Maths

Can you count up to twenty?

Can you count up to a hundred in tens?

Can you do little sums like eight plus nine? (Test yourself by clicking here now.)

Do you understand big numbers like 1024 (one thousand and twenty four)?

If not, then you probably need to find someone who can teach you how to do all these things. The previous Web page will tell them how to teach you.


But if you can do all those things you may be able to learn everything else on your own from this point on.

There's no harm in getting someone to sit with you as you read this, but they should let you try to do everything for yourself first. They should really only help you when you ask them to.

You can already add small numbers, but now you need to learn how to add big ones. Small sums can be written down on paper like this:-

8 + 9 = __

and you would normally write the answer into the space over the line, but big sums usually need to be written down in a special way because they are hard to work out in your head, so the sum 12 + 31 should be written out with the 12 on top and the 31 underneath it like this:-

  12
+ 31
    

Click on these buttons to solve the sum: 2 + 1 = 3 (the column on the right is added up first), 1 + 3 = 4 (and then the other column is added up). When adding the second column we are actually doing the sum 10 + 30 = 40, even though it looks like 1 + 3 = 4. Once both columns have been added up like this, the number at the bottom between the two lines, 43, is the answer to the whole sum, so 12 + 31 = 43. This way of adding by doing one column at a time makes adding big numbers easy. Let's do another one, but with much bigger numbers (1024 + 2573):-

  1024
+ 2573
      

This time there are four columns to do: 4 + 3 = 7; 2 + 7 = 9; 0 + 5 = 5; and 1 + 2 = 3. If you have clicked all four buttons, you can now see the answer: 1024 + 2573 = 3597.

Before we go any further, I need to give you a little tip if you're reading this on a computer with a small screen: you can see much more of the page at a time by pressing the F11 key, and pressing that same key again will return things to normal afterwards.

So adding up big numbers really is easy, but there is one little problem which you haven't met yet. Look at the next sum and see if you can spot the problem:-

  1278
+ 2351
      
  

Click these four buttons: 8 + 1 = 9; 7 + 5 = 12; 2 + 3 = 5; 1 + 2 = 3. But what happened to the orange "1"? When the second column was added up (7 + 5) the answer was 12, but there wasn't enough room to fit the answer in the space underneath without it spreading into the next column to the left. The orange "1" was very important, because the real answer for the sum is actually 3629; not 3529. Press this button to reset the sum, then click the four buttons again to have another look at what happened. When you're ready, do the sum properly by clicking these buttons: 8 + 1 = 9; 7 + 5 = 12; 2 + 3 + 1 = 6; 1 + 2 = 3; . If your screen's too small to see it all at once, click here: .
indentWhenever an answer is too big to fit in its column, as with the 12 in the sum we've just done, the part of the number that won't fit has to be put somewhere in the next column to the left, but it goes under the bottom line of the sum so that it doesn't get in the way of the next answer. The orange "overflow digit" is then added on when the next column is added up. Click the reset button and go through it all again, making sure you understand what happens as you press each button.

Well, you really do know how to add now. Here's a big sum for you to try yourself. See if you can work out the answer for each column before you press the button for it. If you click the wrong button, just click the reset button and start again:-

  5745
+ 6745
      
    

5 + 5 = 10; 4 + 4 + 1 = 9; 7 + 7 = 14; 5 + 6 + 1 = 12. To start again, click: . There is no need to put the last overflow digit under the bottom of the sum as there are no other numbers in the fifth column to add it to, so it can be put straight in alongside the 2 of the 12. Click through the sum several times to make sure you understand it properly.

It is possible to add more than two big numbers together in the same sum: you can stack them as high as you like, and they don't even need to be the same length. Here is 3579 + 789 + 7039.

  3579
   789
+ 7039
      
    

9 + 9 + 9 = 27; 7 + 8 + 3 + 2 = 20; 5 + 7 + 0 + 2 = 14; 3 + 7 + 1 = 11. To start again, click: . Click through the sum several times to make sure you understand it properly.

Now that you have seen how adding should be done, you need to fix the method in your head by doing lots of sums: click here and here for two games which will help you do that. At some point, you will also need to try doing sums on paper with a pencil instead of just clicking buttons on a computer: you must practise writing sums out, lining up all the digits in colums so that they can be added up easily, and then solve them before getting someone to check your answers.