A fraction is a mathematical expression used to represent a part of a whole. They are frequently encountered in daily life, such as when dividing pizza slices or calculating exam scores. For example, if you scored 22 out of 24 on a maths paper, this could be expressed as a fraction.

A set of nine circular diagrams illustrating fractions. Each circle is divided into parts, with one part shaded in green. From left to right, top to bottom: a half, a third, a quarter, a fifth, a sixth, a seventh, an eighth, a ninth, and a tenth of the circles are coloured green, respectively. Each diagram is labelled with its corresponding fraction.

Equivalent Fractions

The same fraction can be represented in multiple ways, as long as the proportion between the numerator (top number) and the denominator (bottom number) remains the same. This occurs because you can always factor out a common term from the numerator and denominator and divide by it to obtain an equivalent fraction.


The fraction \frac{1}{2}, which represents one-half, can also be expressed as \frac{5}{10}, \frac{6}{12}, and an infinite number of other equivalent fractions. This is because 5 is half of 10, 6 is half of 12, and so on. In each case, the ratio between the numerator and the denominator remains the same, maintaining the value of the fraction.

\frac{1}{2} = \frac{5}{10} = \frac{6}{12} = \cdots

To better understand fractions and their applications, remember that the key concept is the proportional relationship between the numerator and the denominator. This will help you simplify, compare, and perform operations with fractions effectively.

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