Fractions - Types of Fractions

A fraction represents equal parts of a whole or a collection, written in the form $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator. Imagine a circular pizza cut into $8$ equal slices; if you eat $3$ slices, you have consumed $\frac{3}{8}$ of the pizza.

Proper Fractions are fractions where the numerator is less than the denominator ($a < b$), such as $\frac{2}{5}$ or $\frac{7}{12}$. Visually, a proper fraction is always less than one whole object, like a rectangle where only some internal segments are shaded.

Improper Fractions have a numerator that is equal to or greater than the denominator ($a \ge b$), such as $\frac{5}{3}$ or $\frac{9}{4}$. Visually, these represent one or more complete objects plus an additional part of another object.

Mixed Fractions (or Mixed Numbers) consist of a whole number and a proper fraction combined, such as $2\frac{1}{4}$. This can be visualized as $2$ fully shaded squares and a $3$rd square where only $1$ out of $4$ equal parts is shaded.

Unit Fractions are a specific type of proper fraction where the numerator is always $1$, such as $\frac{1}{2}$, $\frac{1}{5}$, or $\frac{1}{10}$. On a number line, these represent the basic 'unit' or 'step' size between $0$ and $1$.

Like Fractions are a group of fractions that share the exact same denominator, such as $\frac{1}{9}$, $\frac{4}{9}$, and $\frac{7}{9}$. Visually, they represent parts of a whole that has been divided into the same number of equal-sized pieces.

Unlike Fractions are fractions that have different denominators, like $\frac{1}{2}$, $\frac{2}{3}$, and $\frac{3}{5}$. Because the denominators differ, the 'size' of the parts in each fraction is different, making them harder to compare visually without a common scale.

Equivalent Fractions are different fractions that represent the same part of a whole, such as $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$. If you shade half of a circle, it is the same amount of area whether the circle is divided into $2$ parts or $6$ parts.