The ratio of $25$ to $100$ can be expressed as $1:4$.

To clarify this concept, let’s break it down further. A ratio serves as a means to compare two quantities, illustrating how many times one value is contained within the other. In this instance, we are comparing $25$ to $100$. To simplify the ratio, we first identify the greatest common divisor (GCD) of the two numbers. The GCD of $25$ and $100$ is $25$, as it is the largest number that divides both $25$ and $100$ without leaving a remainder.

Once we have the GCD, we divide both numbers by it. Specifically, we calculate:

and

This results in the simplified ratio of $1:4$. This signifies that for every $1$ unit of the first quantity ($25$), there are $4$ units of the second quantity ($100$).

Ratios play a crucial role in various real-life applications, such as cooking, where you may need to adjust a recipe’s proportions, or in mapping, where distances are represented on a smaller, proportional scale. Mastering the simplification and interpretation of ratios is a fundamental skill in GCSE Maths, enabling you to compare quantities effectively and accurately.