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# Direct and Inverse Proportions Class 8 Notes CBSE Maths Chapter 11 (Free PDF Download)

Last updated date: 13th Sep 2024
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## Revision Notes for CBSE Class 8 Maths Chapter 11 - Free PDF Download

CBSE Class 8 Maths Revision Notes Chapter 11 - Direct and Inverse Proportion will help students of class 8 to master the basic concepts of direct and inverse proportion. The subject-matter experts at Vedantu have made these concepts easy-to-understand by their constant efforts. The revision notes on Vedantu cover all the concepts of direct and inverse proportions based on the latest CBSE guidelines. These notes are provided in a stepwise format so that students don't require much time to revise the topic doing their exam preparation. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions, they can download Class 8 Maths NCERT Solutions to help you to revise complete syllabus and score more marks in your examinations.You can also register Online for Class 8 Science tuition on Vedantu.com to score more marks in CBSE board examination.

Also, check CBSE Class 8 Maths revision notes for All chapters:

## Access Class 8 Maths Chapter 11 – Direct and Inverse Proportions

Variations And Proportions:

When the values of two quantities depend on one another in a way, such that the change in one quantity causes change in the other, the two quantities are said to be in variation.

Direct Proportion:

• Two quantities \$a\$ and \$b\$ are said to be in direct proportion if they vary i.e., they increase or decrease together in such a manner that the ratio of their corresponding values remains constant. That is if \$\dfrac{a}{b}=c\$ [\$c\$ is a positive number, then \$a\$ and \$b\$ are said to change directly.

• To explain the condition, let \${{a}_{1}},{{a}_{2}}\$ be the two values of \$a\$ and \${{b}_{1}},{{b}_{2}}\$ be the values of \$b\$, then \$\dfrac{{{a}_{1}}}{{{b}_{1}}}=\dfrac{{{a}_{2}}}{{{b}_{2}}}\$.

• To represent two quantities related proportionately, we write \$a\propto b\$.

Examples Of Direct Proportion:

• If the quantity of petrol in a car increases, the total distance covered also increases.

• If the radius of a circle increases, the area of that circle also increases.

Inverse Proportions:

• The two quantities \$a\$ and \$b\$ are said to be in inverse proportion if an increment in one causes a proportional decrement in the other or if an decrement in one causes a proportional increment in the other that is, the product of their corresponding values remains constant. Which means, if \$ab=c\$ or \$a=\dfrac{c}{b}\$ [\$c\$ is a constant], then \$a\$ and \$b\$ are said to vary inversely.

• To explain this case, let \${{a}_{1}},{{a}_{2}}\$ be the two values of \$a\$ and \${{b}_{1}},{{b}_{2}}\$ be the values of \$b\$, then \${{a}_{1}}{{b}_{1}}={{a}_{2}}{{b}_{2}}\$

• To represent two quantities related inversely, we write \$a\propto \dfrac{1}{b}\$.

For example:

As the speed of a vehicle(bike) increases, the time taken to cover a particular distance decreases.

Different study material, solutions to the problems, revision notes, sample papers, and previous year question papers provided by Vedantu are helpful to the students to a great extent.

• Access Class 8 Maths Chapter 11 Direct and Inverse Proportions Revision Notes in PDF format on Vedantu's official website and mobile app.

• Vedantu aims to ensure comprehensive learning for every student, providing solved answers to enhance understanding and improve scores.

• Utilize Vedantu Revision Notes as a reliable last-minute resource for effective preparation and revision before final exams.

### About Direct and Inverse Proportion

There are so many situations in our life where we see some direct or indirect relationship between two things, like

• If the number of things purchased is increasing then the bill amount to pay also increases. (direct).

• If the speed of the car will increase then the time to reach the destination will decrease. (indirect).

Any two physical quantities that vary is said to be proportional according to Mathematics if they are multiplicatively connected to each other by a constant term. For example, the more we eat, the more energy we gain, and the more we run, the more energy we lose.

There are two kinds of proportionalities in Mathematics.

When one quantity increases along with the other then it is called directly proportion whereas if one increases and the other decreases then it is inversely proportional.

