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# What is a Proportional Mean in Math?

August 4, 2022
written by Azhar Ejaz

In the world of mathematics, the term “Proportional Mean” is used to indicate the ratio of two quantities, it means that the ratio of one quantity to another quantity is the same as the ratio of one quantity to another. If you have heard this term before and didn’t know what it meant, you are not alone, this is a term that is often found in textbooks. Let’s discuss what this term means and how we can use it in our daily life.

## What Is Proportional Mean?

Proportion is a mathematical comparison between two quantities or numbers.  According to proportion, if two sets of given numbers are decreasing or increasing in the same ratio, ratios are said to be directly proportional to each other. Proportions are represented using the symbol “::” or “=”

Before knowing the exact meaning of proportional mean, it is important to know what proportion means. A proportion is a relation between one quantity and another quantity. Proportion is the relation between two different quantities, and it will always be true that if one quantity is in a relation to another quantity, then it means the ratio of one quantity to another is the same as the ratio of one quantity to another. If you want to understand the meaning of proportional means, you need to understand the meaning of proportion.

Example for proportional

Two ratios are said to be in proportion when the two ratios are equal. For example, the time taken by a car to cover 50km per hour is equal to the time taken by it to cover the distance of 250km for 5 hours. Such as 50km/hr = 250km/5hrs.

## How to Calculate Proportional Mean?

If you want to calculate the proportional mean, the first thing that you need to do is to find the ratio of the two quantities. Then you need to multiply one quantity with another quantity. Finally, you will get the proportional mean of two different quantities.

## Proportional Mean Examples

Let’s have an example of a simple proportion. Suppose you have a jar containing one liter of water and another containing one gallon of water. The ratio of one gallon of water to one liter of water is equal to one gallon of water. That means the ratio of one gallon of water to one liter of water is one to one.

In this example, let’s assume that you have 2 jars of water and you want to know what is the ratio of one gallon of water to one liter of water. For this purpose, you will multiply one jar of water by another jar of water. The result of multiplication will be 2 gallon

Therefore, the ratio of one gallon of water to one liter of water is 2 to 1. In a similar way, you can multiply any number with another number and you will get the proportional mean.

## What is the proportional formula?

Now, let us the two ratios are a:b and c:d. The two terms ‘b’ and ‘c’ are called ‘means terms or mean ’, whereas the terms ‘a’ and are known as ‘extreme terms or extreme

a:b::c:d–> a/b=c/d

a/b = c/d or a:b::c:d.

For example,

let us the number of students in 2 classrooms where the ratio of the number of boys to girls is equal. Our first ratio of the number of girls to boys is 2:5 and that of the other is 4:8, then the proportion can be written as 2:5::4:8 or 2/5 = 4/8. Here, 2 and 8 are the extremes terms, while 5 and 4 are the mean terms

## Types of proportions

Based on the type of relationship two or more quantities share, the proportion can be classified into distinct types. There are two types of proportions.

• Inverse Proportion
• Direct Proportion

Conclusion:

The meaning of proportional means is very simple to understand. It is the ratio of one quantity to another quantity. If you are interested to know the meaning of this term in detail, then you can check the below diagram.

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