CBSE Class 8

On this page, you will find Linear Equations in One Variable Class 8 Notes Maths Chapter 2 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 2 Linear Equations in One Variable will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 2 Notes Linear Equations in One Variable

Linear Equations in One Variable Class 8 Notes Conceptual Facts

1. Statement of equality containing one or more variable (unknown quantity) is called an equation.
For example: 3x – 5 = 6, x – 3y = 7, \(\frac{x}{2}+\frac{y}{3}=5\) , x² + 5 = y² are all equations.

2. Linear equations of one variable contains only one variable.
For example: \(3 x-1=\frac{1}{2}, 5-x=\frac{3}{2}, \frac{6 x}{5}-3=0\)

3. The value of the variable which makes an equation true is called the solution of the equation.
x² + y² = 7 type equations are not linear equations.
(i) Rules for solving an equation.

• Same number can be added to both sides of equality sign (=).
• Same number can be subtracted from both the sides of equality sign (=).
• Same number can be multiplied to both the sides of equality sign (=).
• Both sides of the equation can be divided by the same number.

For example:
3x – 4 = 7
⇒ 3x- 4 + 4- 7+ 4 (adding 4 to both sides)
⇒ 3x = 11
⇒ 3x÷3 = 11÷3 (dividing the both sides by 3)
\(x=\frac{11}{3}\)
Thus, \(x=\frac{11}{3}\) is the solution or root of the equation.

(ii) Rule of transpositions: Any term can be transposed from one side of the equation to the other side by changing its sign, i.e. (+) to (-), (-) to (+), (x) to (-r) and (v) to (x).

On this page, you will find Rational Numbers Class 8 Notes Maths Chapter 1 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 1 Rational Numbers will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 1 Notes Rational Numbers

Rational Numbers Class 8 Notes Conceptual Facts

1. A number which is in the form of \(\frac{p}{q}\), where p and q are co-primes integers and q ≠ 0 is called rational number.
For example, \(\frac{2}{3}, \frac{1}{2}, \frac{4}{5}, 2,-\frac{6}{7}\)

2. Every fraction is a rational number but every rational number need not to be a fraction.
For example: \(\frac{2}{3}\) is a fraction as well as a rational number, o
Whereas -5 is a rational number but it is not a fraction.

3. Standard form of a rational number may be identified when its denominator is positive.
For example: Standard form of is \(\frac{18}{-24} \text { is } \frac{-3}{4}\)

4. Equivalent fraction of \(\frac{p}{q}\) may be denoted by \(\frac{p \times m}{q \times m} \text { or } \frac{p \div n}{q \div n}\)
For example: Equivalent fractions of  \(\frac{12}{16} \text { are } \frac{12+4}{16 \div 4}=\frac{3}{4}\)
or \(\frac{12 \times 2}{16 \times 2}=\frac{24}{32}\)

5. The rational numbers can be compared as:

• \(\frac{a}{b}>\frac{c}{d}\) if and only if ad > bc
• \(\frac{a}{b}=\frac{c}{d}\) if and only if ad = bc
• \(\frac{a}{b}<\frac{c}{d}\) if and only if ad < bc

Properties of rational numbers:
(а) Closure property additions
If a and b are two rational numbers, then a + b will also a rational number
For example: \(\frac{1}{2}+\frac{1}{3}=\frac{1 \times 3+1 \times 2}{6}=\frac{5}{6}\) a rational number.

(b) Commutative property of addition
Two rational numbers can be added in any manner.

(c) Associative property for addition:
While adding three or more rational numbers, they can be grouped in any order.

(d) Additive identity: The sum of any rational number and 0 is always equal to the rational number itself.
Zero is additive identity
For example: 0 + a = a or a + 0 = a

(e) Additive inverse
Additive inverse of \(\frac{a}{b}=-\frac{a}{b}\)
0 is the additive inverse of itself.

Properties of multiplication of rational numbers.
(a) Closure property: The product of two rational number is always a rational number.
For example: Take two rational numbers \(\frac{1}{2} \text { and } \frac{1}{3}\)
∴ \(\frac{1}{2} \times \frac{1}{3}=\frac{1}{6}\) which is also a rational numbers.

