Comparing Quantities Class 7 Notes CBSE Maths Chapter 8 (Free PDF Download)

• Comparing Quantities: In our daily lives, we are frequently asked to compare two quantities. They might be heights, weights, wages, grades, and so on. To compare two quantities, they must have the same units.

• When comparing the heights of two people who are 150 cm and 75 cm tall, we use the ratio \[150:75\]  or \[2:1\].

• A ratio is a mathematical expression that compares two quantities using a specific procedure. 

• Percentage: The numerator of fractions with a denominator of 100 is a percentage. The percentage is denoted by the sign percent, which also denotes a tenth.

• Ratios to Percent: Parts are sometimes given to us in the form of ratios, which we must convert to percentages. which can be converted by simply dividing m by n and then multiplying the result by 100.

• By changing two ratios to like fractions, they can be compared. We say the two supplied ratios are equivalent if the two fractions are equal.

• The four quantities are considered to be in proportion if two ratios are equivalent. For instance, the ratios \[8:2\] and \[16:4\] are comparable, so 8, 2, 16 and 4 are in proportion.

• The Percentage is a method of comparing quantities. The numerator of fractions with a denominator of 100 is a percentage. Per cent refers to one-hundredth of a percent. For example, 82 percent indicates 82 points out of a possible hundred.

• Fractions can be converted to percentages and the other way around. As an example, $\dfrac{1}{2}=\dfrac{1}{2}\times 100\%$ whereas, $65\%=\dfrac{65}{100}=\dfrac{13}{20}$.

• Decimals, like percentages, can be converted to decimals and vice versa.

For example, $0.15=0.15\times 100\%=15\%$.

• Percentages, for Example, are Commonly Employed in Our Daily Lives; 

1. We have learned to find accurate numbers when a percentage of a total quantity is supplied.

2. We've seen how to convert ratios to percentages when parts of a number are presented to us as percentages.

3. A percentage can also be used to show an increase or decrease in a quantity. 

4. The profit or loss incurred in a particular transaction can be stated as a percentage.

5. When calculating interest on a loan, the rate of interest is expressed in percentages. 800, for example, was borrowed for three years at a rate of 12 percent per year.

• Increase or Decrease as Percent
  There are instances when we need to know the percentage growth or reduction in a specific quantity. For example, suppose a state's population grew from 40,000 to 44,000. The growth in population can then be easier understood if we state the population increased by $10\%$.

• Price related to an item or buying and selling

The cost price of an object is its purchase price. In brief, it's abbreviated as CP.

The selling price, or SP for short, is the price at which you sell.

a. If CP is less than SP, you made a profit and it can be calculated as \[\text{= SP -- CP}\].

b. You're in a no-profit, no-loss situation if \[\text{CP = SP}\].

c. And, the loss is equal to \[\text{CP }-\text{ SP}\].

• It is possible to turn the profit or loss into a percentage. It's always done on the basis of the CP.

• Simple Interest: The term "principal" refers to the amount borrowed, Interest is the additional money paid by a borrower for using borrowed funds for a specific period of time (I). The ‘Time Period' refers to the length of time for which the money is borrowed (T). The rate of interest is usually expressed as a percentage per year. 

$\text{SimpleInterest=}\dfrac{\text{P}\times\text{R}\times \text{T}}{\text{100}}$

• The amount refers to the total amount paid by the borrower to the lender.

Class 7 Revision Notes Comparing Quantities - Free PDF

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Revision Notes For Class 7 Maths Chapter 8 Comparing Quantities

8.1 Introduction

• In maths class 7 comparing quantities notes, you will learn that we often, on multiple occasions, are in situations where we compare two different quantities.

• In the previous class, students learned how to make comparisons by seeing how many times one quantity is of the other. In this grade, they learn that it can also be inverted and written as part one quantity is of the other.

• The comparisons are relative and could be different for two contrasting situations and examples.

• The ratio for two different comparisons can and may be different.

• Students should remember that to compare two quantities, the units of both should be the same, and students will learn this from the notes of class 7 revision notes chapter 8.

8.2 Equivalent Ratios

• In the comparing quantities class 7 notes, there can be situations wherein different ratios may be compared with each other to know if they are equivalent or not.

• Different ratios need to be written infractions and then be compared by converting them into like fractions.

• If the result of this is fractions being equal, we determine that the ratios are equivalent.

• The important thing to remember is to keep things in proportion and then to get solutions.

• We have a lot of use of proportions in our everyday daily life.

• In the Unitary method, the students first find one unit's value and then the value of the required number of units.

• The word 'per' is often used to mean 'for each’.

8.3 Percentage - Another Way of Comparing Quantities

• Percentages are calculated as numerators of the fraction with denominator 100, and they have often been used in comparing results all over the world.

8.3.1 Meaning of Percentage

• The word 'percentage' has been derived from its Latin origin word 'per centum,' which translates to 'per hundred.'

• The percent is often referred to by the symbol '%,' which means hundredths. In layman's terms, it means that 1% is 1 out of a hundred or one-hundredths. 

• In many cases, students need to convert the fraction to an equivalent fraction while keeping the denominator 100.

8.3.2 Converting Fractional Numbers to Percentage

• In various cases, fractional numbers may have a different denominator.

• To compare fractional numbers, a common denominator has to be taken. It is well established that it is more convenient when the denominator is 100, which means the fractions are being converted to a percentage. 

• The percentages related to proper fractions are less than 100, whereas percentages related to improper fractions are more than 100.

8.3.3 Converting Decimals to Percentage

• Decimals can be converted into percentages by multiplying the given numbers by 100.

