# Chapter 12 – Ratio and Proportion

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

“I have more pencils than you,” says your classmate. And now you want to prove that you have more. How can you do it? Using the concepts of ratio and proportion.

In mathematics, there are several ways to compare numbers. Ratio and proportion are two such methods. A ratio is a method to compare numbers or quantities, whereas a proportion is used to compare ratios. This will be clearer with the below-mentioned example.

Let’s say you want to calculate the difference between the number of pencils that you and your friend have. For this purpose, you can use the concept of ratio, which is a comparison by division. If you have 10 pencils and your friend has 4 pencils, the comparison by division will give us the following:

This can also be written as: 5:2

Which is the mathematical notation for a ratio. You are basically comparing two quantities and reducing them by division. The ratio of pencils owned by you and your friend is 5:2, which tells us that you have more pencils than your friend. You just proved it mathematically!

Another way to write this would be: the ratio of pencils owned by your friend and you is 2:5. Please note the reversal of numbers and wordings.

Therefore, the action of comparing two similar quantities using a division formula is called a ratio.

Now, let’s take another example of two of your classmates. Suraj has 5 pencils in his pencil box, and Nikita has 2 pencils. How will you calculate the ratio here?

Using comparison by division, the answer will be 5:2.

When you compare this ratio with the one that we got earlier (in the case of you and your friend), you will get a figure that is called proportion. Since both the ratios are the same (5:2), we can conclude that both the quantities are in proportion. If the ratios were 5:2 and 5:3, we could say that they are not in proportion or disproportion.

#### Introduction to Ratio and Proportion

The concept of ratio and proportion are used in day-to-day life, from calculating the speed of a motorcycle to knowing the price difference of vegetables in your local market and a supermarket. Therefore, knowing about them is important.

#### Definition of Ratio

A ratio is defined as the relation between two quantities that are usually denoted in numbers. It allows you to compare or contrast two numbers of the same kind. In the above examples, we calculated the ratio of pencils owned by different people. So, basically, ratio gives you an idea as to how many times a specific event or a quantity is equal to the same event or quantity owned by someone else.

You should keep in mind that a ratio can only be calculated if the quantities being compared are:

• Of the same kind
• Measured in the same unit

A ratio is denoted by the symbol “:” (colon).

#### Definition of Proportion

Proportion is defined as the comparison of two ratios. As seen in the above examples, proportion gives you the equivalence of two ratios. This can help to decide similarities and differences in events. For example, you can use the concept of proportion to compare the vegetable price differences in your city and your cousin’s city (if they are different).

Proportion is usually denoted using the symbols “::” (two colons) and “=” (equal to).

#### Properties of Proportion

The magic of proportion can be described by its properties. For example, if A:B = C:D, then:

• A+B = C+D
• A-C = B-D
• B:A = D:C
• A-B:B = C-D:D
• A+B:B = C+D:D

There are many more such properties that you can learn. You can also learn about the unitary method, which you can use to calculate the value of a single unit from multiple values.

#### Ratio and Proportion Formula

The formula of a ratio is given as A:B

(assuming A and B are two quantities of a similar kind.)

The formula of proportion is given as A:B = C:D

(assuming A:B and C:D are ratios of two similar quantities.)

#### Conclusion

These two concepts of comparison and relationship between numbers are known as ratio and proportion. They are an integral part of mathematics and lay a foundation for advanced concepts, such as probability and statistics.

#### FAQs

• What is the formula of ratio and proportion?

The formula of a ratio is given as A:B. The formula of proportion is given as A:B = C:D.

• What is the concept of ratios?

A ratio is a mathematical tool used to compare or find the relationship between two different quantities. It helps you compare two quantities in its own unit and format.

• What is the ratio formula?

The formula for ratio is given as A:B where A and B are quantities of a similar kind. For example, A and B can be the number of tennis balls that you and your friend own, respectively.

• How do you solve a ratio?

A ratio can be solved by dividing the two numbers or quantities with each other.

• How do you solve ratio and proportion word problems?

You can solve ratio and proportion word problems by first assigning the quantities to the formulae. Read the word problems carefully and extract the numbers as A, B, C, and D (individual quantities). First, calculate the ratios separately and then compare them to check if they are in proportion or not.

• What is a proportion (with an example)?

A proportion is a comparison between two ratios. For example, consider 1:2 and 1:3 as two ratios. When you compare these ratios, you can deduce that they are not equal. This means that the ratios are not in proportion, i.e., they are not equal.

Learn more about ratio and proportion through visualisations and animated videos. Download the MSVgo app from the Google Play Store or the Apple App Store and start easy online learning today. Visit the MSVgo website for more details.

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### Middle School Math

• Area and Its Boundary
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