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Comparing Quantities Class 8 Notes CBSE Maths Chapter 8 (Free PDF Download)

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Last updated date: 17th Apr 2024
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Revision Notes for CBSE Class 8 Maths Chapter 8 - Comparing Quantities Free PDF Download

CBSE Class 8 Maths Chapter 8 Comparing Quantities is a crucial part of this syllabus that teaches students how to compare various mathematical expressions by using their formulas and principles. To make this chapter easier to comprehend, download and refer to the CBSE Class 8 Maths Chapter 8 Comparing Quantities Notes. Experts have designed these notes to offer an easier platform to learn such concepts and use them to solve problems faster.


Free PDF download of Class 8 Maths Chapter 8 - Comparing Quantities Revision Notes & Short Key-notes prepared by expert Maths teachers from the latest edition of CBSE(NCERT) books. To register Maths Tuitions on Vedantu.com to clear your doubts. Register Online for Class 8 Science tuition on Vedantu.com to score more marks in CBSE board examination.

 

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 ,can download Class 8 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Download CBSE Class 8 Maths Revision Notes 2024-25 PDF

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


Access Class VIII Mathematics Chapter 8 - Comparing Quantities Notes

  • Ratio:

  • Ratio is the term for comparing through division. 

  • The unit of ratio quantities is the same. 

  • There is no unit for ratio. 

  • Proportion is the equality of two ratios. It mean that,

$p:q$ are equal proportional to the $s:t$

That is

$\text{p : q :: s : t}$

$\dfrac{p}{q}=\dfrac{s}{t}$

  • \[\text{Product of extremes = Product of means}\]

  • Percentage:

  • The term "percentage" refers to the number of people in a group of  $100$.

  • A percentage is the outcome of any division with a divisor of $100$.

  • Percentage can be calculated as;

$\text{Percentage = }\dfrac{\text{Value}}{\text{Total Value}}\text{ }\!\!\times\!\!\text{ 100}$

  • The divisor is represented by the sign percent, which is read as percent.

  • Profit And Loss:

  1. Cost Price (CP): 

The cost price of an object is its initial unit purchase price.

  1. Selling Price (SP):

Selling price is the amount a buyer pays for it.

  • Overhead expenses are expenses incurred after the purchase of an item and are included in the cost price. These could include costs such as repair costs, labour costs, transportation, and so on.

  • A discount is a reduction in the price of anything that has already been marked down.

\[\text{Discount = Marked Price - Sale Price}\]

The Marked price is the tagged price or list price which is the price on the label of an article or product.

This is the price at which the product will be offered for sale.

  • When a discount $\%$ is specified, the discount can be calculated.

\[\text{Discount = Discount  }\%\text{  of Marked Price}\]

However, there may be a reduction applied to this price, and the product's real selling price may be lower than the marked price.

  1. \[\text{Marked Price > Selling Price}\], when a discount is offered.

  2. \[\text{Marked Price = Selling Price}\], when a discount is not available.

  • Overhead expenses are expenses incurred after the purchase of an item and are included in the cost price.

\[\text{CP = Buying price + Overhead expenses}\]

  • The government levies a sales tax on the sale of an item, which is then added to the total bill amount.

\[\text{Sales tax = Tax }\!\!%\!\!\text{  of Bill Amount}\]

  • GST (Products and Services Tax) is a tax placed on the provision of goods, services, or both.

  • Simple Interest: 

When the principal stays the same during the loan term, the interest paid is referred to as simple interest.

\[\text{SI = }\dfrac{\text{P }\times \text{ R }\times \text{ T}}{100}\]

  • Compound Interest:

Compound interest is interest calculated on the sum from the previous year amount \[\text{A = }P+I\]

1. When Interest Is Compounded Annually, The Total Amount

\[\text{= P }{{\left( \text{1 + }\dfrac{\text{R}}{\text{100}} \right)}^{\text{n}}}\]

Where, \[P\] is principal, \[R\] is rate of interest and \[n\] is time period

2. When Interest Is Compounded Half-Yearly, The Amount

\[\text{= P }{{\left( \text{1 + }\dfrac{\dfrac{\text{R}}{2}}{\text{100}} \right)}^{\text{2n}}}\]

\[\dfrac{R}{2}\] is half-yearly rate and \[\text{2n = No. of ‘half-years’}\]

We compute the interest twice if the interest is compounded half-yearly. As a result, the time period is doubled and the rate is cut in half.

  • Applications of Compound Interest:

In our daily life, the Compound Interest applicable for determining the following areas;

  1. Population growth (or decline).

  2. Bacterial growth if the rate of growth is known.

  3. The value of an object if its price rises or falls over the course of several years.


Importance of CBSE Class 8 Maths Chapter 8 Comparing Quantities Notes

Class 8 Maths Chapter 8, Comparing Quantities, is one such topic that enables students to learn about various mathematical expressions and principles to compare them. this chapter explains various mathematical terms and their formulas so that students can apply them to compare and find the differences. This chapter, thus, prepares a strong conceptual foundation among the students. Preparing it will need revision notes, the perfect study guide designed by the experts.


