Ratio and Proportion
The ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers say a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion. The concept of ratio and proportion is majorly based on ratios and fractions. The ratio and proportion are the key foundations for various other concepts in mathematics. Ratio and proportion have their applications in solving many daily life problems, while we are comparing heights, weights, distance or time or dealing with business transactions or while adding ingredients in cooking, and so on.
What is Ratio and Proportion?
A comparison by division is termed as ratio and the equality of two ratios is called proportion. When it comes to measuring the speed of a car or an airplane, it is miles per hour. However, this is called a rate which is a type of ratio. Thus, a ratio is a way to compare two quantities using the division method, such as in $2 per pound where we compare dollars(money) and pound(quantity). A ratio is read as "the ratio of x to y" but can be written or in three different forms:
 x to y
 x:y
 x/y
On the other hand, a proportion is an equation that says that two ratios are equivalent. A proportion is read as "x is to y as z is to w". x/y = z/w; w & y not equal to 0. And thus, x:y::z:w
Definition of Ratio
The ratio refers to the relationship between the quantities of two or more objects and it indicates the amount of one object contained in the other. It is used in certain situations when it comes to the comparison of two quantities and follows the method of division which is considered efficient enough. In other words, the ratio is defined as the comparison of two quantities of the same kind. This relation depicts how many times one quantity is equal to the other quantity. It is the number that can be used to express one quantity as a fraction of the other ones. Ratios are denoted by the symbol ":"
Definition of Proportion
Proportion refers to a part, share, or number considered in relation to a whole, majorly a comparative relation. Two equivalent ratios are always in proportion. It is an equation or statement that is used to depict that the two ratios or fractions are equal. It is a mathematical comparison between two numbers. Accordingly, the ratios are said to be directly proportional to each other, if two sets of given numbers are increasing or decreasing in the same ratio. Proportions are denoted by the symbol "::" or "=".
There are two types of proportions.
 Direct Proportion
 Inverse Proportion
Direct Proportion
It describes the direct relationship between two quantities, "if one quantity increases, the other quantity also increases and viceversa". Thus, a direct proportion is written as y ∝ x. Let's take an example, you must have noticed that if the speed of a car is increased, then it covers more distance in a fixed amount of time.
Inverse Proportion
It describes the indirect relationship between two quantities, "if one quantity increases, the other quantity decreases and viceversa". Thus, an inverse proportion is written as y ∝ 1/x. Let's take the example of a vehicle. As the speed of a vehicle is increased, it will cover a fixed distance in less time.
Ratio and Proportion Formula
For any two quantities say a and b, in order to find the ratio, the formula for ratio is defined as a:b ⇒ a/b, where,
 “a” is called the first term or antecedent.
 “b” is called the second term or consequent.
For example, in ratio 2:7, is represented by 2/7, where 2 is antecedent and 7 is consequent. 2:7 is the required ratio.
Now, in order to find proportion for the two ratios, a:b and c:d. Then, \(a: b:: c: d \longrightarrow \frac{a}{b}=\frac{c}{d}\)
 The two terms ‘b’ and ‘c’ are called ‘mean terms’.
 The two terms ‘a’ and ‘d’ are known as ‘extreme terms.’
This implies, a/b = c/d or a:b::c:d. Now, let us consider the two ratios  3:5 and 15:25. 3:5 = 3/5 = 0.6 and 15:25 = 15/25 = 3/5 = 0.6. Since both the ratios are equal, we can say that these are two are proportional. Thus, 3:5::15:25. Here, 3 and 25 are the extremes, while 5 and 15 are the means. In a proportion, the product of the means = the product of the extremes. In the proportion a: b:: c: d, we get b × c = a × d.
Difference Between Ratio and Proportion
Let's recall ratio and proportion through some points of differences between them.
Ratio  Proportion 

