Here's a simple fact: When you cut a cake into two equal pieces, each piece is half of the cake. As a fraction, you write that as 1/2. In the figure, the shaded piece is half of the cake.
Every fraction is made up of two numbers separated by a line, or a fraction bar. The line can be either diagonal or horizontal — so you can write this fraction in either of the following two ways:
The number above the line is called the numerator. The numerator tells you how many pieces have a specific characteristic. In this case, you have one dark-shaded piece of cake, so the numerator is 1.
The number below the line is called the denominator. The denominator tells you how many equal pieces the whole cake has been cut into. In this case, the denominator is 2.
Similarly, when you cut a cake into three equal slices, each piece is a third of the cake.
This time, the shaded piece is one-third — 1/3 — of the cake. Again, the numerator tells you how many pieces have a specific characteristic (for example, how many pieces are shaded), and the denominator tells you how many equal pieces the whole cake has been cut up into.
Here are a few more examples of ways to represent parts of the whole with fractions.
In each case, the numerator tells you how many pieces are shaded, and the denominator tells how many pieces there are altogether.
The fraction bar can also mean a division sign. In other words, 3/4 signifies 3 divided by 4. If you take three cakes and divide them among four people, each person gets 3/4 of a cake.
