# NCERT Solutions for Grade 7 Mathematics Chapter 8 Comparing quantities (Ex. 8.2) Exercise 8.2 (2023)

Exercise 8.2

1. Convert the given fractions to percentages:

a) The fraction is $\dfrac{1}{8}$.

answer: To convert a fraction to a percent, the given fraction is multiplied by $100\%$.

The given fraction is $\dfrac{1}{8}$.

Multiply the given fraction by $100\%$ and simplify to get the corresponding percentage.

$\dfrac{1}{8} \times 100\% = \dfrac{{25}}{2}\%$

$\dfrac{1}{8} \times 100\% = 12.5\%$

Therefore, the fraction $\dfrac{1}{8}$ is equal to $12.5\%$.

b) The fraction is $\dfrac{5}{4}$.

answer: To convert a fraction to a percent, the given fraction is multiplied by $100\%$.

The given fraction is $\dfrac{5}{4}$.

Multiply the given fraction by $100\%$ and simplify to get the corresponding percentage.

$\dfrac{5}{4} \times 100\% = 5 \times 25\%$

$\dfrac{5}{4} \times 100\% = 125\%$

Therefore, the fraction $\dfrac{5}{4}$ is equal to $125\%$.

c) The fraction is $\dfrac{3}{{40}}$.

answer: To convert a fraction to a percent, the given fraction is multiplied by $100\%$.

The given fraction is $\dfrac{3}{{40}}$.

Multiply the given fraction by $100\%$ and simplify to get the corresponding percentage.

$\dfrac{3}{{40}} \times 100\% = \dfrac{{3 \times 5}}{2}\%$

$\dfrac{3}{{40}} \times 100\% = 7.5\%$

Therefore, the fraction $\dfrac{3}{{40}}$ is equal to $7.5\%$.

d) The fraction is $\dfrac{2}{7}$.

answer: To convert a fraction to a percent, the given fraction is multiplied by $100\%$.

The given fraction is $\dfrac{2}{7}$.

Multiply the given fraction by $100\%$ and simplify to get the corresponding percentage.

$\dfrac{2}{7} \times 100\% = \dfrac{{200}}{7}\%$

$\dfrac{2}{7} \times 100\% = 28\dfrac{4}{7}\%$

$\dfrac{2}{7} \times 100\% = 28.571428...$

So the fraction $\dfrac{2}{7}$ is equal to $28\dfrac{4}{7}\%$ or $28.571428..\%$.

2. Convert the given decimal fractions to a percent:

a) The number is $0.65 answer: The given decimal is$0.65$. The specified decimal number can also be written in the form$\dfrac{p}{q}$as$\dfrac{{65}}{{100}}$. Now, when converting a fraction to a percent, multiply the given fraction by 100$\%$. Multiply the given fraction by$100\%$and simplify to get the corresponding percentage.$\dfrac{{65}}{{100}} \times 100\% = 65\% $So the decimal number $0.65$ is equal to$65\%$. b) The number is$2.1$answer: The specified decimal is$2.1$. The specified decimal number can also be written in the form$\dfrac{p}{q}$as$\dfrac{210}{{100}}$. Now, when converting a fraction to a percent, multiply the given fraction by 100$\%$. Multiply the given fraction by$100\%$and simplify to get the corresponding percentage.$\dfrac{210}{{100}} \times 100\% = 210\% $So the decimal $2.1$ is equal to$210\%$. (C) The number is$0.02$answer: The specified decimal is$0.02$. The specified decimal number can also be written in the form$\dfrac{p}{q}$as$\dfrac{2}{100}$. Now, when converting a fraction to a percent, multiply the given fraction by$100%$. Multiply the given fraction by$100%$and simplify to get the corresponding percentage.$\dfrac{2}{100}\times 100%=2\%$Therefore, the decimal$0.02$is equal to$2\%$. (D) The number is$12.35.

answer: the given decimal is $12.35$.

The specified decimal number can also be written in the form $\dfrac{p}{q}$ as $\dfrac{1235}{100}$.

Now, when converting a fraction to a percent, multiply the given fraction by $100%$.

(Video) Comparing Quantities - Ex 8.2 | NCERT Maths Class 7 Chapter 8

Multiply the given fraction by $100%$ and simplify to get the corresponding percentage.

