add each column from right to left, regrouping as needed.

\begin{align*}_{1} \quad \ \, &\\
203890&\\
\underline{+ \ 12201}&\\
216091&\\\end{align*}

The answer is 216,091.

### Review

Find each sum.

- \begin{align*}87 + 95 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
87+95=−−−−− - \begin{align*}341 + 12 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
341+12=−−−−− - \begin{align*}673 + 127 = \underline{\;\;\;\;\;\;\;\;\;}\end{align*}
673+127=−−−−− - \begin{align*}549 + 27 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
549+27=−−−−− - \begin{align*}87 + 95 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
87+95=−−−−− - \begin{align*}124 + 967 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
124+967=−−−−− - \begin{align*}1,256 + 987 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
1,256+987=−−−−− - \begin{align*}2,345 + 1,278 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
2,345+1,278=−−−−− - \begin{align*}3,100 + 5,472 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
3,100+5,472=−−−−− - \begin{align*}3,027 + 5,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
3,027+5,471=−−−−− - \begin{align*}13,027 + 7,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
13,027+7,471=−−−−− - \begin{align*}23,147 + 5,001 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
23,147+5,001=−−−−− - \begin{align*}23,128 + 7,771 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
23,128+7,771=−−−−− - \begin{align*}43,237+5,071 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
43,237+5,071=−−−−− - \begin{align*}22,027+6,001 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
22,027+6,001=−−−−− - \begin{align*}45,627+2,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
45,627+2,471=−−−−− - \begin{align*}83,027+51,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
83,027+51,471=−−−−− - \begin{align*}94,127+5,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
94,127+5,471=−−−−− - \begin{align*}83,777+3,321 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
83,777+3,321=−−−−− - \begin{align*}95,527+12,471 =\underline{\;\;\;\;\;\;\;\;\;}\end{align*}
95,527+12,471=−−−−−

### Review (Answers)

To see the Review answers, open this PDF file and look for section 1.1.