## Subtract Whole Numbers

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

Example: 3,150 − 1,732 = (3,000 + 100 + 50) − (1,000 + 700 + 30 + 2)
= (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.

Think: 3,000 + 100 can be written as 2,000 + 1,100.
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 onesSubtract the ones. 3 thousands 1 hundred =2 thousands 11 hundredsSubtract 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.