These notes are designed to offer a simpler version of all these mathematical principles, terms and formulas. Students will find it easier to grab the concepts and learn how to solve the problem faster. Upon focusing on these notes, they will realise how easy these formulas are to comprehend and use. Once the chapter is complete, they will solve the exercise problems without hassle.


Hence, the Class 8 Maths Chapter 8 Comparing Quantities Notes are an integral part of the study material for this chapter.


Benefits of CBSE Class 8 Maths Chapter 8 Comparing Quantities Notes

  • These notes can be accessed online for free. Students can also download them from here, making their offline study sessions more productive. These notes can be accessed at your convenience to give your preparation session the right boost.

  • Resolve doubts related to the concepts and mathematical principles taught in this chapter. focus on how simple the description of the topics is given in these notes to enhance your knowledge level.

  • Use these notes to revise this chapter faster before an exam. You will not have to waste time hovering throughout the entire chapter when you do it easily by using these notes. In fact, you will also be able to recall what you have studied in these notes better and compile precise answers.


Download CBSE Class 8 Maths Chapter 8 Comparing Quantities Notes Free PDF

Add these notes in a PDF version and refer to them whenever you want. Make your study sessions more productive using the knowledge delivered through these notes. Take less time to prepare the chapter by using these notes. Complete your revision even faster and recall what you have studied during an exam to score more. 

Conclusion 

For an enhanced comprehension of this chapter, the “Comparing Quantities”, Class 8 notes, thoughtfully prepared by experienced teachers at Vedantu, are your invaluable companions. These notes break down the complexities of Chapter 8 Comparing Quantities into easily digestible sections, helping you grasp new concepts, master formulas, and navigate through questions effortlessly. By immersing yourself in the Class 8 Maths Notes Chapter 8 Comparing Quantities, you not only prepare for your exams more efficiently but also develop a profound understanding of the subject matter. 

FAQs on Comparing Quantities Class 8 Notes CBSE Maths Chapter 8 (Free PDF Download)

1. Where can I download the latest Chapter 8 Comparing Quantities of Class 8 Mathematics notes?

Ans. Class 8 Mathematics revision notes are very beneficial revision tools as well as for enhancing your understanding of the chapter. Here is how to download them easily:

  1. Go to Vedantu's Revision Notes for Class 8 Mathematics and choose Chapter 8 "Comparing Quantities."

  2. Scroll down to the next page and click on the "Download PDF" button.

  3. You will be taken to a page containing the link for automatic download of the PDF.

You can also download the same using Vedantu's mobile app.


2. How do you understand Chapter 8 Comparing Quantities of Class 8 Mathematics?

Ans. "Comparing Quantities" is a very useful chapter as this concept has several real-time applications. To understand this chapter effectively, here is what you can do:

  1. Read the explanation provided in your NCERT textbook two-three times. Try to solve the exercises on your own first.

  2. Following that, refer to Vedantu's solutions and explanations of the chapter here. 

  3. Try to relate the concepts learned to similar situations around you.

  4. Look up Vedantu's conceptual videos and masterclasses for further understanding of the concepts.

3. What concepts are taught in Chapter 8 Comparing Quantities of Class 8 Mathematics?

Ans. The concepts taught in Chapter 8 "Comparing quantities" are as follows:

  1. Recalling Ratios and Percentages

  2. Finding the Increase or Decrease per cent

  3. Finding Discounts

  4. Estimation in percentages

  5. Prices Related to Buying and Selling (Profit and Loss)

  6. Finding cost price/selling price, profit %/loss%

  7. Sales Tax/Value Added Tax/Goods and Services Tax

  8. Compound Interest

  9. Deducing a Formula for Compound Interest

  10. Rate Compounded Annually or Half Yearly (Semi-Annually)

  11. Applications of Compound Interest Formula

4. What are the formulas for comparing quantities?

Ans. Class 8 Mathematics Chapter 8 is an important chapter containing important formulas like:

  1. Discount = Marked Price – Sale Price

  2. Cost Price = buying Price + Overhead Expenses

  3. Profit% = Profit/Cost Price X 100  

  4. Amount = P (1 + R/100)n  where P is principal, R is the rate of interest, n is time period

  5. Compound Interest= A-P 

You can find more such formulas and important pieces of information from this chapter on Vedantu's Revision Notes for Class 8 Mathematics Chapter 8 "Comparing Quantities."


5. Why do we need to learn Chapter 8 Comparing Quantities of Class 8 Mathematics?

Ans. The concepts taught in Chapter 8, "Comparing Quantities", are crucial fundamentals that will help you in your life. Finding percentages, ratios, calculating taxes, compound interest, profit, loss, discount, etc. are concepts that you will come across undoubtedly in your life. Whether you choose any profession or field of interest, you will need to have much knowledge of these concepts to work effectively.


This chapter is the building block of these concepts, and you will learn the basics of these principles.


These solutions are available on Vedantu's official website (vedantu.com) and mobile app free of cost.