Adding Larger Whole Numbers
Introduction
Adding two large whole numbers can be tricky because there are lots of parts to combine. However, the principles are the same as adding two small numbers. 3 + 6 isn't any different to 3,333 + 66,666. The important thing is to get the numbers organized so you can break a big number down into lots of smaller numbers.
Terms
Lesson
The first step when you're adding two numbers is to line them up so that all the columns are in line. For example, you need to make sure that you're combining the tens column with the tens column, and the hundreds column with the hundreds column. The easiest way to do this is with a table.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
Write both of the numbers to be added into a table like this. The last number before the decimal point (i.e. the ones column) should be the furthest to the right.
So, if we were to add the following numbers:
278,456 + 28,907
We would start by putting them in the table:
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 |
| 2 | 8 | 9 | 0 | 7 |
Because the second number has one fewer digit, the hundred-thousands column can stay empty.
Now we can combine the numbers column by column, starting from the furthest right. So we add 6 and 7 from the ones column. Since 6 + 7 is 13, we need to add 3 as the answer in the ones column, and put a 1 in the carryover column for the next column up (the tens):
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 3 | |||||
| Carryover | 1 | |||||
Then we add together the tens column. 5 + 0 = 5, and then we add the 1 from the carryover row, giving an answer of 6. We can add 6 as the result, and there's nothing left to carry over.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 6 | 3 | ||||
| Carryover | 1 | |||||
Then we add the hundreds column. 4 + 9 = 13, and there's nothing else to add in the carryover row, so 13 is the answer. Again, we just add the 3 and place the one in the next carryover column, because 13 is larger than 10.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 3 | 6 | 3 | |||
| Carryover | 1 | 1 | ||||
Now the thousands column. 8 + 8 = 16, and we have to add the one from the carryover column, giving us 17. Because 17 is bigger than 10, 7 goes in the result, and one in the next carryover column.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 7 | 3 | 6 | 3 | ||
| Carryover | 1 | 1 | 1 | |||
In the ten-thousands column, we add 7 and 2 to get 9, and then the 1 from the carryover, which gives us 10. We, therefore, put 0 in the result, and 1 in the carryover column
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 0 | 7 | 3 | 6 | 3 | |
| Carryover | 1 | 1 | 1 | 1 | ||
Finally, we add the hundred-thousands column, in which there is just the 2 and the carryover 1, giving us 3 in the result column.
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 2 | 7 | 8 | 4 | 5 | 6 | |
| + | 2 | 8 | 9 | 0 | 7 | |
| Result | 3 | 0 | 7 | 3 | 6 | 3 |
| Carryover | 1 | 1 | 1 | 1 | ||
The answer to 278,456 + 28,907 is 307,363
We can repeat this as high as we need to go. Just follow the same steps. If you need to include columns to the right for decimals (tenths, hundredths etc.) then you follow exactly the same principle, starting from the furthest right.