Ratio and Proportion - Concept of Ratio

A ratio is a way of comparing two quantities of the same kind by division. For example, if we have $5$ red balls and $3$ blue balls, the ratio tells us how many red balls there are for every blue ball, which can be visualized as a group of $8$ items split into two specific parts.

A ratio is denoted using the colon symbol $:$. If the first quantity is $a$ and the second quantity is $b$, the ratio is written as $a:b$ and read as '$a$ is to $b$'. Visually, the colon acts as a separator between two comparable numerical values.

The order of terms in a ratio is very important. The ratio $3:2$ is not the same as $2:3$. For instance, in a map where the ratio of distance to actual ground is $1:100$, reversing it to $100:1$ would change the entire scale and visual representation of the map.

To calculate a ratio, both quantities must be expressed in the same unit. If you are comparing $20\text{ minutes}$ to $2\text{ hours}$, you must first convert the hours to minutes ($120\text{ minutes}$) so that they can be compared on the same visual scale.

A ratio is usually expressed in its simplest form. This is done by dividing both terms by their Highest Common Factor (HCF). For example, a ratio of $10:20$ can be simplified to $1:2$, which visually represents that the second quantity is double the first.

Equivalent ratios are obtained by multiplying or dividing both the terms by the same non-zero number. Just as a small photograph and its enlargement maintain the same visual proportions, the ratios $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent as they represent the same comparison.

A ratio does not have any units. Since it is a comparison of two similar quantities with the same units, the units cancel out during division, leaving a pure numerical value.