(b) Commutative property: The two rational numbers can be multiplied in any order,
i.e. a x b =b x a

(c) Associative property: Three or more rational numbers can be multiplied by grouping in different order,
i.e. (a x b) x c = a x (b x c)

(d) Multiplicative identity: If \(\frac{a}{b}\) is a rational number, then \(\frac{a}{b} \times 1=1 \times \frac{a}{b}=\frac{a}{b}\)
For example: \(\frac{2}{3} \times 1=1 \times \frac{2}{3}=\frac{2}{3}\)
1 is called the multiplicative identity of a rational number.

(e) Distributive property of multiplication over addition.
If \(\frac{a}{b}, \frac{c}{d} \text { and } \frac{e}{f}\) are three rational number,
For example:

For example: Let us consider three rational numbers \(\frac{2}{3}, \frac{4}{5} \text { and } \frac{5}{6}\)

Existence of multiplicative inverse (i.e. Reciprocal)
For every non-zero rational number \(\frac{a}{b}\), there exists its multiplicative inverse \(\frac{a}{b}\).

• i.e… \(\frac{a}{b} \times \frac{b}{a}=1\)
• Reciprocal of zero (0) is not defined.
• 1 and -1 are the only two rational numbers which are Reciprocal of their own.
• Reciprocal of a reciprocal of a number is the number itself.

Representation of rational numbers on number line.

Here A represents \(\frac{1}{3}\) and B represents \(\frac{-2}{3}\) on the given number line.

Rational numbers between two given rational numbers:

Let us consider the rational numbers \(\frac{3}{10} \text { and } \frac{7}{10}\)

So, the rational numbers between \(\frac{3}{10} \text { and } \frac{7}{10} \text { may be } \frac{4}{10}, \frac{5}{10} \text { and } \frac{6}{10}\)

On this page, you will find NCERT Class 8 Civics Chapter 10 Notes Pdf free download. CBSE Class 8 Social Science Notes Civics Chapter 10 SST Law and Social Justice will seemingly, help them to revise the important concepts in less time.

Law and Social Justice Class 8 Notes Social Science Civics Chapter 10

CBSE Class 8 Civics Chapter 10 Notes Understanding the Lesson

1. Markets almost everywhere tend to be exploitative of people, whether as consumers, producers or as workers.

2. The government makes certain laws and these laws try to ensure that the unfair practices are kept at a minimum in the markets.

3. Private companies, contractors, etc. in order to gain maximization of profits, might deny workers their rights and not pay them wages.

4. As per the law on minimum wages, which is meant to protect workers, there are also laws that protect the interests of producers and consumers in the market.

5. These laws help ensure that the relations between the three parties – the worker; consumers and producer are governed in a manner that is not exploitative.

6. Enforcement of law becomes even more important when the law seeks to protect the weak from the strong.

7. To ensure that every worker gets fair wages, government has to regularly inspect worksites and punish those who violate the law.

8. Through making, enforcing and upholding the laws, the government can control the activities of individuals or private companies so as to ensure social justice.

9. The Right against Exploitation says that no one can be forced to work for low wages or under bondage.

10. Constitution also lays down that “A child below the age of 14 years shall not be employed to work in any factory or mines or engaged in any other hazardous employment”.

11. One reason why foreign companies come to India is for cheap labour. For lower pay, the companies can get longer hours of work. This can help in saving costs and earning higher profits.

12. Being lawmaker and enforcer, the government is supposed to ensure that safety laws are implemented.

13. Safety laws and non-enforcement of weak safety laws are seen in India.

14. Bhopal Gas Tragedy was the world’s worst industrial tragedy which took place in Bhopal where Union Carbide (UC) an American company had a factory in the city which was pesticides producer, there at midnight on 2^nd December 1984 methyl – isocyanite (MIC) started leaking killing a huge number of people. The installation of an MIC production unit in 1978 was a safety violation, the position of the government was that the state needs continuous investment of the Bhopal plant which provide job.

15. Therefore, government inspectors continued to approve the procedure in the plant.

16. People safety was being disregarded both by the government and by private companies.

17. In 1984, there were very few laws protecting the environment in India.

18. The environment was treated as a ‘free’ entity and any industry could pollute the air and water without any restrictions.

19. Bhopal tragedy causing disaster has brought the environment issues to the forefront.

20. Following the Bhopal gas tragedy the government under pressure introduced new laws on the environment. The polluter was to be held accountable for the damage done to the environment.

21. The court gave several judgments upholding the right to a healthy environment as intrinsic to the Fundamental Right to Life.

22. In Subash Kumar Vs State of Bihar (1991), the Supreme Court held that the Right to Life is a Fundamental Right under Article 21 of the Constitution and it includes the right to the enjoyment of pollution-free water and air for full enjoyment of life.

