Ratios in Daily Life

In a ratio, we are not interested in the absolute values of the parameters compared. We are interested only in the way they change, relative to each other. It helps us to isolate parameters that we are interested in and study their relation and thus get more information about the relation. Hence the meaning of a ratio depends on the context. Expressing in ratios also allows for easy rough comparisons.

Ratios are such a powerful concept that they are used in almost every walk of life to convey important relationships. So much so that we use many of them frequently without even realizing that they are ratios!

Let us see some examples. We are devoting an entire chapter to these examples since ratios are one of the most important concepts to be learnt through primary math.

Health

A rough idea of physical fitness is estimated by BMI (Body Mass Index). It is the ratio of the weight of a person in Kgs to the square of his/her height in meters. Though its units are Kg/, it is known just by the numerical value.

Science & Technology

Speeds of supersonic jets are expressed as a ratio of the speed of sound. The ratios are called Mack, Mack1 being equal to the speed of sound.

Density is the ratio of the mass of an object and its volume.

Miniature scale models of large buildings, ships and aircraft are built to test their safety in the laboratory before being built on full scale.

Commerce

Apart from unit price, the percentages we use to express many ideas themselves are ratios. Percentage is a number expressed as a ratio in relation to 100. So if a person saves th of her income, we say that she has saved 20% of her income (i.e Rs 20 out of every Rs 100 of income)

Academic Performance

Percentages are used in schools also. The performance in various tests can be expressed in percentage, whatever was the total marks of each test.

Economy

Economic data of various countries are expressed as ratios, irrespective of the relative sizes of the economies.

Taxes like Sales Tax & Income Tax are expressed as percentages.

Music

Different notes in the musical scale (Indian or any other) are in fixed ratios. The melody depends not on the absolute frequency of the notes but on the ratio between notes. When Pythagoras discovered this, he was convinced that numbers & math were the basis of everything in the universe!

Geometry

As we have seen earlier, the famous number π, was discovered to be the ratio of the circumference of any circle to its diameter. The similarity of 2 plane figures was seen as the result of the ratio of their sides being equal.

A particular kind of rectangle with its sides being in a particular ratio was considered most aesthetic to look at. This particular ratio was even called the Golden Ratio.

Beauty & Aesthetics

The ideas of similarity were extended to beauty of paintings, sculpture and the human body itself. Certain ratios between parts of the body were considered more beautiful than others.

Ancient Hindus developed a science of aesthetics which was known as Alankara Sastra, based on ratios.

Recipes

All cooking recipes are ratios, since the actual quantity of food to be cooked is not known in advance.

If 2 cups of coffee are prepared with varying amounts of milk and decoction, we can say that the cup where the ratio decoction/ milk is more would be stronger. Even if the cups are of different sizes.