Question

How are scales and ratios related?

Answer 1

Hint: The scale and ratio are important aspects not only in mathematics but also in our everyday life. Scale usually refers to the measurement ratio of the taken value and the actual value whereas ratio refers to the comparison between two or more quantities.

Complete step-by-step answer:
According to the question, we are provided with two aspects: scale and ratio. We have to describe each of these.
We will begin with scale.
A Scale describes how much of the actual value is reduced so that it can be quantified in minimum space. It is written as a ratio of the taken measurement to the actual measurement. It is used while drawing graphs, maps, etc.
For example: In graphs, we know that each consecutive number differs by one unit. If suppose, we have to plot large units (values like 100, 200…1000). In that case, we can assume a different scale, that is, \[1cm=100units\].
In maps also, we have seen distance represented in the ratio \[1mm=50,000km\]. It is because we cannot represent \[50,000km\] in a single sheet of paper so we scale it down to \[1mm\]. This way the representation gets easy and readable as well.

A ratio on the other hand is a comparison between quantities. It is not restricted only to mathematics. It is widely used and in all forms. It can be used to represent differences in the life-expectancy in male and females, birth rates, performance of boys and girls in a class, etc.
For example: In a class of 70 students, male and female ratio is \[4:3\]. This means for every 4 boys in the class there are only 3 girls.
That is,
Number of boys in the class: \[\dfrac{4}{7}\times 70=40\] boys
Number of girls in the class: \[\dfrac{3}{7}\times 70=30\] girls.

Therefore, a scale is the ratio of the value taken with respect to the actual value.

Note: Both the quantities are useful in some or the other way. They have a clear line of difference between them. So, one should not get confused while using either of them. They both have a variety of applications as well.