• For example, 0.75 multiplied by 100, i.e., 0.75 * 100= 7%

8.3.4 Converting Percentages to Fractions or Decimals

• Percentages can be converted to fractions by putting the denominator as 100. For example, 1/100

• Percentages can be converted into a decimal by dividing the percentage number by 100. For example, 1/100 = 0.01

• All the parts that form the whole when they are added will give the result of whole or 100%.

8.3.5 Fun with Estimation

• In various cases, percentages even help us in estimating the parts of an area.

8.4.1 Interpreting Percentages

• Using percentages in comparison, converting percentage to a fraction, decimal, and vice-versa have been shown in the stages mentioned above.

• Percentages can also be used in real life by interpreting them in various ways by using real-life examples.

8.4.2 Converting Percentage to 'How Many'

• Percentages may also be used to find the solution to problems by asking 'how many.'

• For example, in many 40 students, 25% liked playing football, so "how many" students liked playing football?

8.4.3 Ratios to Percent

• In many scenarios, the information in the question might be such; parts are given in the form of ratios, and the problem is to convert that into a percentage.

8.4.4 Increase or Decrease As Percent

• Many situations may lead to knowing the increase or decrease in a certain quantity by knowing it in percentage.

• For example, in ch 8 class 7 Maths revision notes, everyone would better understand if it is said that the population increased by 10% when calculating the increase in population.

• The formula can calculate this percentage: Percentage increase = amount of change/original amount or base * 100.

8.5 Prices Related to an Item or Buying and Selling

• The price at which a substance is bought is known as the Cost Price. In short, it is usually written as CP.

• The price at which a substance is sold is known as the Selling price. In short, it is usually written as SP.

• It is easy to decide whether any sale was profitable and depended on the SP and CP.

• If the CP<SP, then there was a profit. Which can be calculated as SP-CP

• If the CP=SP, then a no profit and no loss situation occurs.

• If CP>Sp, then there was a loss. This can be calculated as CP-SP.

8.5.1 Profit or Loss as a Percentage

• The outcome, either profit or loss, can be converted into a percentage. This is always to be done and calculated based on the CP, and the profit% or loss% can easily be found out.

• The method of this is: Profit/CP * 100 = Profit percentage, or

• Loss/CP * 100 = Loss percentage

8.6 Charge Given on Borrowed Money or Simple Interest

• Whenever a person borrows money, that amount is known as the sum borrowed or Principal.

• When someone borrows money, in most situations, the borrower has to pay an extra amount of money to the place or person they are borrowing from. This is known as Interest.

• The amount repayable can be calculated as Amount = Principal + Interest.

8.6.1 Interest for Multiple Years

• If the amount of money borrowed, more than a year, the interest is calculated for the total period the money is kept for.

• In class 7 maths revision notes chapter 8, it is seen that when calculating interest, where the principal is not being changed is known as simple interest.

How Can Comparing Quantity Class 7 Note Help Students To Score Good Marks in Exams?

Some benefits of studying and practising Comparing Quantity Class 7 notes are discussed below:

• This revision notes Class 7 Maths Chapter 8 covers the basic fundamental of the chapter while discussing the important topics of Comparing quantities in detail.

• Many Class 7 students must be preparing for Olympiad exams. Well, in the Olympiad exam 1-2 questions usually come from this chapter. So, students are suggested to revise these notes thoroughly as it will help them to score good marks in other competitive exams also.

• The expert teacher at Vedantu has prepared these revision notes in a concise way so that students can easily understand the concepts and solve all the numerical questions at no time.

• Students will not lose their marks if the important topics and the questions given in each exercise are on the tip. Moreover, practicing solved questions and revising the important topics repeatedly are more than sufficient to score good marks in exams.

About CBSE Class 7 Maths Chapter 8 Comparing Quantities

NCERT Chapter 8 Comparing quantities is an important chapter as it not only helps students to learn comparison by saying how many times one quantity is more or less than another but also helps them to see that it can be inverted and written as what part one quantity is of another quantity. This chapter includes various important concepts and helps students to polish their skills. This chapter helps students to determine ratios, percentage, interest, and other numbers.

Some of the Important Topics Covered in Chapter 8 Comparing Quantities Are Discussed Below:

• Equivalent Ratios

• Percentage -  Another Method of Comparing Quantities

• Percentage when the total is not 100

• Converting Fractional Numbers to Percentage

• Converting Decimals to Percentage

• Converting Percentage to Fractions or Decimals

• Uses of Percentage

• Interpreting Percentage

• Converting Percentage to “ How Many”

• Ratios to Percents

• Increase or Decrease as Percents

• Profit or Loss as a Percentage

• Simple Interest

• Interest For Multiple Years

Class 7 Maths Chapter 8 Comparing Quantities is one of the most important chapters as it enables the students to learn different important topics listed above. Real-Life examples, Try These’ activities. solved examples, exercise questions are given at the end of each topic prove to be greatly helpful for the students. Summarising points given at the end of the chapter and Comparing Quantities Class 7 Notes provided by Vedantu helps students to remember all the important concepts and revise them at a glance.

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Conclusion

In the "Comparing Quantities" chapter of CBSE Class 7 Maths, we learned about various important concepts. We explored the idea of ratios and proportions, which are crucial for comparing quantities. We also delved into the concept of percentages and their application in real-life situations like discounts and profit and loss. Furthermore, we studied simple interest and its calculation.

To summarize, this chapter equipped us with valuable mathematical tools to analyze and compare quantities in practical scenarios. It's important to understand how ratios, percentages, and interest work, as they play a significant role in our everyday lives, from shopping to financial planning. These concepts will continue to be useful in higher classes and real-world situations.