A proportion is an equation that asserts the equality of two ratios.

In mathematics, a ratio is a way to compare two quantities through division. For example, if you have $2$ apples and $3$ oranges, the ratio of apples to oranges can be expressed as $2:3$. A proportion, in contrast, is a statement indicating that two such ratios are equivalent. For instance, if you have another set of fruits containing $4$ apples and $6$ oranges, the ratio of apples to oranges remains $2:3$. Thus, the ratios $2:3$ and $4:6$ constitute a proportion because they simplify to the same value.

To represent a proportion, you place an equality sign between two ratios. For example, the proportion relating the ratios $2:3$ and $4:6$ can be written as:

This statement implies that if you multiply or divide both terms of one ratio by the same number, you will obtain the other ratio. In this case, multiplying both terms of $2:3$ by $2$ yields $4:6$.

Proportions play a crucial role in solving problems related to scaling, resizing, and comparing various quantities. For example, if you know that $3$ pencils cost £$1.50$, you can use a proportion to determine the cost of $5$ pencils. You would set up the proportion:

where $x$ represents the unknown cost. By cross-multiplying and solving for $x$, you can find the answer.

Grasping the concept of proportions is vital for many real-world applications, such as cooking recipes, creating models, and working with maps. It enables you to make accurate comparisons and predictions based on available data.