Number - Introduction to Fractions

A fraction represents a part of a whole object or a group that has been divided into equal pieces. For example, if a circular pizza is cut into $4$ equal slices and you take $1$, you have $\frac{1}{4}$ of the pizza. Visually, this looks like one shaded wedge in a circle divided into four equal parts.

The Numerator is the top number in a fraction that tells us how many equal parts are being shaded or counted. In the fraction $\frac{2}{3}$, the number $2$ is the numerator, meaning we are looking at two specific pieces.

The Denominator is the bottom number that tells us the total number of equal parts the whole is divided into. If a square is divided into $4$ smaller equal squares, the denominator is $4$. A larger denominator means the whole is divided into more, smaller pieces.

Unit Fractions are fractions where the numerator is always $1$, such as $\frac{1}{2}$, $\frac{1}{3}$, or $\frac{1}{10}$. They represent exactly one part of the whole. On a number line from $0$ to $1$, $\frac{1}{2}$ is located exactly in the middle.

Fractions must consist of equal-sized parts. If a shape is divided into parts that are not the same size, they cannot be accurately named using a simple fraction. For instance, a rectangle split into one huge piece and one tiny piece is not divided into halves.

Fractions can be shown on a number line. The distance between $0$ and $1$ is treated as the 'whole.' If the line is divided into $5$ equal intervals, each tick mark represents a multiple of $\frac{1}{5}$, starting from $\frac{1}{5}, \frac{2}{5}, \frac{3}{5}$ and so on.

Comparing fractions with the same denominator is simple: the fraction with the larger numerator is the greater fraction. For example, $\frac{5}{6} > \frac{2}{6}$ because $5$ equal parts of a bar are more than $2$ parts of the same sized bar.

Fractions can also describe a part of a set. If you have a collection of $8$ marbles and $3$ of them are green, then $\frac{3}{8}$ of the set of marbles is green.