Fractions help describe the situation when you need to deal with part of something. Any time you say things like "I drank half the glass of water", or "we ate a quarter of the pizza", you are dealing with fractions. Lets look at an example with a circle, or if you want to pretend it's a pizza that would work as well.
We can say we have 1 circle. What happens when someone eats up half of that pizza? How do we describe it?
Well simply enough, we say we have one half of a circle. How do we describe a half in numbers? Well we say we have 1 piece left of a whole made up of two equal pieces. In this case we have our circle divided up into 2 equal pieces. Since we only have one of those pieces we have 1 part of 2 pieces. We denote this as the following:
The 1 on the top, called the
numerator, indicates how many sections we have, while the bottom, the
denominator, indicates how sections are needed to make a whole.
Lets take a look at another example using our circles. Imagine our pizza is cut up into 8 equal pieces as shown below:
Today we are really hungry and we decide to eat 3 pieces of pizza.
We now have 5 pieces left so we can say the following:
We ate 3/8 (pronounced three eighths) of the pizza and we have 5/8 (pronounced five eighths) of the pizza left.
Important note about fractions!
The one thing to remember about fractions is that we are always dealing with equal size pieces. If we are really messy about cutting our pizza and we may have something like this:
Here we can't use fractions. There are 6 pieces here, but two of them are bigger than the others so we are not dealing with equal parts.