$\dfrac{1235}{100}\times 100%= 1235\%$

So the decimal $12.35$ is equal to $1235\%$.

3. Estimate how much of the numbers is colored in to find the percentage that is colored in:

i) The given number is,

(image will be updated soon)

From the given figure, it can be estimated that the colored part of the circle is the ${\dfrac{1}{4}^{th}}$ part.

So ${\text{The colored part}} = \dfrac{1}{4}$.

Now, to find the percentage of fraction colored, convert the fraction obtained from fraction colored to percent. This can be done by multiplying the fraction by $100\%$ and then simplifying.

Therefore,

${\text{Percentage of colored part}} = \dfrac{1}{4} \times 100\%$

${\text{Percentage of colored portion}} = \dfrac{{100}}{4}\%$

${\text{The percentage of the colored part}} = 25\%$

Therefore, the percentage of the colored part of the given figure is 25$\%$.

ii) The given number is,

(image will be updated soon)

The figure shows that the circle is divided into 5 equal parts.

Therefore, the colored part of the circle can be estimated to be the ${\dfrac{3}{5}^{th}}$ part.

So ${\text{The colored part}} = \dfrac{3}{5}$.

Now, to find the percentage of fraction colored, convert the fraction obtained from fraction colored to percent. This can be done by multiplying the fraction by $100\%$ and then simplifying.

Therefore,

${\text{Percentage of colored part}} = \dfrac{3}{5} \times 100\%$

${\text{Percentage of colored part}} = \dfrac{{300}}{5}\%$

${\text{Percentage of colored part}} = 60\%$

Therefore, the percentage of the colored part of the given figure is 60$\%$.

iii) The given number is,

(image will be updated soon)

The figure shows that the circle is divided into 8 equal parts.

Therefore, the colored part of the circle can be estimated to be the ${\dfrac{3}{8}^{th}}$ part.

So ${\text{The colored part}} = \dfrac{3}{8}$.

Now, to find the percentage of fraction colored, convert the fraction obtained from fraction colored to percent. This can be done by multiplying the fraction by $100\%$ and then simplifying.

Therefore,

${\text{Percentage of colored part}} = \dfrac{3}{8} \times 100\%$

${\text{Percentage of colored portion}} = \dfrac{{300}}{8}\%$

${\text{Percentage of colored part}} = 37.5\%$

Therefore, the percentage of the colored part of the given figure is 37.5$\%$.

4. Find the percentage of the following values:

a) $15\% {\text{ }}$ de 250

answer: The specified number is 250.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$15\%$ is also represented in fractional form as $\dfrac{{15}}{{100}}$.

Therefore, $15\%$ of 250 is represented as $\dfrac{{15}}{{100}} \times 250$.

Evaluate the previous expression.

$\dfrac{{15}}{{100}} \ times 250 = 15 \ times$2.5

$\dfrac{{15}}{{100}} \ times 250 =$37.5

So it turns out that $15\% {\text{ of 250}}$ is $37.5$.

b) $1\%$ of 1 hour.

answer: It is known that 1 hour has 60 minutes.

Also, 60 minutes equals $\left( {60 \times 60} \right)$ seconds.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

So if you find $1%$ of 1 hour, you will find $1%$ of $\left( {60 \times 60} \right)$ seconds. $1\%$ is also represented as $\dfrac{1}{{100}}$.

With that,

$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{1}{{100}}\left( {60 \times 60} \ right){\text{seconds}}$.

$1\% {\text{ de }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{{3600}}{{100}}{\text{ seconds}}$ .

$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = 36{\text{ seconds}}$.

(Video) Q.1, Ex.8.2 Chapter:8 Comparing Quantities | Ncert Maths Class 7 | Cbse

c) $20%$ of ₹2500

answer: The value given is ₹2,500.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$20\%$ is also represented in fractional form as $\dfrac{{20}}{{100}}$.

Therefore, $20\%$ of 2500 is represented as $\dfrac{{20}}{{100}} \times 2500$.

Evaluate the previous expression.

