Addition '+' | Basics of Arithmetic
This page is part of our series covering the basics of arithmetic, the simplest way of manipulating numbers.
Here you'll learn the basics of addition (+): how to add, sum or combine two or more numbers to make a new number - a total. The ability to 'add up' is important in all aspects of life, at home, school, work and socially.
Addition Quick Facts:
- Addition is the term used to describe adding two or more numbers together.
- The plus sign ‘+‘ is used to denote an addition: 2 + 2.
- The + can be used multiple times as required: 2 + 2 + 2.
- For longer lists of numbers it is usually easier to write the numbers in a column and perform the calculation at the bottom.
- The word 'sum' or the symbol ∑ may also be used for addition.
- It doesn’t matter in which order you add a group of numbers together as the answer will always be the same:
1 + 2 + 3 + 4 gives the same answer (10) as 4 + 2 + 1 + 3
- Adding 0 to any number makes no difference 2 + 0 = 2.
Basic addition is a step on from counting and usually picked up easily by learners.
Once a learner can count to ten they can usually quickly perform additions up to ten.
For example, if a learner is given two piles of cards, one pile containing 4 cards and the other containing 3 cards, they can count all the cards and come up with the answer: 7.
Using fingers is common when learning how to count and add. Adding dots drawn on a piece of paper, then using a ‘number line’, are the next steps in learning addition, this time there are no physical items to handle.
Finally when digits are recognised the same sum can be performed by looking at 3 + 4.
Adding the same number to itself (or doubling) is also fairly straightforward once a basic understanding of multiplication has been grasped, 3 + 3 = 6 for example.
Adding the same number to itself is the same as multiplying a number by 2:
3 + 3 can also be written as
3 x 2 (verbally 3 times 2).
When adding lots of numbers together it is helpful to write them in columns, denoting units, tens and hundreds (see our numbers page for examples of this). If we needed to add 4, 15, 23, 24, 35, 42
Arrange the numbers in columns, Hundreds, Tens and Units as needed:
Add the numbers in the right (units) column. This should give you an answer of 23. Two tens and three units. Write a 3 in the total for the units column.
Carry over the 2 tens - it is usual to put this number underneath the total, we'll need it in the next step.
Add together the numbers in the tens column remembering to include the 2 that was carried over. You should get an answer of 14.
That is 4 tens (as we are working in the tens column) and 1 to carry over to the next column, hundreds.
The next step would be to add together the numbers in the hundreds column.
There are no numbers in the hundreds column except for the 1 that was carried over from the tens column.
As there is nothing else to add, bring the one up to the total.
We have no numbers left to add and therefore have arrived at our answer: 143.
You can use exactly the same method to add larger and larger numbers, by adding extra columns on the left as needed for thousands, tens of thousands etc.
Examples of Addition
There are many examples of when addition is useful in everyday situations. When working out a route for travel you may want to add up the number of miles (or kilometres) for each step of the journey to find the total number of miles you will travel. This could help you plan for fuel stops, for example.
You can use addition to work out how long something will take. For example, if you get on the bus at 11:00 and the journey takes 25 minutes what time will you arrive? Similarly you can add up days, weeks, months or years.
Always remember when adding minutes or seconds that there are 60 seconds in a minute and 60 minutes in an hour. Therefore 100 minutes is not equal to an hour but 1 hour and 40 minutes. See our page on Calculating with Time for more information.
Perhaps one of the most common everyday uses for addition is when working with money. For example, adding up bills and receipts. The following example is a typical receipt from a supermarket. Add all the individual prices to find the total for the visit.
As SkillsYouNeed is a British site, the currency symbol used is £ (pounds). Adding in $ (dollars), € (euros) or any other currency is the same - just change the currency symbol.
Add the prices on the receipt in the same way as the previous example.
This time you have a decimal point (.) to show fractions of one unit (a Pound £). When doing your column addition calculation, you can ignore the decimal point until you get to the end. Start by adding together the numbers in the right-hand column as before, working through the columns from right to left and carrying over any ‘tens’ to the next column.
Remember to include the decimal point at the end of your calculation; you should have two columns to the right of it. Technically these columns should be labelled 'Tenths' and 'Hundredths'. However, try to add the numbers without using column headings.
You may find it easier to write or print this example.
Your final answer should be: £17.81.
If you have arrived at a different answer, then check your working and try again.
It is important to note that not all global currencies are based on a decimal system and not all currencies have two decimal places. For example, some have zero decimal places (e.g. Japanese yen), and some have three decimal places (e.g. the dinar in many countries).
There are very few examples of non-decimal currencies. Mauritania (where 1 ouguiya = 5 khoums) and Madagascar (where 1 ariary = 5 iraimbilanja) are only theoretically non-decimal, as in both cases the value of each sub-unit is too small to be of any practical use today and coins of sub-unit denominations are no longer in circulation. The official currency of the Sovereign Military Order of Malta is the Maltese scudo, which is subdivided into 12 tarì, each of 20 grani with 6 piccioli to the grano.
All other global currencies are either decimal or have no sub-units at all, either because they have been abolished or because they have lost all practical value and are no longer used. For more information about the decimal system, see our page on Systems of Measurement.