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 $100%$.
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)
answer: The given figure has a circle with a shaded part.
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)
answer: The given figure has a circle with a shaded part.
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)
answer: The given figure has a circle with a shaded part.
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,
$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{1}{{100}}\left( {60 \times 60} \ right){\text{seconds}}$.
$1\% {\text{ de }}\left( {60 \times 60} \right){\text{ seconds}} = \dfrac{{3600}}{{100}}{\text{ seconds}}$ .
$1\% {\text{ of }}\left( {60 \times 60} \right){\text{ seconds}} = 36{\text{ seconds}}$.
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,
$x = \dfrac{{500 \times 100}}{{40}}$
$x = \dfrac{{50000}}{{40}}$
$x = 1,250{\text{km}}$
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.
$\dfrac{1}{5} = 0,2$
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
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