## Let's learn by an example.

The natural numbers to add:

399 + 675 + 412

#### Method used below: column adding, from right to left (traditional).

### Stack the numbers on top of each other.

#### The ones digits line up in the first column from the right.

#### The tens digits line up in the next column to the left.

#### And so on...

3 | 9 | 9 | ||

6 | 7 | 5 | ||

+ | 4 | 1 | 2 | |

? |

## Add column by column; start from the column on the right.

### Add the digits in the ones column:

#### 9 + 5 + 2 = 16

#### How did we add the digits? Explanation below.

#### Group the ones together in order to make tens:

#### 9 + 5 + 2 =

#### 9 + 5 + 2 =

#### 9 + 7 =

#### 9 + 7 =

#### 9 + 1 + 6 =

#### 9 + 1 + 6 =

#### 10 + 6 =

#### 16

#### Change the order in which the numbers are added, the sum stays the same.

Break some number(s) into component parts, the sum stays the same.

#### The sum is a two-digit number: 16.

#### 6 is the ones digit.

Write it down at the base of the ones column.

#### 1 is the tens digit.

Carry it over to the tens column.

Write the digit above that column.

Add it with the rest of the digits in that column.

1 | ||||

3 | 9 | 9 | ||

6 | 7 | 5 | ||

+ | 4 | 1 | 2 | |

6 |

### Add the digits in the tens column:

#### 9 + 7 + 1 + 1 = 18

#### How did we add the digits? Explanation below.

#### Group the ones together in order to make tens:

#### 9 + 7 + 1 + 1 =

#### 9 + 7 + 1 + 1 =

#### (9 + 1) + 7 + 1 =

#### 10 + 7 + 1 =

#### 10 + 7 + 1 =

#### 10 + 8 =

#### 18

#### The sum is a two-digit number: 18.

#### 8 is the tens digit.

Write it down at the base of the tens column.

#### 1 is the hundreds digit.

Carry it over to the hundreds column.

Write the digit above that column.

Add it with the rest of the digits in that column.

1 | 1 | |||

3 | 9 | 9 | ||

6 | 7 | 5 | ||

+ | 4 | 1 | 2 | |

8 | 6 |

### Add the digits in the hundreds column:

#### 3 + 6 + 4 + 1 = 14

#### How did we add the digits? Explanation below.

#### Group the ones together in order to make tens:

#### 3 + 6 + 4 + 1 =

#### 3 + 6 + 4 + 1 =

#### 3 + 10 + 1 =

#### 3 + 10 + 1 =

#### 10 + (3 + 1) =

#### 10 + 4 =

#### 14

#### The sum is a two-digit number: 14.

#### 4 is the hundreds digit.

Write it down at the base of the hundreds column.

#### 1 is the thousands digit.

Write it down at the base, next to the hundreds digit.

1 | 1 | |||

3 | 9 | 9 | ||

6 | 7 | 5 | ||

+ | 4 | 1 | 2 | |

1 | 4 | 8 | 6 |