$\dfrac{{20}}{{100}} \times 2500 = 20 \times 25$

$\dfrac{{20}}{{100}} \times 2500 = 500$

So $20%$ of ₹2500 is ₹500.

d) $75%$ of 1kg

answer: It is known that 1 kg is 1000 g.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$75\%$ is also represented in fractional form as $\dfrac{{75}}{{100}}$.

Therefore, $75\%$ of 1000 is represented as $\dfrac{{75}}{{100}} \times 1000$.

Evaluate the previous expression.

$\dfrac{{75}}{{100}} \times 1000 = 750{\text{g}}$

Therefore,

$750{\text{ g}} = \dfrac{{750}}{{1000}}{\text{ kg}}$

$750{\text{g}} = 0,75{\text{kg}}$

So $75\%$ of 1 kg is $0.75{\text{ kg}}$.

5. Find the total if:

a) $5\%$ of which are 600

answer: Let $x$ be the assumed size.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$5\%$ of $x$ can be represented as $\dfrac{5}{{100}}$ of $x$, which equals 600.

This can be formulated as follows,

$5\% {\text{ of }}x =$600

Therefore,

$\dfrac{5}{{100}} \times x =$600

evaluate more,

$x = \dfrac{{600 \times 100}}{5}$

$x = \dfrac{{60000}}{5}$

$x = 12000$

Therefore, the quantity is determined to be 12,000.

b) $12\%$ of which are ₹1080.

Respondedor:Let $x$ be the amount assumed.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$12\%$ of $x$ can be represented as $\dfrac{{12}}{{100}}$ of $x$, which is ₹1080.

This can be formulated as follows,

$12\% {\text{ of }}x = 1080$

Therefore,

$\dfrac{{12}}{{100}} \times x = 1080$

evaluate more,

$x = \dfrac{{1080 \times 100}}{{12}}$

$x = \dfrac{{108000}}{{12}}$

$x = 9000$

Therefore, the amount is £9,000.

c) $40\%$ of which are 500 km.

answer: The default amount is $x$.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$40\%$ of $x$ can be represented as $\dfrac{{40}}{{100}}$ of $x$, which equals 500 km.

This can be formulated as follows,

$40\% {\text{ de }}x = 500{\text{ km}}$

Therefore,

$\dfrac{{40}}{{100}} \times x =$500

evaluate more,

$x = \dfrac{{500 \times 100}}{{40}}$

$x = \dfrac{{50000}}{{40}}$

(Video) Q 1, Ex 8.2 - Comparing Quantities - Chapter 8 - Maths Class 7th - NCERT

$x = 1,250{\text{km}}$

Therefore, the amount is 1250 km.

d) $70%$ of which is 14 minutes

Respondedor:The assumed amount is $x$.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$70\%$ of $x$ can be represented as $\dfrac{{70}}{{100}}$ of $x$, which is 14 minutes.

This can be formulated as follows,

$70\% {\text{ de }}x = 14{\text{ minutos}}$

Therefore,

$\dfrac{{70}}{{100}} \times x =$14

evaluate more,

$x = \dfrac{{14 \times 100}}{{70}}$

$x = \dfrac{{1400}}{{70}}$

$x = 20{\text{minutes}}$

Therefore, the value is 20 minutes.

e) $8\%$ of which are 40 liters

answer: The default amount is $x$.

The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

$8\%$ of $x$ can be represented as $\dfrac{8}{{100}}$ of $x$, which is 40 liters.

This can be formulated as follows,

$8\% {\text{ de }}x = 40{\text{ litros}}$

Therefore,

$\dfrac{8}{{100}} \times x =$40

evaluate more,

$x = \dfrac{{40 \times 100}}{8}$

$x = \dfrac{{4000}}{8}$

$x = 500$

This results in a quantity of 500 liters.

6. Convert the given percentages to decimal fractions and in the simplest forms to fractions as well:

a) The percentage is $25\%$.

Respondedor:The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

The specified percentage $25\%$ can also be represented as $\dfrac{{25}}{{100}}$.

Therefore, the fractional form of the given percentage is $\dfrac{{25}}{{100}}$.

Simplify the fraction form obtained to determine the simplest form of the given percentage.

$\dfrac{{25}}{{100}} = \dfrac{1}{4}$

So the simplest form is $\dfrac{1}{4}$.

