Comparing Quantities

An Overview of Comparing Quantities

In this chapter, you will learn more about the practical and daily use of comparing quantities. NCERT solutions for class 7th maths chapter 8 help you understand the benefits of ratios, percentages and interactions between simple numbers to solve the questions that will come in your exams.

The word ‘percent’ comes from a Latin word - per centum. It translates to ‘every hundred’ or ‘per hundred’. You will learn how percentages are measured here.

Another aspect of chapter 8 is comparing quantities using proportion.

In this chapter, we shall practise:

  • How to convert fractional measures into percentages.

  • How to change decimal points into percentages.

  • How to convert any ratio into a percentage.

Once we understand percentages, we will be able to successfully solve questions in comparing quantities class 8.

Important Comparing Quantities for Class 7

Here are some solved examples of questions you are likely to face.

Comparing Quantities Exercise 8.1

Question 1:

Calculate the ratios of the following quantities:

  1. Rs 5 to 50 paise 

  2. 30 days to 36 hours

  3. 9 metres to 27cm

Solutions:

To solve problems related to ratios in currency terms, you must bring both sides down to a common unit.

  1. We know 5 x 100 paise is Rs 5. Re 1 has 100 paise. To calculate the ratio:

  • 500/50= 10 : 1. 

  1. Similarly, we will break down time into hours and minutes to calculate ratios.

30 days have 30x24 or 720 hours. The ratio is 720/36=20 : 1.

  1. Again, we will break down these quantities into their lowest denominations.

9 metres equals 9 x 100 or 900 cm. The ratio here is 900/27 or 100/3=30:1.

Here is another example to help you face questions in class 8 maths comparing quantities.

The state of Rajasthan has an area of 3 Lakh km2. It has a population of 570 lakhs. UP has an area of 2 Lakh km2 but it has a population of 1660 lakhs. Solve:

  1. Which state has a higher population density?

  2. How many people live in each square kilometre in these states?

Solution: Comparing quantities helps you solve this easily. 

Answers: Population density is calculated based on the number of people living in one square km. Hence, in Rajasthan, it is 570 Lakh/3 lakhs every km2= 190 people every km2.

Using a similar equation, UP’s population density is 1660 lakhs/2 Lakh km2= 830 people in every square kilometre. 

Thus, UP has a higher density of population. This is a textbook case of class 7 maths comparing quantities. 

Did you know? UP is one of the most densely populated states in India. Take a look at this map based on data obtained via the 2011 Census!

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NCERT Solutions for Class 8 Maths Comparing Quantities

Exercise 8.2

In this section, we will learn how to convert any fractional numbers to percentages.

Question 1: Convert these fractions into percentages:

  1. 1/8           B. 5/4                  C. 3/40               D. 2/7

Solution: A: 1/8=1/8 x 100%=12.5%

Likewise, B: 5/4=5/4 x 100%=5 x 25%=125%

Again, C: 3/40=3/40x100=3/2x5%=7.5%

Finally, D: 2/7=2/7x100=200/7=28.47%

Task for you: To sharpen your class 7 comparing quantities, solve the following problem:

Question

Here are three circles with coloured parts. You have to calculate the percentage of the coloured bits.

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Solution: 

  1. In circle A, the total coloured part is ¼ or 25%.

  2. In circle B, the coloured section is 3 out of 5. Hence, the percentage is 3/5 or 60%.

  3. In circle C, there are 8 divisions. 3 are coloured. Thus, the percentage is 3/8 or 37.5%.

NCERT Maths Solution Class 8 Comparing Quantities

Here, we will learn how to use comparing quantities to convert ratios into percentages.

Question:

Here are four ratios. You must convert them into percentages.

  1. 3:1                            B. 2:3:5                    C: 1:4                             D: 1:2:5

Solutions

A: 3:1

Here, total fractional part is 3+1 or 4.

That means fractional parts are ¾: ¼.

Percentage is derived by multiplying each with 100. 

Thus, Percentage of Parts is 75%:25%

B: 2:3:5

Here, total fractional part is 2 + 3 + 5=10.

Fractional parts are 2/10: 3/10: 5/10.

Percentage of Parts is: 20%:30%:50%

C: 1:4

Here, total fractional part is 1 +4=5.

Fractional parts are 1/5: 4/5.

Percentage of Parts is: 20%:80%

D: 1:2:5

Here, total fractional part is 1 + 2 + 5=8.

Fractional parts are: 1/8: 2/8: 5/8.

Percentage of Parts is: 12.5%:25%:62.5%

Tip for advanced students: Form a team where you can collect previous years’ question papers. Set timers and check who finishes comparing quantities class 8 NCERT solutions first. It will give you an idea of how quickly time runs out in such examinations.

As an addition, you will achieve mastery over NCERT solutions class 8 comparing quantities.

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FAQ (Frequently Asked Questions)

1. Why is Learning Comparative Quantities Essential?

Ans. With comparative quantities, you will be able to mentally solve matters related to money, investments and miscellaneous calculations. You will also learn how to calculate simple and compound interest later. Finally, without practising comparative quantities, it will be difficult for you to move on to more complex questions.

2. How can Ratios be Converted into Percentages?

Ans. Yes, all ratios involving regular numbers can be converted into percentages. However, there are some very advanced ratios involving irregular numbers. These cases may be different.

3. How can I Calculate Percentages of Amounts in Different Currencies?

Ans. To do this, you need to know the prevailing exchange rate of the foreign currency. Once you have that data, the methods shown above will work just fine.