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.