Operations and calculations
2. Addition
Addition is the process of combining two or more numbers, or quantities, together to find the total value, or sum. The addition, or plus, (+) operator is used to indicate this operation.
Any amount of numbers can be added together in one operation, and in any order.
3 + 2 + 5 = 10 and 5 + 3 + 2 = 10
Long addition | Multiply Highland, 1:42
When we want to add two or more larger numbers together, we can use a method called long addition.
As an example in this video, we will calculate the total of 312, 265, 27 and 10.
To do this we start by listing the numbers we want to add together as a stack, lining them up in columns of units, tens, hundreds and so on.
Starting with the units column on the right hand side, we need to add up all the numbers in that column and write the total value in the answer space at the bottom. In this example our total is 14 which is greater than 9, so we write the units part, four, into the answer space and then write the one for the tens part underneath the answer space for the tens column to the left.
We now move on to add up the numbers in the tens column, including any that were written underneath the answer space, so that includes the one we added in this example. Again, write the total in the answer space separating out the tens and units if necessary. Here the total is 11, so we put a one in the answer space and another one beneath the answer space for the hundreds column.
We repeat this process until we have added up every column. So in this example we have a total of 614.
Long addition worked example
Some numbers, or combinations of numbers are fairly easy to add up in our head, or on our fingers, but for larger numbers, or longer lists of numbers, it is usually easier to write them out first, taking care to keep them in columns according to their place value.
When adding up in columns, we work from right to left.
In the following steps we'll find the sum of 312, 265, 27 and 10.
Write out the numbers to be added, one above the other, with individual digits in columns according to place value - units, tens and hundreds etc. (headings are included here as a reminder).
Add the digits in the units column.
2 + 5 + 7 + 0 = 14
Add the four units below the line in the units column and carry the ten over to the tens column – mark it below the space for the tens total - we'll need to include it in the next step.
Add the digits in the tens column, including the number carried over.
1 + 6 + 2 + 1 + 1 = 11
Add 1 below the line in the tens column and carry 1 over to the next (Hundreds) column.
Add the numbers in the hundreds column, including the number carried over.
3 + 2 + 1 = 6
Add 6 below the line in the hundreds column.
Following this process shows us that the sum of 312, 265, 27 and 10 is 614.