• Direct proportion meaning: Two quantities are said to be directly proportional to each other if the ratio of their values is constant at any instant of time. The increase in one quantity results in the increase of the other. For example, the more we exercise, the more fit is our body.

• Inverse proportion: Two quantities are said to be inversely proportional to each other if the product of their values at any instant is a constant. The increase in one quantity results in a decrease in the other. Example: The more we eat junk, the less is our physical fitness.

The key difference between direct and inverse proportion are listed in the table below:

## Difference Between Direct and Inverse Proportion

 Direct Proportion Inverse Proportion The two measurable quantities vary directly with each other. The two physical quantities vary inversely with each other. The increase in one quantity results in the increase of the other. The increase in one quantity decreases the other. The decrease in one quantity results in a decrease of the other. The decrease in one quantity results in the increase of the other. The ratio of the values of two quantities at any instant is constant. The product of the values of the two quantities at any instant is a constant. Ex: Force and workIf the amount of force applied increases, the amount of work done also increases, and vice versa. Ex: Pressure and volumeThe volume of any substance decreases with the increase in pressure and vice versa,

### Symbol Of Proportion

When two quantities say l and m are in proportion, then they are written as l ∝ m where ∝ represents “is proportion to”.

There are two methods to solve the problems related to direct proportion-

1. Tabular Method

2. Unitary Method

### Why Choose Vedantu for Direct and Inverse Proportion Revision Notes?

• Vedantu's mathematician experts have crafted these revision notes to encompass vital concepts, equations, formulas, and solved examples.

• The revision notes aim to boost students' confidence, empowering them for better performance in their final exams.

• Aligned with the updated CBSE syllabus, Vedantu's Revision Notes ensure relevance to current educational standards.

• Highly qualified teachers at Vedantu strategically emphasize key topics, aligning with the exam perspective.

• Students can rely on these notes for a comprehensive understanding and effective exam preparation.

## Conclusion

For an enhanced comprehension of this subject, NCERT - Class 8 Maths Chapter 11 - Direct and Inverse Proportions, thoughtfully prepared by experienced educators at Vedantu, is your invaluable companion. These notes break down the complexities of Direct and Inverse Proportions into easily digestible sections, helping you grasp new concepts, master formulas, and navigate through questions effortlessly quickly in the last minute as well. By immersing yourself in these notes, you not only prepare for your studies more efficiently but also develop a profound understanding of the subject matter.

## FAQs on Direct and Inverse Proportions Class 8 Notes CBSE Maths Chapter 11 (Free PDF Download)

1. Why is CBSE Class 8 Maths Revision Notes Important?

Revision Notes play a vital role in preparation for the final exam. Every student must have a copy of revision notes before they appear for the exam. Studying the whole syllabus before the exam is a very tedious job. And also students might skip some important concepts in the pressure of studying the bulky syllabus. Hence revision notes prove very beneficial before exams. As it covers all the important concepts there is no chance of missing any topic.

The Class 8 Revision Notes Chapter 11 PDF is accessible free of cost. Students can easily download this PDF and fetch maximum benefits from it. Using this online revision notes also saves time and energy.

Vedantu’s online revision notes are proving so helpful to the students during this COVID-19 Pandemic. No need for parents and students to worry about their study material. We at Vedantu serve the best study material for the students.

3. How to Score Good Marks in CBSE Class 8 Maths Exam? How does Vedantu Solve this Issue?

Ans: Along with conceptual knowledge students need lots of practice by solving a large  number of problems to score good marks in CBSE Class 8 Maths exam. This not only enhances the understanding of students but also helps them prepare for exams and other competitive tests. Vedantu provides solutions to problems in a well-explained manner so that students can understand the concepts.

4. What topics are covered in the "Direct and Inverse Proportions Class 8 Notes"?

The notes comprehensively cover the concept of direct and inverse proportions, providing insights into their definitions, properties, and practical applications. It includes solved examples and exercises to reinforce understanding.

5. How can these Class 8 Maths notes assist in exam preparation?

The Class 8 Maths notes on Direct and Inverse Proportions serve as a valuable resource for exam preparation by offering clear explanations, step-by-step solutions, and practice exercises. They enhance conceptual clarity and aid students in mastering the principles of direct and inverse proportions for successful exams.