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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:
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How to convert fractional measures into percentages.
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How to change decimal points into percentages.
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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:
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Rs 5 to 50 paise
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30 days to 36 hours
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9 metres to 27cm
Solutions:
To solve problems related to ratios in currency terms, you must bring both sides down to a common unit.
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We know 5 x 100 paise is Rs 5. Re 1 has 100 paise. To calculate the ratio:
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Similarly, we will break down time into hours and minutes to calculate ratios.
30 days have 30×24 or 720 hours. The ratio is 720/36=20 : 1.
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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:
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Which state has a higher population density?
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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:
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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=3/40×100=3/2×5%=7.5%
Finally, D: 2/7=2/7×100=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:
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In circle A, the total coloured part is ¼ or 25%.
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In circle B, the coloured section is 3 out of 5. Hence, the percentage is 3/5 or 60%.
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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.
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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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