Parts of a Whole

A fraction represents a part of a whole. Imagine a whole circle, like a pie. If we cut that pie into pieces, each piece is a fraction of the whole pie. For something to be a true fraction, every single piece must be the exact same size. We call these equal parts. If one slice of pie is huge and another is tiny, they aren't fair fractions! When we talk about fractions, we are usually looking at how many equal pieces we have compared to how many pieces make up the entire object.

Every fraction has two main numbers separated by a line. The bottom number is the denominator. It tells us the total number of equal parts the whole was divided into. A good way to remember this is 'D' for 'Denominator' and 'D' for 'Down.' The top number is the numerator. It tells us how many of those parts we are actually talking about or 'counting.' For example, in the fraction $\frac{1}{4}$, the $4$ tells us there are four parts total, and the $1$ tells us we are looking at just one of them.

A unit fraction is a special kind of fraction where the numerator is always $1$. It represents exactly one equal part of the whole. Common unit fractions include one-half ($\frac{1}{2}$), one-third ($\frac{1}{3}$), and one-fourth ($\frac{1}{4}$). The larger the denominator, the smaller the piece! Think about it: if you share a pizza with $10$ people ($\frac{1}{10}$), your slice will be much smaller than if you only shared it with $2$ people ($\frac{1}{2}$).

To partition a shape means to split it up. When we represent fractions, we partition shapes like circles, rectangles, or squares into equal areas. If you want to show $\frac{3}{4}$ of a rectangle, you first draw the rectangle, then split it into $4$ equal columns or blocks, and finally shade in $3$ of them. This visualizes the fraction perfectly!