Mathematicians love to save time and effort - and even to be lazy if they can. That's why a lot of youngsters enjoy maths. Once you know the various maths codes and tricks you can save a lot of effort.

Fractions are one example of all this. Let me go back a bit in your studies.

After you learnt your numbers you were probably told how to add them up ~ and your life experience helped with this. If I want an apple and you want two then we need to buy three apples. Somehow you do not even have to think about that ~ you just know it.

As you ate apples ~ or grapes ~ you learned about subtraction ~ taking awy ~ minus ~ or just the way quantities get smaller as they are eaten.

Next came multiplying ~ times-ing ~ finding products ~ once again lots of words to cover a simple idea. If five people need to buy concert tickets at £3 each then there will be £5 change from a £20 note.

These are called the three rules of mathematics ~ there is a fourth. It is usually kept to last because people do not know the tricks and the make it seem difficult.

If I have to share seventeen somethings amongst five people I could avoid all the working out simple by leaving it as 17÷5. Another way is to say 17/5. It is the same thing. It is called a fraction. To say 'seventeen somethings to be divided into five piles' is a very long winded way of saying 17/3. Using a fraction saves all the bother of working it out.

As we all know life is not always as easy as it seems. Our **sharing problem** remains unsolved. By now you will have realized that each person gets three somethings ~ whatever they were. What is more there are two somethings left over. In real life dealing with the left overs can be tricky. A mathematician would take the easy way out and say two somethings to be shared amongst five people ~ easy ~ just do it.The mathematician can sit back and say 'my job is done' ~ 'two things have to be divided by five ~ I can do no more since I do not now what the **things** are'.

As a mathematician you have to be versatile with the many codes and tricks that other people use. 17/5 is the way I have to key-in a fraction when writing on one line of text ~ as I am now. If I was writing on a board or paper I would put a line under the seventeen, and a five under the line. Something is written ~ then underlined ~ then something else is written underneath. all that is represented by the ÷ sign ~ it is a dot underlined with another dot under the line.

Mathematicians as well as enjoying being lazy also take a great delight in sounding really clever. They have fancy names for the two dots ~ or whatever the dots represent. The top one is called the **numerator**. The bottom one is the **denominator**. You probably will not need to know about those words for ages ~ stick to **top** and **bottom** ~ everyone knows what you mean.

In the example above ~ if the things are roound cakes ~ everyone's favourite ~ then the 2/5 can be represented as two cakes ~ each cut into five slices ~ and one sllice from each cake to each person. Analternative would be to think of one cake cut into five slices ~ two slices to each person ~ one slice left over ~ the other cake cut into five slices ~ two slices to each person and one person gets one slice from each cake. If there are chocolate cakes and madeira cakes and Dundee cakes ~ well that all gets too difficult. You need a referee ~ or umpire ~ to sort it out. Please allow the mathematician to play with pencil and paper.