Long Subtraction
Long Subtraction with Whole Numbers
We show in steps how to substract two whole numbers using this example 454 - 182.
• Start by stacking the two numbers and aligning them to the right.
| 4 | 5 | 4 | |
| − | 1 | 8 | 2 |
| = |
• Subtract the digits of the same column starting from the right column (ones columns).
4 - 2 = 2 and put the result (=2) in the result line at the same column
| 4 | 5 | 4 | |
| − | 1 | 8 | 2 |
| = | 2 |
• We repeat this process with the tenths column,
But since 8 is greater than 5, we cannot calculate 5 - 8. So we borrow 1 from the hundreds column that we add to the 2d digit of hundreds column.
| 4 | 15 | 4 | |
| − | 1+1 | 8 | 2 |
| = | 2 |
So 5 becomes 15 and 1 becomes 2.
15 - 8 = 7 so put 7 in the result line (column 2).
For the third column, 4 - 2 = 2 we put 2 in the result.
| 4 | 15 | 4 | |
| − | 1+1 | 8 | 2 |
| = | 2 | 7 | 2 |
Long Subtraction with decimal numbers
We show the following subtraction example in steps 12.4547 - 3.82.
• Start by stacking the two numbers and aligning them from the decimal point. So, the decimal dots are in the same column and the digits of the ones (2 and 3) are in the same column, and so on. We get,
| 1 | 2 | . | 4 | 5 | 4 | 7 | |
| − | 3 | . | 8 | 2 | |||
| = |
• Fill the blank places after the decimal separator with zeros.
| 1 | 2 | . | 4 | 5 | 4 | 7 | |
| − | 3 | . | 8 | 2 | 0 | 0 | |
| = |
• We proceed exactly as in the previous case with whole numbers (see 1st paragraph for more details).
The long subtraction is as follows,
| 1 | 12 | . | 14 | 5 | 4 | 7 | |
| − | +1 | 3+1 | . | 8 | 2 | 0 | 0 |
| = | 0 | 8 | . | 6 | 3 | 4 | 7 |
First column
7 - 0 = 7
Put 7 in the result.
Second column
4 - 0 = 4
Put 4 in the result.
Thirth column
5 - 2 = 3
Put 3 in the result.
Forth column
We cannot calculate 4 - 8, borrow 1 from next column to the left.
So 4 becomes 14 and 3 becomes 4.
14 - 8 = 6 so, put 6 in the result.
Fifth column
Column of decimal separators that we keep in the result.
Sixth column
We cannot calculate 2 - 4. borrow 1 from next column to the left.
2 becomes 12 and "empty" (or 0) in the last column becomes 1.
12 - 4 = 8 so we put 8 in the result.
Seventh column
1 - 1 = 0
put 0 in the result.
See also
Long Addition
Long Multiplication
Long decimal Division
Long Euclidean division
Big numbers Calculator
Number Calculators
Mathematics Calculators