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On this page, you will find Playing with Numbers Class 6 Notes Maths Chapter 3 Pdf free download. CBSE NCERT Class 6 Maths Notes Chapter 3 Playing with Numbers will seemingly help them to revise the important concepts in less time.

CBSE Class 6 Maths Chapter 3 Notes Playing with Numbers

Playing with Numbers Class 6 Notes Conceptual Facts

1. A number which divides a given number exactly is called a factor of the given number.

2. Every number is a factor of itself and 1 is a factor of every number.

3. Every number is a multiple of its factors.

4. Every factor is less than or equal to its multiple.

5. Every multiple of a given number is greater than or equal to that number.

6. A natural number which is not divisible by any number except 1 or itself is called prime number.

7. 2 is the only natural number which is even as well as prime. All the prime numbers except 2 are odd.

8. 2 is the smallest prime number.

9. Numbers which are not prime are called composite numbers.

10. 1 is neither prime nor composite number.

11. Two numbers are called co-prime if they have only 1 as common factor.

12. Pairs of prime numbers differ by 2 are called twin primes.

13. The factors of a given number are Finite but it may have infinite number of multiples.

14. Rule for divisibility:

• A number is divisible by 2 if it has 0 or even digits at its units place.
• A number is divisible by 3 if the sum of its digits is also divisible by 3.
• A number with 3 or more digits is divisible by 4 if the number found by last two digits of the number is divisible by 4.
• A number is divisible by 5, if it has only 0 or 5 in its units place.
• A number is divisible by 6, if it is divisible by 2 and 3 both.
• A number with 4 or more digits is divisible by 8 if the number formed by its last 3 digits are divisible by 8.
• A number is divisible by 9 if the sum of all the digits of the number is divisible by 9.
• A number is divisible by 11 if the difference between the sum of the digits at odd places taken from the right, and the sum of all the digits at even places is either 0 or divisible by 11.

15. The HCF of two or more given numbers is called the highest common factor.

16. The LCM of two or more given numbers is called lowest common multiple.

17. HCF of co-prime numbers is 1.

18. LCM of co-prime numbers is equal to their product.

19. Product of any two numbers is equal to the product of their HCF and LCM.

20. To simplify expressions involving brackets, the four fundamental operations (-, +, x, ÷) and ‘of operations, we always use the BODMAS Rule.

21. To simplify numerical expressions, we remove parenthesis ( ), curly brackets { } and square brackets [ ], strictly in this order.

On this page, you will find Whole Numbers Class 6 Notes Maths Chapter 2 Pdf free download. CBSE NCERT Class 6 Maths Notes Chapter 2 Whole Numbers will seemingly help them to revise the important concepts in less time.

CBSE Class 6 Maths Chapter 2 Notes Whole Numbers

Whole Numbers Class 6 Notes Conceptual Facts

1. The numbers 1, 2, 3, 4, 5, … which are used for counting are known as natural numbers. They are represented by N.

2. All natural numbers together with zero are called whole numbers. They are represented by W.
So, W = 0, 1, 2, 3, 4, …

3. Every natural number is a whole number but reverse not true.

4. 0 is the smallest whole number whereas 1 is the smallest natural number.

5. We have no largest natural number or whole number.

6. The successor of a whole number is 1 more than the whole number.

7. The predecessor of a whole number is 1 less than the whole number but 0 has no predecessor.

8. All the natural numbers and whole numbers can be represented on number line.

9. On number line, positive numbers are taken on right side of the zero and negative numbers on left side.

Properties of whole numbers

If a, b, e are any whole numbers, then

• Closure property for addition: a + b is a whole number.
• Closure property for multiplication: a x b is a whole number.
• Commutative property for addition: a + b = b + a.
• Commutative property for multiplication: a x b = b x a
• Associative property for addition: a + (b + c) = (a + b) + c
• Associative property for multiplication: a x (b x c) = (a x b) x c
• Distributive property: a x (b + c) = a x b + a x c
• Identity for addition: a+0 = 0+a=a
• Identity for multiplication: a x 1 = 1 x a=a
• 0 ÷ a = 0 but a ÷ 0 is not defined.

On this page, you will find Knowing Our Numbers Class 6 Notes Maths Chapter 1 Pdf free download. CBSE NCERT Class 6 Maths Notes Chapter 1 Knowing Our Numbers will seemingly help them to revise the important concepts in less time.

CBSE Class 6 Maths Chapter 1 Notes Knowing Our Numbers

Knowing Our Numbers Class 6 Notes Conceptual Facts

1. To represent any number, we use ten symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 which are called digits or figure.

2. Numbers help us to compare collection of two or more similar objects and we can decide which collections is bigger or smaller.

3. Comparison of numbers helps us to arrange the objects in increasing or decreasing order.

4. If we shift the digits of a given number, then the new number is different from the original one. 853 is different from 358 but 202 remains same even after changing the unit place and hundredth place of the number. Why?

5. If we add one more to the greatest 5-digit number, we get the smallest 6-digit number
99999 (5-digit) + 1 = 100000 (6-digit).

6. Generally, numbers are written in two types of charts:

• Hindu Arabic Place – Value Chart
• International Place – Value Chart.

7. Estimation gives us a rough idea of the answer to a question involving operations on number.

8. In Roman numeration system, only symbols are used to express a number instead of digits.
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M =1000

9. Zero on the extreme left of a number has no value.

10. Ascending order means arrangement from the smallest to the greatest.

11. Descending order means arrangement from the greatest to the smallest.

On this page, you will find Practical Geometry Class 7 Notes Maths Chapter 10 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 10 Practical Geometry will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 10 Notes Practical Geometry

Practical Geometry Class 7 Notes Conceptual Facts

1. By using properties of a transversal and parallel lines, a line parallel to a given line passing through a given point lying not on the line can be drawn.
Let P is any point outside of the given line T. P is joined to any point Q on the line T.
Join P and Q. Draw an angle 2 equal to angle 1. We get m || l.

2. We can draw a triangle if any one of the following conditions are given:

• Three sides (By SSS criterion)
• Two sides and the angle between them (By SAS criterion)
• Two angles and the side included between them (By ASA criterion)
• The hypotenuse and a leg of a right-angled triangle (By RHS criterion)

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.