Now the decimal form of the given percentage is obtained by dividing the simpler form obtained above.

$\dfrac{1}{4} = 0,25$

So, for $25\%$, the fractional form is $\dfrac{{25}}{{100}}$, the simplest form is $\dfrac{1}{4}$, and the decimal form is $0.25$.

b) The percentage is $150\%$.

Respondedor:The percentage of any number $n$, that is, $n\%$, is written as $\dfrac{n}{{100}}$.

The specified percentage $150\%$ can also be represented as $\dfrac{{150}}{{100}}$.

Therefore, the fractional form of the given percentage is $\dfrac{{150}}{{100}}$.

Simplify the fraction form obtained to determine the simplest form of the given percentage.

$\dfrac{{150}}{{100}} = \dfrac{3}{2}$

So the simplest form is $\dfrac{3}{2}$.

Now the decimal form of the given percentage is obtained by dividing the simpler form obtained above.

$\dfrac{3}{2} = 1,5$

So, for 150$\%$, the fractional form is $\dfrac{{150}}{{100}}$, the simplest form is $\dfrac{3}{2}$, and the decimal form is 1, $5. c) The percentage is$20\%$. Respondedor:The percentage of any number$n$, that is,$n\%$, is written as$\dfrac{n}{{100}}$. The specified percentage$20\%$can also be represented as$\dfrac{{20}}{{100}}$. Therefore, the fractional form of the given percentage is$\dfrac{{20}}{{100}}$. Simplify the fraction form obtained to determine the simplest form of the given percentage.$\dfrac{{20}}{{100}} = \dfrac{1}{5}$So the simplest form is$\dfrac{1}{5}$. Now the decimal form of the given percentage is obtained by dividing the simpler form obtained above.$\dfrac{1}{5} = 0,2$(Video) Q.2, Ex.8.2 Chapter:8 Comparing Quantities | Ncert Maths Class 7 | Cbse So, for$20\%$, the fractional form is$\dfrac{{20}}{{100}}$, the simplest form is$\dfrac{1}{5}$, and the decimal form is$0.2 $. d) The percentage is$5\%$. Respondedor:The percentage of any number$n$, that is,$n\%$, is written as$\dfrac{n}{{100}}$. The specified percentage$5\%$can also be represented as$\dfrac{5}{{100}}$. Therefore, the fractional form of the given percentage is$\dfrac{5}{{100}}$. Simplify the fraction form obtained to determine the simplest form of the given percentage.$\dfrac{5}{{100}} = \dfrac{1}{{20}}$So the simplest form is$\dfrac{1}{{20}}$. Now the decimal form of the given percentage is obtained by dividing the simpler form obtained above.$\dfrac{1}{{20}} = 0,05$So, for$5\%$, the fractional form is$\dfrac{5}{{100}}$, the simplest form is$\dfrac{1}{{20}}$, and the decimal form is$0.05 $. 7. In a city, 30% are women, 40% are men, and the rest are children. What percentage are children? Respondedor:The proportion of women is given as 30\%$ and the proportion of men in a city as 40\%$. Therefore, the total percentage of men and women in a city is the sum of the two given percentages.${\text{Overall percentage of men and women in a city}}$= 30% + 40%${\text{Total percentage of men and women in a city}} = 70\% $The total percentage of children in the city is the difference between the total percentage of the city's population and the total percentage of men and women in the city.${\text{Percentage of children in the city}} = {\text{Overall percentage}} - {\text{Percentage of men and women}}{\text{Percentage of children in the city}} = 100 % - 70%$Therefore,${\text{The percentage of children in the city}} = 30\% $Therefore, the percentage of children in the city is 30$\%$. 8. Of 15,000 voters in a constituency,$60\% voted for $. Find the percentage of voters who did not vote. Now find out how many really didn't vote. answer: the total number of voters in a constituency is given as$60\%$. Of the specified number of voters,$60\% $chose candidates. The percentage of candidates who did not vote is the difference between the total percentage of candidates and the percentage of candidates who voted.${\text{The percentage of candidates who did not vote}}$= 100% - 60%${\text{Percentage of candidates who did not vote}} = 40\% $Now, the actual number of candidates who did not vote is calculated as 40$\%$of the total number of voters in the electoral district, that is, H.$40%$of 15,000.${\text{Number of candidates who did not vote}} = \dfrac{{40}}{{100}} \times 15000{\text{The number of candidates who did not vote}} = $6,000 Therefore, the number of candidates who did not vote is 6,000. 9. Meeta saves ₹4000 from her salary. If that is$10%$of your salary. what is your salary Respondedor:Let's say Meeta's total salary is ₹$x$. You are supposed to save ₹4000 of your salary, which is ₹10% of your total salary. This can be represented as follows,$ 10\% {\text{ del salario total}} = 4000{\text{ Rs}}$The percentage of any number$n$, that is,$n\%$, is written as$\dfrac{n}{{100}}$. Therefore,$ 10\% {\text{ de }}x = 4000{\text{ }}\dfrac{{10}}{{100}} \times x = $4000 After further evaluation and cross multiplication,$x = \dfrac{{4000 \times 100}}{{10}} x = 40000 $Therefore, Meeta's total salary is Rs 40,000. 10. A local cricket team played 20 matches in one season. He earned$25%$from them. How many games have they won? answer: It is believed that the local cricket team played 20 matches in one season, earning$25\%$in matches. So the total number of games they won is$25\%$of the number of games they played, represented as follows:${\text{Total number of games won by the team}} = 25\% {\text{ of }}20$Now the percentage of any number$n$, that is,$n\%$, is written as$\dfrac{n}{{100}}$. Therefore,${\text{Total number of games won by the team}} = \dfrac{{25}}{{100}} \times {\text{ }}20{\text{Total number of games won by the team}} = \dfrac{1}{4} \times {\text{ }}20{\text{Total number of games won by the team}} = \$5

