NCERT Solutions for Class 7 Mathematics Chapter 8
NCERT Solutions for Class 7th Mathematics Chapter 8 Comparing Quantities are available on Extramarks to encourage and motivate students with their preparation for this chapter. In NCERT Solutions Class 7 Mathematics Chapter 8, students will find detailed step-by-step solutions to all exercises given in Chapter 8 of their Class 7 NCERT Mathematics textbook.
The important topics covered in NCERT Class 7 Mathematics Chapter 8 are as follows:
- Converting Fraction Numbers to Percentage
- Converting Decimals to Percentage
- Converting Percentages to Fractions or Decimals
- Converting Ratios to Percent
- Increase or Decrease as Percent
- Simple Interest
- Interest in Multiple Years
NCERT Solutions for Class 7 Mathematics Chapter 8 – Comparing Quantities
Access NCERT Solutions for Class 7 Mathematics Chapter 8 – Comparing Quantities
NCERT Solutions for Class 7 Mathematics Chapter 8 – Comparing Quantities
The quantitative relation between two quantities which reflects the relative size of both the quantities is what is covered in the chapter: comparing quantities. It is simply the means to compare any two given quantities.
In daily life, there are many occasions when we compare two quantities.
While comparing quantities, the ratio for two different comparisons must be the same. But there’s a rule in comparing quantities that states if the unit of the two quantities is not the same, it cannot be compared.
Some important facts covered in this chapter are:
- Various quantities that are of the same kind are compared using their ratios.
- If two fractions are equal, their ratios are also equal.
- When two ratios are equal, then the four quantities are in proportion.
- Percentages are numerators of fractions with the denominator 100 and they are also a way of comparing quantities.
- For conversion of a percentage into a decimal, you need to drop the sign of percentage and then shift the decimal point two places to the left.
- For conversion of a fraction into a percentage, you need to multiply the fraction by 100 and write the “%” sign on the right of the number.
- Profit = SP – CP (when SP > CP).
- Loss = CP – SP (when CP > SP).
- Profit or Loss per cent is always calculated on CP.
- Money borrowed is known as the principal.
- Simple interest = (P x R x T)/100
- Amount = Principal + Interest
Ratio:
Comparison through ratio means to know “how many times one quantity is of the other”, or to know “what part of one quantity is the other”.
The ratio of two numbers ‘b’ and ‘c’ (c ≠ 0) is b/c and it is denoted by b:c. A ratio in the simplest form is also known as the ratio in the lowest terms.
Note: To compare two quantities or to find the ratio of two quantities, the general rule remains the same i.e. their units must be the same.
Different ratios can also be compared by writing them as ‘like-fractions’.
To make your concepts more clear, you can refer to the exercises in NCERT Solutions Class 7 Mathematics Chapter 8 from Extramarks.
Equivalent Ratios:
As mentioned earlier, we can compare various ratios by converting them to like fractions. If the like fractions obtained are equal, then the given ratios are said to be equivalent.
Percentage:
Percentages are numerators of fractions having denominators as 100 which are used in comparing results. As mentioned earlier, the percentage is represented by “%” and it is expressed as parts of hundredths.
For example, 8 % means 8 out of 100. It is written as 8% = 8/100 = 0.08.
If the total is not a hundred, then we need to convert the fraction into an equivalent fraction with denominator 100.
Ratios To Percent:
Sometimes, the parts of a whole quantity are given in the form of ratios that we can convert into percentages.
Note: Here, by converting we mean to convert the increase or decrease in a quantity as a percentage of the initial amount as per the given question.
Profit Or Loss As A Percentage:
We know that the price of any item at which it is bought is called its cost price (CP) and the price at which it is sold is called its selling price (SP).
Note:
If CP < SP, then there is a profit in the monetary transaction, and Profit = SP – CP.
If CP > SP, then there is a loss in the monetary transaction and Loss = CP – SP.
The percentage of profit or loss is always calculated on the CP.
Simple Interest:
The money borrowed is known as the Principal amount. For using a bank’s money, the borrower pays some extra money to the bank which is called Interest. The total money paid back with interest is known as the Amount.
Thus, Amount = Principal + Interest
Interest is generally given in per cent for a period for which the loan is taken. Generally, the rate of interest is expressed as a percentage per year or annum.
So, Principal is denoted by P, Rate of interest by R, and Time by T.
Now, simple interest, or Interest = (Principal x Rate x Time)/100, or I = PRT/100
NCERT Solutions for Class 7 Mathematics–
You can access the NCERT Solutions for Class 7 Mathematics from Extramarks and practise the questions from the link given below.
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NCERT Solutions for Class 7 Mathematics
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NCERT Solutions for Class 7
Extramarks offers multiple benefits beyond what was presented to you through the conventional teaching methods. The solutions offered by Extramarks can help you in the following ways:
- Engaging study material – The solutions of Mathematics Class 7 made available on our website are simple and easy to comprehend. As a result, you don’t get confused, in fact, they are motivated to practise more sample test papers, and questions to improve their score.
- Concepts made easier- Solving Mathematics questions through a study guide makes your mind actively involved in learning at a deeper level to understand better.
- Important concepts emphasised and explained- As you will practice Mathematics with Extramarks’ solutions, you’ll know key topics and highlight the main concepts of the chapter which will help you gain confidence and score good marks in your exams.
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