Fractions in everyday life

Is the glass half full or half empty?

Fractions are used under different aspects. Some of them are already familiar to you from your daily life:

For example, you waited three quarters of an hour for the bus, used a quarter litre of milk to bake a cake or your best friend lives half a kilometre away from you. It is also good to know that a can contains a third of a litre of cola.

The tank of the car is still filled to a third, two thirds of the way are already done or your mum complains that only a quarter of your desk is free...

Fractions can also describe a ratio beschreiben. For instance, if a group of five is made up of 3 boys and 2 girls, then obviously there are three fifths of boys and two fifths of girls.


Can Oliver eat a whole cake?

Fractions also describe a part of a whole:

Grandma made a delicious cake. This is cut into 8 equally sized pieces. Each piece then equals one eighth of the whole cake. It is written like this:


one eighth of a cake

Oliver has just returned from soccer and is very hungry. He shovels three pieces onto his plate. It is written like this:


three eighth of a cake


The family party

One week later, there is a family party and Grandma baked a lot of delicious cakes. There are 3 of Oliver's favorite cakes on the table. Of course, Oliver takes a piece of every cake:

How do you think this is expressed as a fraction?



If Grandma used the same baking pan for all 3 cakes, then Oliver ate three eighths of cake again.


A fraction
numerator, denominator, fraction bar

In Maths terms you write three eighths this way:

First you think about the number of pieces the cake was divided into. This number is written below the fraction bar and is called thedenominator of the fraction. In our example, this is the number eight. You can easily remember because this number denominates the fraction: Eighths.
You can also easily remember: denominator → down.

Obviously, you can count or numerate Oliver's pieces of cake. This is why the number above the fraction bar is called the numerator.

The line in the middle is called fraction bar.

This is how the fraction came into being:

Definition fraction: origination


Online Exercise: Naming fractions

You can practice naming fractions online:

The exercises are not difficult, so I recommend that you take a look at them. The visual representations are very important for the understanding of fractional arithmetic!



You now have a clear picture of a fraction: Ein A piece of cake.

If you see a fraction, try to imagine it that way. Of course, this can be difficult with large numbers - admittedly then there are more cake crumbs than pieces of cake ...

Nevertheless, it is a good trick to visualize tasks before calculating. Often you will see the solution easier and make fewer mistakes!

Of course you can also choose another picture, for example a bag of candy or anything else you like. Give the numbers a meaning!

Video: Introduction to Fractions

Finally, a funny video about: Introduction to Fractions:


Let's continue with: "Mixed Numbers"