Ratio and Proportion Formula

Ratios are everywhere. They are one of the most important concepts in mathematics because of just how important they are in our day-to-day life. They play a major role in several things. For example, things like just comparing shoe sizes, or shirt sizes. Ratios are perhaps one of the most commonly used concepts that you definitely should know about. Even if you are new to the concept of ratio and proportions, chances are, nine out of ten times, you have heard of the two terms “ratio” and “proportions”. We are surrounded by them. They are everywhere. 

However, if you have not and you are completely new to the concept, then we are here to help you out with that. Ratio and proportions are simple to understand and can be practised easily to master so that the fundamentals that you learn can be used in your everyday life. This article majorly focuses on the concept of the ratio and proportion formula. It is a very well-written and detailed approach towards the formula that we suggest is going to help you a lot in understanding how things work in the world of ratios.

Ratio and proportions are an integral part of our day-to-day lives. Math is all around us because of topics and concepts like these. We hope that this article was successful in telling what exactly the study of ratio and proportion is all about and gave you a good explanation of the idea and concept of the ratio and proportion formula. We recommend that students use the examples given in the article as references every time they solve and use the formula. Thank you so much for reading and we hope that this article helped!

What do we know about the concept of ratios and proportions in general arithmetic? When we talk about the speed of a car and the distance it covers per km or maybe a recipe of a dish, we are talking about it in relation to ratios and proportions. But what actually are the concepts of ratio and proportions? What is the ratio and proportion formula? And why do we use the ratio and proportion formula? Why are they important to us? How do we use them in our day-to-day life? Let us elucidate all the clouds of questions one by one.

What are Ratios?

We always compare two or more things in our everyday life as per the need. This comparison between two or more quantities using the method of division is extremely efficient. So, it will not be wrong if we say that ratio is actually, the comparison or simplification of two quantities of the same kind. This relation explains to us how many times is one quantity equal to the other quantity. In simple words, the ratio is the number that we use to express one quantity as a fraction of the other ones.

We can only compare two numbers in a ratio if they have the same unit and the sign that we use to denote a ratio is “:”. In a fraction, it is written using “/” and we also use “to” to represent a ratio.

What are Proportions?

Proportion validates if the two ratios are equivalent to each other. It judges the equality of two ratios. Now, for example, consider that two sets of numbers are given to you that are increasing or decreasing in the same ratio. So in proportion, we will say that the ratios are directly proportional to each other. Let us take another example, a train that is covering 100km per hour is actually equivalent to a train covering the distance of 500km for 5 hours because 100km/hr = 500km/5hrs = 100km/hr.

Two Faces of a Coin

I think we are now very clear about the concepts of ratio and proportion. Ratios and proportions are actually the two faces of the same coin. If two ratios are equal, then it is a proportion. Ratios and proportions are normally defined on the basis of fractions. When we define a fraction using “:”, it becomes a ratio and when we represent two ratios using “::”, it is a proportion. Both ratio and proportion are an important foundation that helps us to understand many crucial concepts in Maths and Science. The formula for ratio proportion is the foundation of many such concepts.

Ratio and Proportion Formula

The ratio and proportion formula is the key to solve any ratio and proportion problems. Using the ratio proportion formula actually makes our work much easier and we save a lot of time. So, here are the ratio and proportion formulas.

Ratio Formula

a:b ⇒\[\frac{a}{b}\]

Proportion Formula

a:b::c:d⇒\[\frac{a}{b}\]=\[\frac{c}{d}\]

Solved Examples for Ratio and Proportion Formula

Example 1) Suppose person A and person B started a partnership business and decided to divide the profit between them in a ratio of 2:4. By the end of the financial year, the total profit would be rs. 10,000. What will be their part of profit?

Solution 1)  Their profit is to be divided into a ratio of 2:4.

So we can find the profit of each one of them by:

A= 10,000 x (2/6) = 3333.33

B = 10,000 x (4/6) = 6666.67

Therefore, their respective profit will be 3333.33 and 6666.67.

Example 2) Find a:b:c if the given ratios are as follows:

a:b = 2:3

b:c = 5:2

c:d = 1:4

Solution 2) If we multiply the first ratio by 5, the second ratio by 3, and the third ratio by 6, we will have: 

a:b = 10:15

b:c = 15:6

c:d = 6:24

The ratios above have equal mean scores.

Therefore, a:b:c:d = 10:15:6:24.

Example 3) In a handwriting competition, there are 5 boys and 3 girls. What will be the ratio between girls and boys?

Solution 3) The ratio between girls and boys will be 3 is to 5. We can also write it as 3/5. 

Example 4) If Sam in 2 hours covers a distance of 40 km. What distance will he cover in 8 hours?

Solution 4) Let the distance be x. With time, the distance also increases. 

Therefore, 2:8 = 40:y

y = (40 x 8) / 2

= 160 km.

Sam can cover a distance of 160km in 8 hours. 

Example 5) Find the numbers whose sum is 60 and they are in the ratio of 2:3.

Solution 5) Let the numbers be 2x and 3x, respectively. According to the question, the sum of these two numbers is 60.

So, 2x + 3x = 60

5x = 60

x = 12

Therefore, the two numbers are 

2x = 2 x 12 = 24

3x = 3 x 12 = 36

24 and 36 are the two numbers.

Practise more and more solved examples for ratio and proportion formulas for better understanding of the topic. This will also help you to learn the formula for ratio proportion quickly.