23. The government is responsible for setting up laws and procedures that can check pollution, clean rivers and induce heavy fines for those who pollute.

24. Laws are necessary in many situations, whether this be the market, office or factory for the purpose of protecting people from unfair practices.

25. The government has to make ‘appropriate laws’ and also has to enforce the laws.

26. Laws weak in nature and poorly enforced can cause serious harm.

27. The government has the leading role in this respect, people can exert pressure so that both private companies and the government act in the interests of society.

Law and Social Justice Class 8 CBSE Notes Important Terms

Consumer: An individual who buys goods for personal use and not for resale.

Producer: A person or organisation that produces goods for sale in the market. At times, the producer keeps a part of the produce for his own use, like a farmer.

Investment: Money spent to purchase new machinery or buildings or training so as to be able to increase/ modernise production in the future.

Worker’s union: An association of workers.

On this page, you will find NCERT Class 8 Civics Chapter 9 Notes Pdf free download. CBSE Class 8 Social Science Notes Civics Chapter 9 SST Public Facilities will seemingly, help them to revise the important concepts in less time.

Public Facilities Class 8 Notes Social Science Civics Chapter 9

CBSE Class 8 Civics Chapter 9 Notes Understanding the Lesson

1. Water is essential for life and for good health.

2. India has one of the largest number of cases of diseases such as diarrhoea, dysentery, cholera. Over 1600, Indians, most of them children below the age of five, reportedly die everyday because of water-related diseases.

3. The deaths can be prevented if people have access to safe drinking water.

4. The Constitution of India recognizes the right to water as being a part of the Right to Life under Article 21. In other words, there should be universal access to water.

5. The High Courts and the Supreme Courts have held that the right to safe drinking water is Fundamental Right.

6. Same as water there are other essential facilities that are needed to be provided to everyone, for eg. healthcare, sanitation, electricity, public transport, schools and colleges. These all are known as public facilities.

7. The important characteristic of the public facilities is that once it is provided, its benefits can be shared by many people.

8. One of the most important function of the government is to ensure that the public facilities are made available to everyone.

9. Though private companies provide the public facilities but they provide it with the purpose of profit-making and they provide facilities at a price that only some people can afford. This facility not available to all at an affordable rate.

10. Many people who cannot afford to pay for such facilities will be deprived of the opportunity to live a decent life.

11. The Right to Life that is guranteed in Constitution is for all persons living in this country.

12. There is no doubt that public facilities should be made available to all, in reality we see that there is a great shortage of such facilities.

13. The burden of shortfalls in water supply falls mostly on the poor. The middle class when faced with such shortages are able to cope up through a variety of private means.

14. Apart from the availability of water, access to safe drinking water is also available to some and this depends on what one can afford.

15. The supply of water per person in an urban area in India is about 135 litres per day.

16. A shortage of municipal water is often taken as a sign of failure of the government.

17. The facts say that:

• Throughout the world, water supply is a function of the government.
• There are areas in the world where public water supply has achieved universal access.
• The cases where the responsibility for water supply was handed over to private companies, there was seen a steep rise in the price of water, making if unaffordable for many.
• Within India, there are several cases of success in government water departments, though these are few in number and limited to certain areas of their work.
• Public facilities relate to our basic needs and the Indian Constitutions recognizes the right to water, health, education, etc., a being a part of the Right of Life.
• One of the major roles of the government is to ensure adequate public facilities for everyone.
• But progress on this front has taken far from satisfactory.
• There is a shortage in supply and there are inequalities in distribution.
• The important fact is, that every citizen of the country has a right to these facilities, and this should be provided to all in an equitable manner.

Public Facilities Class 8 CBSE Notes Important Terms

Sanitation: Provision of facilities for the safe disposal of human urine and faeces. This is done by construction of toilets and pipes to carry the sewerage and treatment of wastewater. This is necessary so as to avoid contamination.

Company: A company is a form of business set up by people or by the government. Those that are owned and promoted by individuals or groups are called private companies.

Universal access: It is achieved when everyone has physical access to a good and can also afford it. for instance, a tap connection at home will allow physical access to water, and if the price of water is low or is provided free, everyone will be able to afford it.

Basic needs: Primary requirements of food, water, shelter, sanitation, healthcare and education necessary for survival.

