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Arabic Numbers --- Introduction --- Add --- Subtract --- Multiply --- Divide --- Practise sums --- Less than 1 --- Types of numbers

If you want to practise your mental arithmetic at addition, click here.

Add is sometimes also known as plus or and (although AND can mean something different in Mathematics.)

Arabic numbers are better for arithmetic. You make less mistakes, and it's easier to see what you are doing. But you do have to learn the results of simple calculations. Once you know these then you can do complicated calculations with just pen and paper.

Addition tables

Multiplication tables are well known. There are addition and subtraction tables as well. We don't learn these as a table, we just pick them up as we start doing sums. But here are the addition tables laid out for you to look at. Click on numbers at the top and the side.

Commutative and associative

If you have problems with simple additions, then you can always count on your fingers. But it is worth learning them, as it makes arithmetic and mathematics far easier to do. If you look at the table, you will see that the top right half is the same as the bottom left half. For example, 6 + 8 is the same as 8 + 6. This halves what you have to learn. This is because addition is commutative. This means that if you add numbers together, it doesn't matter what order you add them - from left to right - from right to left - or jumbled! Addition is also associative. If you add three or more numbers together, you add them in pairs. For example, you may add the first two, then add the third one to the result. Or you may add the last two, then add the first one to the result. Since adding is associative, this gives the same result. For example: (2 + 3) + 5 = 5 + 5 = 10 and 2 + (3 + 5) = 2 + 8 = 10

Pairs that add to ten

You will find that it helps with mental arithmetic if you learn the numbers that add up to ten. Click on Get sum for some practise in this.

Once you know the pairs of numbers that add up to ten, it can help you to work out the rest.
Usually people can add together numbers to less than ten (use fingers if necessary!)
If you meet a sum like 8 + 7, you know that 8 + 2 = 10.
So break down 7 into 2 + 5.
Then you have 8 + 2 + 5 or 10 + 5 which is 15.

Adding larger numbers

Now for the more complicated calculations!

To add together longer numbers, write one number under another so that they line up on the right-hand side. The units (green) are in the right-hand column, the tens (red) are the next column, the hundreds (blue) are the next column, and so on. You add each column in turn and write it at the bottom. If none of the columns add up to more than nine, then you have the answer.

If you find this hard to understand, it may help you to use this abacus.


Adding with carry

If one of the columns adds up to more than nine, then you need to take the ten onto the next column on the left. This is called carrying. Since each column is ten more than the one to it's right, this means that you add one to the next column. Write a one under the bottom line of the answer to remind you to do this.

If you need to add a long string of numbers, then it is easy to make mistakes. You should double-check the answer by adding them up a second time. If you do it the same way, you might make the same mistake again, so add them from bottom to top the second time!

Practise adding

Click on Get sum for some practice in adding. When the sum appears, enter the answer in the boxes. There are boxes provided for carries, but you don't have to use them.


Adding decimals

If you have calculations of numbers with decimals in, like money, then line up the decimal points, rather than lining up on the right-hand side. Any whole numbers are assumed to have their decimal point at the end.


Adding using calculation machines

Throughout history, people have used an abacus to help them with addition and subtraction. Even earlier, people used their fingers. Now we tend to use a calculator.

However, it's best to make sure that you can do simple sums in your head. Click here to learn to do mental arithmetic quickly and accurately.