Subtracting Larger Whole Numbers
Introduction
Subtraction means reducing the value of one number by another to find the new value. For example, if you have 7 apples, and give away 3, you are left with 4 (7-3=4). Subtraction is one of the first things you learn in math.
Working with very large numbers isn't much different from working with small numbers; you follow the same processes, just more times.
Terms
Lesson
To subtract numbers from one another, you do it column by column. The same is true of large numbers.
Let's take the sum:
489,563 - 38,741 = ?
The first thing to do is to write them on top of one another, making sure we line up the digits:
| 4 | 8 | 9 | 5 | 6 | 3 |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
Then we start from the furthest right and subtract the bottom digit from the top.
Since 3 - 1 = 2, we can put that in the answer row:
| 4 | 8 | 9 | 5 | 6 | 3 |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 2 |
We then move on to the tens column. Since 6-4 = 2, we can add that to the answer row:
| 4 | 8 | 9 | 5 | 6 | 3 |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 2 | 2 |
Then we come to the hundreds column. This presents us with a bit of a problem since 5-7 is a negative number. Therefore, we need to 'borrow' from the column one to the left. To do that, we take the 9 that's in the thousands column, strike through it and change it to 8 (because we are 'borrowing' 1). Then, with the borrowed 1, we put in front of our 5 to make 15.
| 4 | 8 | 15 | 6 | 3 | |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 2 | 2 |
We can now do the sum of 15 - 7 in the hundreds column, which gives us 8.
| 4 | 8 | 15 | 6 | 3 | |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 8 | 2 | 2 |
In the thousands column, our new value at the top is 8, so we do 8-8, which gives us 0 for the answer row:
| 4 | 8 | 15 | 6 | 3 | |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 0 | 8 | 2 | 2 |
Next, we move to the ten-thousands column, and do 8-3, and add the 5 to the answer row.
| 4 | 8 | 15 | 6 | 3 | |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 5 | 0 | 8 | 2 | 2 |
In the final column (hundred-thousands) we only have the 4, and nothing to subtract from it, so we can put it unchanged in the answer row.
| 4 | 8 | 15 | 6 | 3 | |
|---|---|---|---|---|---|
| - | 3 | 8 | 7 | 4 | 1 |
| 4 | 5 | 0 | 8 | 2 | 2 |
Therefore, the answer is:
489,563 - 38,741 = 450,822
If you need to work with even larger numbers, the process is exactly the same.