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Longhand Addition
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Terms You Might Need
Any number being added is called an addend.
The result of an addition is called the sum.

Introduction
Small additions are easy to remember, such as 2 + 2 or 5 + 3. We don't figure these out, we simply remember the sums. As numbers get larger, they would be harder to remember. Did you ever memorize 54 + 31 or 12 + 513 + 856 + 2?

How We Could Do It
We could start with the first number and count through the rest. For example, we could start with 154, and then count by one 31 times to add 154 and 31. We would count 31 times from 154: 155, 156, 157, 158, 159, ... all the way up to 185. This works, but we have to admit, it's time-consuming and impractical. It could take hours to add 4657, 2342, and 1985.

An Easier Way
We could use a calculator. A calculator is a great solution; they are fast and accurate. But what if you had to add two really, really large numbers, like 389,475,123,985,234,232,101 and 758,302,375,192,845,629,943? Try that on a calculator. You probably won't be able to add it because most calculators do not allow such large numbers.

The Longhand Way
We can use a pen and paper. We write the numbers onto the paper, one underneath the other, and add them column by column. This way, for two big numbers, we are only adding smaller one-digit numbers at a time. Since we have memorized all of the one-digit additions starting from 0 + 0 = 0 all the way to 9 + 9 = 18, adding in columns should be easy. Let's try one to make this clearer. Let's add 154 and 31.

Step 1
Write the two numbers onto the paper. Write them in such a way that the digits line up underneath each other. Since 154 has more digits than 31, write them in such a way too that the digits on the right line up underneath each other. It does not matter which number is on top. Try it:
154
 31


Step 2
Add the column on the far right and write the sum below the addends. 4 + 1 = 5:
154
 31
  5


Step 3
Add the next column to the left and write the sum below the addends. 5 + 3 = 8:
154
 31
 85


Step 4
Add the next column to the left and write the sum below the addends. In this case this is the last column on the left; our addition will be finished after this. Since the digit underneath 1 is blank, we consider the blank as the number 0. 1 + 0 = 1:
154
 31
185

The addition is now complete: 154 + 31 = 185. To double-check this answer, start with 154 and count up by one 31 times.

It Gets A Little More Complicated
What do we do, if while adding column by column, the sum of any two columns is a two-digit number? For example, if we were to add 154 and 78, in the right-most column we would be adding 4 + 8 to get a sum of 12. Would we start out:
154
 78
  12
 ? No!

If we were to continue this way, the next sum in the column to the left would also be 12, and the sum in the last column to the left would be 1, so our sum of 154 + 78 would be 11,212. If we were to add 154 and 78, either by counting or on a calculator, we would find that 154 + 78 = 232. So, writing down the sum of 12 from adding 4 + 8 must somehow be incorrect.
154
 78
11212
 ? Incorrect!



The Correct Way
The correct way is to use a process called carrying. In a two-digit sum, like 12, we take the left digit, the 1, out of the sum and carry it into the column to the left. Then we write down only the right digit of the sum, the 2, like this:

Step 1
Add 4 and 8 for a sum of 12. Write down the 2 and carry the 1 into the next column to the left.
 1 
154
 78
  2

The red 1 in the middle column is the 1 we carried from 12.

Step 2
There are now three numbers to add: the 5 and the 7 from the original addends and 1 that was carried, so 1 + 5 + 7 = 13. Write down the 3 and carry the 1 into the next column to the left.
11 
154
 78
 32


Step 3
Add the 1 that we carried from the sum of 13 in the last step to the 1 of 154. Again, because there are only two digits in 78, we consider the blank as 0:
11 
154
 78
232

The addition is now complete: 154 + 78 = 232. To double-check this answer, try it on a calculator.

Make Math Work Can Help
The Add command will add a series of numbers showing the carries if carries were necessary. You can try these examples:
* This is our carrying lesson from above: Add 154, 78
* This will make a new column to the left when the sum contains more digits than than do the individual addends: Add 154, 978
* This will add several number of various sizes: Add 48154, 7538, 12, 94756