Overview:

⚡ Ratio is the fraction of two or more similar quantities written in the form of a:b:c: ... :n.
⚡ The first term of a ratio is called antecedent and the last term is called consequent.
⚡ Proportion is the way of expressing two or more equal ratios, together in the form of a:b::c:d.
⚡ In this blog, you will learn ratio and proportion, their properties and other related terms.



Ratio

When we divide two or more similar quantities, the answer that we get in fractional form is considered as the ratio of those quantities.

Example: Let 'a' denote a quantity and 'b' represent the similar quantity, the ratio of a to b is a/b which is written as a:b.

Ratio can be simply understood as 'to how much' value of a quantity (or anything), the similar quantity can be measured.

Example: The height of person 'A' is 10cm and that of person 'B' is 20 cm. Now, to how much height of person 'A' can the height of person 'B' be measured.

First, divide A/B = 10/20
Now, A/B = 1/2
To write ratios, keep :(colon) in between the two values.
So, the ratio of heights of A:B = 1:2.

This means for every 1cm height the person 'A' gains, person 'B' gains 2cm height.




Terms Of Ratio

There are two important terms that one should know while writing the ratios.

When we find the ratio of two similar quantities, the quantity that is written first or the first term is called antecedent. And, the quantity that is written last or second term is called consequent.

For example;
In the ratio a:b, a is the first term or antecedent. And, b is the second term or consequent.

Fact: In mathematics, normally 'a' represents the first term and 'b' represents the last term.




Composition Of Ratios

Compounded ratio of a:b and c:d is ac:bd.
Duplicate ratio of a:b is a²:b².




Proportion

When we write two or more equal ratios together, it is said that the terms of the ratios are in proportion.

Example;
Let us consider that we have a ratio a:b which is equal to another ratio c:d.

We can write this as; a:b=c:d or a:b::c:d. In above condition, the four quantities a,b,c and d are said to be proportional.

It is read as: "a is to b as c is to d".

In proportion, change in value of one ratio directly affects the value of another ratio.