## Let's learn by an example.

Subtract the numbers:

2,043 - 1,959

#### Method used below: column subtracting, 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...

2 | 0 | 4 | 3 | |

- | 1 | 9 | 5 | 9 |

? |

## Subtract column by column; start from the column on the right

### Subtract the digits in the ones column:

#### 3 - 9 = ?

#### The second digit is larger than the first.

Borrow from the next column to the left.

#### The borrowing is a two step process:

#### Subtract 1 from the top digit in the column of the tens: 4 - 1 = 3.

Cross out the top digit you've borrowed 1 from: ~~4~~.

Write the answer above that digit: 3.

#### When borrowing, 1 ten = 10 ones.

Add 10 to the top digit in the column of the ones: 10 + 3 = ^{1}3.

3 | ||||

2 | 0 | ^{1}3 | ||

- | 1 | 9 | 5 | 9 |

#### After borrowing, the subtraction has become:

13 - 9 = 4.

4 is the ones digit.

Write it down at the base of the ones column.

3 | ||||

2 | 0 | ^{1}3 | ||

- | 1 | 9 | 5 | 9 |

4 |

### Subtract the digits in the tens column:

~~4~~ 3 - 5 = ?

#### The second digit is larger than the first.

Borrow from the next column to the left.

#### Subtract 1 from the top digit in the column directly to the left.

But that digit is zero. You need to go further left.

#### Subtract 1 from the nearest column to the left with a non-zero top digit.

That is the column of the thousands: 2 - 1 = 1.

Cross out the top digit you've borrowed 1 from: ~~2~~.

Write the answer above that digit: 1.

#### Cross out the zero(s) that you were going across to the left: ~~0~~.

Write a 9 above each one of the crossed out zeros.

Why? In fact we have subtracted 1 from 20: 20 - 1 = 19.

#### When borrowing, 1 hundred = 10 tens.

Add 10 to the top digit in the column of the tens: 10 + 3 = ^{1}3.

1 | 9 | ^{1}3 | ||

^{1}3 | ||||

- | 1 | 9 | 5 | 9 |

4 |

#### After borrowing, the subtraction has become:

13 - 5 = 8.

8 is the tens digit.

Write it down at the base of the tens column.

1 | 9 | ^{1}3 | ||

^{1}3 | ||||

- | 1 | 9 | 5 | 9 |

8 | 4 |

### Subtract the digits in the hundreds column:

~~0~~ 9 - 9 = 0.

0 is the hundreds digit.

Write it down at the base of the hundreds column.

1 | 9 | ^{1}3 | ||

^{1}3 | ||||

- | 1 | 9 | 5 | 9 |

0 | 8 | 4 |

### Subtract the digits in the thousands column:

~~2~~ 1 - 1 = 0.

0 is the thousands digit.

Write it down at the base of the thousands column.

1 | 9 | ^{1}3 | ||

^{1}3 | ||||

- | 1 | 9 | 5 | 9 |

0 | 0 | 8 | 4 |