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. 

2. 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.

3. 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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