On this page, you will find NCERT Class 8 Civics Chapter 8 Notes Pdf free download. CBSE Class 8 Social Science Notes Civics Chapter 8 SST Confronting Marginalisation will seemingly, help them to revise the important concepts in less time.

Confronting Marginalisation Class 8 Notes Social Science Civics Chapter 8

CBSE Class 8 Civics Chapter 8 Notes Understanding the Lesson

1. The choice of struggle depended upon on the circumstances that the marginalized found themselves in.

2. The Fundamental Rights in the Constitution are available to all Indians equally. As far as the marginalized are concerned, they deserve these rights in two ways:

3. Marginalized have forced the government to recognise the injustice done to them.

4. Marginalized people have insisted that the government enforces these laws.

5. Article 17 of the Constitution states that untouchability has been abolish. In vital sense to society, untouchability is a punishable crime.

6. Article 15 of the Constitution states that no citizen of India shall be discriminated on the basis of religion, race, sex or place of birth.

7. The above-mentioned articles from the Constitution help to strengthen the argument against untouchability.

8. Dalits have used these to seek equality where it has been denied to them. They have drawn the attention of the government of India to the Constitution, demanding that the government abide by it and do justice to them.

9. Dalits and other minority groups have particularly drawn upon the right to freedom of religion and cultural and educational rights.

10. By granting different forms of cultural rights, the Constitution tries to ensure cultural justice to the people from different culture.

11. There are specific laws and policies for the marginalized, in our country. There are policies and schemes that emerge through other means like setting up of committee or by undertaking a survey etc. The government then makes an effort to promote such policies in order to give opportunities to the specific groups.

12. Both State and central governments create specific schemes for implementation in tribal areas or in areas that have a high Dalit population.

13. In addition to providing certain facilities, the government also operates through laws to ensure that concrete steps are taken to end inequality in the system.

14. The reservation policy works as Governments across India have their own list of Scheduled Castes, Schedule Tribes and backward and most backward castes. The central government too has its list. The students or person seeking benefits from government are expected to furnish proof of their caste or tribe status in the form of caste and tribes certificates.

15. Our country also has specific laws that guard against the discrimination and exploitation of marginalized communities.

16. The Scheduled Castes and the Scheduled Tribes (Prevention of Atrocities) Act, 1989 was framed in 1989 in response to demands made by Dalits and others that the government must take seriously the ill treatment and humiliation Dalits and tribals face in an everyday sense.

17. The Act contains a very long list of crimes, some of which are too horrible even to contemplate.

18. The Act does not only describe horrible crimes, but also lets people know what dreadful deeds human being are capable. Laws such as these seek to both punish as well as influence the way we think and act.

19. The Act distinguishes several levels of crimes.

20. Firstly: It lists made of humiliation that are both physically horrible and morally reprehensible and seeks to punish those who:

• force member of a SC’or a ST to drink or >eat any inedible or obnoxious substance.
• forcibly removes clothes from the person of a member of a SC or a ST or parades him or her naked or with painted face or body or commits any similar act which is derogatory to human dignity.

21. Secondly: The Act lists the actions that dispossess Dalits and Adivasis of their meagre resources or which force them into performing slave labour. The Act sets out to punish anyone who:

• wrongfully occupies or cultivates any land owned by, or allotted to a member of a SC or a ST or gets the land allotted to him transferred.

22. At another level, the Act recognizes that the crimes against Dalit and tribal women are of a specific kind and, therefore, seeks to penalise anyone who:

• assaults or uses force on any woman belonging to a SC or a ST with intent to dishonour her.

23. The 1989 Act is important for another reason-Adivasis activist refer to it to defend their right to occupy land that was traditionally theirs.

24. Constitution guarantees the right of tribal people to repose their land.

25. The government must draw up plans and policies for the tribals to live and work elsewhere in case tribals have been evicted and cannot go back to their lands.

26. Desire for dignity, equality and respect is not new. It has existed in different forms throughout our history. In a democratic society, similar process of struggle, writing, negotiation and organising need to continue.

Confronting Marginalisation Class 8 CBSE Notes Important Terms

Assertive: An assertive group or person is one that can express themselves and their views strongly.

Confront: to come face to face or to challenge someone or something.

Dispossessed: to possess is to own something and to be dispossessed is to have to give up ownership or to give up authority.

Ostracise: This means to exclude or banish an individual or a group.

Policy: A Stated course of action that provides direction for the future, set goals to be achieved or lays out principles or guidelines to be followed and acted upon.