Fractions - Types of Fractions

A fraction represents a part of a whole or a collection. It is written as $\frac{a}{b}$, where $a$ is the numerator (parts taken) and $b$ is the denominator (total equal parts). Visually, if a circle is divided into 4 equal slices and 1 is shaded, the shaded part is $\frac{1}{4}$.

Proper Fractions are fractions where the numerator is strictly less than the denominator ($Numerator < Denominator$). These fractions always represent a value less than 1. For example, $\frac{3}{5}$ is proper because 3 is smaller than 5, looking like a smaller portion of a single whole unit.

Improper Fractions are fractions where the numerator is greater than or equal to the denominator ($Numerator \ge Denominator$). These represent a value equal to or greater than 1. Visually, $\frac{5}{4}$ represents one full object plus one-quarter of another identical object.

Mixed Fractions (or Mixed Numbers) consist of a whole number and a proper fraction combined together. For example, $2 \frac{1}{3}$ represents 2 whole items and $\frac{1}{3}$ of a third item. It is another way to express an improper fraction.

Like Fractions are groups of fractions that have the exact same denominator, such as $\frac{1}{7}$, $\frac{3}{7}$, and $\frac{5}{7}$. They are easy to compare or add because the 'size' of the parts (the denominator) is identical.

Unlike Fractions are fractions that have different denominators, such as $\frac{1}{2}$ and $\frac{2}{3}$. To compare or operate on them, they usually need to be converted to like fractions using the Least Common Multiple (LCM).

Unit Fractions are a specific type of proper fraction where the numerator is always $1$. Examples include $\frac{1}{2}$, $\frac{1}{10}$, and $\frac{1}{100}$. Visually, these represent a single piece of a whole divided into many parts.

Equivalent Fractions are different fractions that represent the same value or the same part of a whole. For instance, $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{4}{8}$ are all equivalent. Visually, shading half a rectangle is the same area as shading two out of four equal parts of that same rectangle.