Number - Fractions and Equivalent Fractions

A fraction represents a part of a whole or a part of a set, written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator. Visually, imagine a pizza divided into 8 equal slices; if you take 3 slices, you have $\frac{3}{8}$ of the pizza.

Equivalent fractions are different fractions that represent the exact same value or proportion. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent. Visually, if you shade half of a circle, it looks identical to shading two quadrants of the same circle.

Proper fractions have a numerator that is smaller than the denominator (e.g., $\frac{3}{5}$), meaning the value is less than 1. Improper fractions have a numerator larger than or equal to the denominator (e.g., $\frac{7}{4}$), meaning the value is 1 or greater.

A mixed number consists of a whole number and a proper fraction, such as $2\frac{1}{3}$. Visually, this represents two complete shapes and one-third of a third identical shape.

To simplify a fraction to its lowest terms, divide both the numerator and the denominator by their Highest Common Factor (HCF). A fraction is in its simplest form when the only common factor between the numerator and denominator is 1.

Fractions can be represented on a number line between integers. For example, $\frac{3}{4}$ is located three-quarters of the way between $0$ and $1$. If the number line is divided into four equal segments, $\frac{3}{4}$ sits on the third tick mark.

Comparing fractions requires a common denominator or a common numerator. Visually, it is easier to see that $\frac{2}{3} > \frac{1}{2}$ by dividing two identical bars into 3 segments and 2 segments respectively and comparing the shaded lengths.