Long Addition

Long addition is a method for adding numbers. Long addition involves writing the numbers to be added one underneath another, so the digits are in columns. The numbers are added a column at a time. Many numbers of any length (including decimals) can be added in this way.

How to Do Long Addition

Step-by-Step:

1

Write the numbers you wish to add, one underneath the other.

2

Add up the numbers in the right-most column.

3

Check if the answer from the previous Step is 9 or less:
  • If Yes, write the number below the column (between the lines) and move to Step 4.
  • If No, the answer will have two digits. Write the digit on the right underneath the column (between the lines). Write the digit on the left underneath the column to the left of the current column (below the two lines). This is carrying. Move to Step 4.

4

Move to the column to the left. Add up the numbers in this column, including any numbers below the two lines.

5

Go to Step 3 and repeat until all columns have been added.

A Real Example of How to Do Long Addition

Doing long addition is easy.

Question

Add the numbers below.

Step-by-Step:

1

Write the numbers you wish to add, one underneath the other.

2

Add up the numbers in the right-most column.
7 + 4 = 11

3

Check if the answer from Step 2 is 9 or less: No. 11 is not 9 or less.
  • If No, the answer will have two digits.
  • Write the digit on the right underneath the column (between the lines).
  • Write the digit on the left underneath the column to the left of the current column (below the two lines). This is carrying. Move to Step 4.

4

Move to the column to the left. Add up the numbers in this column, including any numbers below the two lines.
2 + 8 + 1 = 11

5

Go to Step 3 and repeat until all columns have been added.

3

1st repeat Check if the answer from the previous Step 4 is 9 or less: No. 11 is not 9 or less.
  • If No, the answer will have two digits.
  • Write the digit on the right underneath the column (between the lines).
  • Write the digit on the left underneath the column to the left of the current column (below the two lines). This is carrying. Move to Step 4.

4

1st repeat Move to the column to the left. Add up the numbers in this column, including any numbers below the two lines.
3 + 1 + 1 = 5

5

1st repeat Go to Step 3 and repeat until all columns have been added.

3

2nd repeat Check if the answer from the previous Step 4 is 9 or less: Yes. 5 is 9 or less.
  • If Yes, write the number below the column (between the lines).
There are no more columns to the left. All columns have been added.

Answer:

The solution to 327 + 184 is 511.

Lesson Slides

It is possible to add decimals together, as well as to add more than two numbers together. The slider below shows another real example of how to do long addition.

Parts of an Addition

  • The numbers you add together are addends.
  • The result of adding the numbers is the sum (or total).

The Order of Addition

The order in which numbers are added does not matter. For example:
2 + 3 = 5
If the 2 and 3 are swapped around, the sum is the same:
3 + 2 = 5
This is the commutative property of addition - changing the order does not change the result.

Digits and Place Value

Numbers consist of digits. In a decimal, the digits can take values 0 through to 9. The value of the digits depend on its place value. The place value is the place in the number where the digit is. Place values include hundreds, tens and units. For example, 123 consists of:
  • 1 hundred
  • 2 tens
  • 3 units
That is: Each place value is 10 times bigger than that to its right. A hundred is 10 times a ten, a ten is 10 times a unit. The same system applies to the right of the decimal place:

Place Value and Columns in Long Addition

The columns in long addition correspond to the place values of the digits in the numbers to be added. This ensures that when you add the digits, they are of the same value - you are adding units to units and tens to tens.

Place Value and Carrying

Digits in a decimal system go from 0 through to 9. The numbers 0 through to 9 can be written just using the units place value.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
To write numbers after 10, the tens place value must be used:
10, 11, 12...
A 1 in the tens place value is 10 times bigger than a 1 in the units column. Similarly, the numbers up to 99 use the tens and units place values. After 100, the hundreds place value also has to be used:
100, 101, 102...
where, 100 is 10 tens. Which ever place value we are at, once the digit in that place value becomes greater than 9, we need represent the larger number by placing digits in the place value to the left. This is why when doing long addition, if the numbers in any column add up to be greater than 9, a digit is placed below the column to its left: