## Subtract Whole Numbers

Subtraction of whole numbers can also be completed by using the addition properties and expanded notation.

= (3,000 − 1,000) + (100 − 700) + (50 − 30) + (0 − 2)

When working with whole numbers, 700 cannot be subtracted from 100 and 2 cannot be subtracted from 0, so renaming is necessary.

50 can be written as 40 + 10.

= (2,000 − 1,000) + (1,100 − 700) + (40 − 30) + (10 − 2)

= 1,000 + 400 + 10 + 8

= 1,418

The method is still long and cumbersome. The subtraction algorithm provides a simple, compact method of completing such calculations. As in addition, digits are aligned according to place value and the computation is completed from right to left.

Rename. |
Subtract the tens |
Rename. |
Subtract the thousands |

5 tens 0 ones = 4 tens 10 ones Subtract the ones. |
3 thousands 1 hundred = 2 thousands 11 hundreds Subtract the hundreds. |

**Estimating Sums and Differences**

When an exact answer is not necessary, an estimate can be used. The most common method of estimating sums and differences is to round each number to a specific place and then add or subtract the rounded numbers.

Estimate 4,894 + 2,429. | |

4,894 → | 5,000 |

2,429 → | + 2,000 |

7,000 |

Round each number to the

nearest thousand.

Add the rounded numbers.

Estimate 6,209 − 383. | |

6,209 → | 6,200 |

383 → | − 400 |

5,800 |

Round each number to the

nearest hundred.

Subtract the rounded numbers.

Mental math can often be used to complete estimates. At this grade level, however, errors can be more easily identified if students write down their work when estimating answers.

As students gain experience and confidence estimating sums and differences, point out that estimates can often be used to check computations. Students should realize that if both addends are rounded up, the estimated sum will be greater than the actual sum, and if both addends are rounded down, the estimated sum will be less than the actual sum. Such generalizations are not possible with subtraction.

**Teaching Model 5.2:** Relate Addition and Subtraction