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How to Add (Mathematics Lesson)

What Is Addition?

Addition is the bringing together of two or more numbers (or objects) to make a total or sum.

For example, 2 apples plus 3 apples makes 5 apples:



In numbers:



Addition is denoted by the plus sign, +.

How to Add

The method used to add numbers will differ depending on the difficulty of the sum.

Adding short numbers together is easier than adding long numbers together.

How to Add Short Numbers Together

It is easy to add short numbers. Children learn to count fingers or objects for small sums.

A number line can be used to add. For example, 2 + 3 can be performed on a number line:

How to Add Long Numbers Together

It is more difficult to add numbers greater than 10 together.

For example:



This sum is made easier when we notice numbers are made of hundreds, tens and units (i.e. the place value of the digits in the number).



This allows the numbers to be broken down:



Each part - the hundreds (in blue), the tens (in yellow) and the units (in red) - can then be added to each other:



These 3 parts can then be added to give the answer:



The solution to 225 + 63 is 288.

This method of breaking numbers down into hundreds, tens and units is the basis for long addition, which offers a more systematic way of doing addition.

How to Do Long Addition

Long addition involves writing each number in columns and adding a column at a time.

As each column represents the hundreds, tens and units of the numbers, long addition implicitly breaks the addition down into adding the hundreds, tens and units, but without you having to think about it:

Step 1
Write the numbers you wish to add, one underneath the other.

Ensure they are aligned with each other so the units of one number is directly underneath the units of the other:



Step 2
Add up the numbers in the units column.
5 + 3 = 8.



Step 3
Add up the numbers in the tens column.
2 + 6 = 8.



Step 4
Add up the numbers in the hundreds column.
2 + 0 = 2.



The solution to 225 + 63 is 288.

The slider below shows another example of how to do long addition: Read more about long addition

Try a long addition
Interactive Widget
Here is an interactive widget to help you learn about long addition.
Interactive Test
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Note

PARTS OF AN ADDITION



  • The numbers you add together are addends.

  • The result of adding the numbers is the sum (or total).

ORDER OF ADDITION

The order in which numbers are added does not matter.

For example:



If the 2 and 3 are swapped around, the sum is the same:



This is the commutative property of addition - changing the order does not change the result.

LINE UP THE COLUMNS!

When doing long addition, ensure you align the numbers in the correct columns, so the units are all in the units column etc.

For example, the following would be incorrect:



The units of 63 (3) is underneath the hundreds of 225 (2).

Adding the columns would give:



which is incorrect.

Note

CARRYING

When adding numbers in a column, sometimes the sum may be 10 or more:



Adding the units above gives 12.

To do long addition correctly,

  • Write the 2 in 12 immediately below the numbers just added:



  • Write the 1 in 12 underneath the column to the left (this is carrying the 1):



  • When adding the left column, be sure to add the 1 along with the other numbers (2 and 6):