It is used to compare the size of two quantities with the same unit.  It is used to express the relation of two ratios. 
Symbols used are  a colon (:), slash (/)  Symbols used are  the double colon (::) 
It is referred to as an expression.  It is referred to as an equation. 
In a problem, the ratio can be identified with the keyword “to every”  In a problem, the proportion can be identified with the keyword “out of” 
Tips and Tricks
 The two quantities with the same units only can be compared.
 The two ratios are said to be in proportion only if they are equal.
 To check whether two ratios are equal and form a proportion, we can also use crossproduct method.
Important Notes
 If we multiply and divide each term of a ratio by the same number, it doesn’t affect the ratio.
 For any three quantities, if the ratio between the first and the second is equal to the ratio between the second and the third, then these are said to be in a continued proportion
 Similarly, in the case of any four quantities in a continued proportion, the ratio between the first and the second equal to the ratio between the third and the fourth.
 For ratio and proportion, we can write in two ways, either by using equal to sign as a/b = c/d or using a colon, a:b = c:d.(a/b and c/d being equal fractions)
Related Articles on Ratio and Proportion
Solved Examples on Ratio and Proportion

Example 1: Determine if the ratios 6:8 and 24:32 are in Proportion.
Solution:
Given ratios are 6:8 and 24:32. 6:8= 3/4 = 0.75 and 24:32 = 3/4= 0.75. Here, both the ratios are equal. Therefore, 6:8 and 24:32 are in proportion.

Example 2: Out of the total number of students in a class that is 30. The number of students who like Math and the ones who like Science is in the ratio 2:3. Find the number of students who like Math and the ones who like Drawing.
Solution:
Total number of students = 30. Let the number of students who like Math = 2x and the number of students who like Science = 3x. We can say that 2x + 3x = 30 ⇒ 5x = 30 ⇒ x = 6. Putting the value of x, we get: the numbers of students who like Math = 2x = 12 and the number of students who like Science = 3x = 18.
FAQs on Ratio and Proportion
What are Ratios and Proportions?
The ratio is defined to be the relationship between the quantities with the same unit. On the other hand, proportion is defined to be a comparative relation between two ratios.
What is the Formula for Ratio and Proportion?
The ratio formula for any two quantities is defined as a:b ⇒ a/b. On the other hand, the proportion formula is \(a: b:: c: d \longrightarrow \frac{a}{b}=\frac{c}{d}\).
What is the Difference Between Ratio and Proportion?
A ratio depicts a comparison between two quantities whereas proportion depicts equality of two ratios.
How the Principles of Ratio and Proportion are Used in Biological Method?
The biological method involves the use of Applied Mathematics for computation and analysis of the biological data. This may even include finding protein structure in the gene, proteinprotein interaction, and other such ratios which determine the effective functioning of the human body.
What is Ratio and Proportion Example?
When construction work is going on, concrete is made to fix bricks by mixing cement, sand, stones, and water (an example of ratio), and before construction even starts, a blueprint is prepared which is an application of proportion.
What are the Two Types of Ratios and Proportions?
Two types of ratios are part to part and part to whole ratio whereas two types of proportions are direct proportion and inverse proportion.
How is Measurement Connected to Ratio and Proportion?
Measurement is connected to ratio and proportion in the following ways:
 Length, weight, and other unit conversions
 In architecture, for preparing blueprints.
 Scale models, maps, etc.
How do I Calculate a Ratio as a Percentage?
We often express the ratio in the form m:n or m/n. Now, to calculate a ratio as a percentage, simply divide m by n and then multiply the result by 100.
What are the Two Parts of Proportion?
Actually, there are four parts of the proportion but based on their arrangement in the proportion, these are separated into two groups, the means, and the extremes. From lefttoright and toptobottom, the extremes are referred to: the very first number and the very last number.
What is the Difference Between Direct and Inverse Proportion?
The direct and inverse proportion are used to show how the quantities and amount are related to each other: In direct proportion, the increase in one quantity leads to an increase in the other or vice versa whereas, in inverse proportion, the increase in one quantity leads to a decrease in the other or visa versa