Imagine you have a pizza and you want to share it equally with a friend. You cut it right down the middle into two equal slices. Each of you gets one of those slices. You didn't get a whole pizza, just a part of it. That's exactly what a fraction represents.

They show up everywhere, from splitting a dinner bill to following a recipe that calls for half a cup of flour. Fractions help us talk about amounts that are not whole numbers.

Every fraction has two key numbers, stacked on top of each other and separated by a line. Let's look at the fraction for one slice of that two-slice pizza:

The top number is called the numerator. It tells you how many parts you have. In this case, you have 1 slice.

The bottom number is the denominator. It tells you how many equal parts the whole was divided into. Our pizza was divided into 2 equal slices.

Fractions come in a few different flavors, each telling a slightly different story about the relationship between the parts and the whole.

Proper fractions are the most common type you'll see. They're always just a piece of the pie, never the whole thing or more.

Imagine you have two pizzas, each cut into four slices. If you eat five slices, you've eaten 5/4 of a pizza. That's one whole pizza and one extra slice.

Mixed numbers are just another way to write improper fractions. Saying you ate $1 \frac{1}{4}$ pizzas is often easier to picture than saying you ate $\frac{5}{4}$ pizzas.

Sometimes the easiest way to understand a fraction is to see it. We can use diagrams called area models and number lines to visualize them.

An area model, like a circle or a rectangle, shows a whole shape divided into equal parts. Shading some of those parts shows the fraction.

A number line helps us see where a fraction lives in relation to other numbers. To find $\frac{2}{3}$, you take the space between 0 and 1, divide it into 3 equal sections, and count over 2 sections from 0.

Fractions can also be thought of as division. The fraction $\frac{3}{4}$ is another way of writing the division problem $3 \div 4$. If you share 3 cookies among 4 friends, each friend gets $\frac{3}{4}$ of a cookie.

Finally, fractions express ratios. A ratio compares two quantities. If there is 1 teacher for every 20 students in a class, the ratio of teachers to students is 1 to 20, which we can write as the fraction $\frac{1}{20}$.

Now that you've got the basics, let's test your understanding.