Therefore, the number of games won by the team is determined to be 5.

## NCERT Solutions for Grade 7 Mathematics Chapter 8 Comparing Sets Exercise 8.2

Opting for NCERT solutions for Ex 8.2 Grade 7 Math is considered the best option for CBSE students when it comes to exam preparation. This chapter consists of many exercises. Of them, we have provided the NCERT solutions for Exercise 8.2 Grade 7 Mathematics on this page in PDF format. You can download this solution at your convenience or study online directly from our website/app.

The problems/questions in the exercise were resolved with the utmost care by Vedantu's in-house experts and in accordance with all CBSE guidelines. 7th grade students who are well acquainted with all the concepts in the math book and are well acquainted with all the problems of the exercises in it, so that any student can easily get the highest possible score in the final exam. With the help of these solutions for Class 7 Mathematics Chapter 8 Exercise 8.2, students can easily understand the pattern of questions that can be asked in the exam in this chapter and also learn the weighting of chapter grades. So that they can prepare properly for the final exam.

In addition to these NCERT solutions to Exercise 8.2 in Chapter 8 of Class 7 Mathematics, there are many exercises in this chapter that also contain numerous questions. As already mentioned, all these questions are resolved/answered by our internal technical experts. Therefore, they must all be of the highest quality and can be consulted by anyone during the exam preparation period. To get the best possible grades in the classroom, it is very important to understand all the concepts in the textbook and to solve problems in the adjacent exercises.

Don't hesitate anymore. Download NCERT Answers for Grade 7 Math Chapter 8 Exercise 8.2 now from the Vedantu website to better prepare for the exam. If you have Vedantu app on your phone, you can also download it through the app. The best thing about these solutions is that they can be accessed both online and offline.

(Video) Class 7 Maths Chapter 2 l NCERT EXERCISE-8.2 l Campering Quantities l CBSE Board l Solution l 7th

## Videos

1. Q 5, Ex 8.2 - Comparing Quantities - Chapter 8 - Maths Class 7th - NCERT
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3. Q 7, Ex 8.2 - Comparing Quantities - Chapter 8 - Maths Class 7th - NCERT
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4. Q.no.1&2; Ex.8.2/Class7 Maths/Comparing Quantities/Chapter 8/In Malayalam
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5. Q.1 to Q.8 | Class 7th | Exercise 8.2 | Math | Chapter 8 | Comparing Quantities | PSEB |
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